Project at a glance
What we are building, why, and how we will know it works.
The problem
The wider programme aims to test new room-temperature solid-state quantum-memory materials: P3HT microcavities and α-MoO₃ single-photon emitters. The project’s premise is that you cannot meaningfully test an unproven material on an uncalibrated bench. If storage fails, you would not know whether the material or the optics was at fault. So the project first builds a calibrated atomic reference: a warm ⁸⁷Rb vapour cell in which electromagnetically induced transparency (EIT) and light storage are well understood and reproducible.
Objectives covered here
- Objective 1: construct a precise optical platform using a locked 795 nm laser and a Rubidium-87 cell.
- Objective 2: demonstrate EIT and light storage in the atomic rubidium platform.
Next stage (outside this guide): Objective 3 replaces the Rb cell with P3HT microcavities and uses α-MoO₃ emitters as the probe source. Every alignment and calibration habit built here carries over.
Milestones (project plan)
Laser frequency locked to the ⁸⁷Rb line: SAS signal plus a closed feedback loop to the DFB.
Light storage and retrieval demonstrated in the ⁸⁷Rb cell.
Why an atomic reference platform
- Every ⁸⁷Rb atom is identical, and the D1 line and ground-state splittings are known to many digits. That makes the atom a ruler, not a variable.
- Warm vapour needs no vacuum chamber or cooling, only a cell, a heater and magnetic shielding.
- EIT gives you three measurable handles (OD, ODEIT, γEIT). These are the same figures of merit you will later use to judge solid-state memories.
planned / project plan hardware or protocol in the project plan.
Steck Steck, “Rubidium 87 D Line Data”: verify against the current revision before citing.
design estimate our own estimate or illustrative model. Not a measurement and not a sourced value.
gap / to procure needed but not yet in the equipment plan.
Glossary
Every term used on this page. Type to filter, or pick a category. Longer explanations: Reading Section.
- EIT (electromagnetically induced transparency)theory
- A strong control field makes an otherwise opaque atomic medium transparent for a weak probe in a narrow window around two-photon resonance. The cause is destructive quantum interference: atoms are steered into a dark state that cannot absorb.
- CPT (coherent population trapping)theory
- The same dark-state physics, usually with two fields of comparable strength. Atoms are “trapped” in a superposition near maximal coherence. CPT is the common term in clocks and magnetometers. EIT usually means a strong control and a weak probe.
- Dark state |D⟩theory
- The superposition (Ωp|2⟩ − Ωc|1⟩)/Ω of the two ground states, which has zero coupling to the excited state. Atoms in it do not absorb or fluoresce.
- Bright state |B⟩theory
- The orthogonal superposition (Ωp*|1⟩ + Ωc*|2⟩)/Ω, which is coupled to the excited state with effective Rabi frequency Ω.
- Λ (lambda) schemetheory
- Two long-lived lower states |1⟩, |2⟩ coupled to one excited state |3⟩ by probe and control. It is the most common EIT configuration because the coherence sits between ground states.
- Ladder (cascade) schemetheory
- Ground → intermediate → highly excited state (e.g. Rydberg). The two-photon coherence involves an excited state, so its decay limits the linewidth. Counter-propagating beams minimise Doppler broadening.
- V schemetheory
- One ground state coupled to two excited states. EIT is possible but offers little advantage for atoms (paper, ref. 17).
- Hyperfine structureatom
- Splitting of an electronic level by the coupling of electron angular momentum J and nuclear spin I into levels of total angular momentum F. For ⁸⁷Rb (I = 3/2) the 5S₁/₂ ground state has F = 1 and F = 2, about 6.835 GHz apart.
- Zeeman structureatom
- A magnetic field splits each F level into 2F+1 sublevels labelled mF. In weak fields the shift is gF μB mF B.
- mF (magnetic quantum number)atom
- Projection of F on the quantization axis, from −F to +F. Absorbing σ⁺ light changes mF by +1, σ⁻ by −1, π by 0.
- gF (hyperfine Landé factor)atom
- Sets the Zeeman shift per mF per field. For ⁸⁷Rb 5S₁/₂: gF ≈ +1/2 for F=2 and ≈ −1/2 for F=1, i.e. about ±0.70 MHz/G = 0.70 kHz/mG per unit mF.
- Landé g-factoratom
- The general factor relating a level’s magnetic moment to its angular momentum (gJ for the electron, gF for hyperfine levels).
- Quantization axisatom
- The direction against which mF and σ/π polarizations are defined. In Zeeman EIT it is the solenoid field B along the beam direction z.
- D1 / D2 linesatom
- Alkali transitions from nS₁/₂ to nP₁/₂ (D1) and nP₃/₂ (D2). For Rb, D1 ≈ 795 nm and D2 ≈ 780 nm. D1 has fewer excited hyperfine levels, which gives cleaner Λ systems.
- Rabi frequency Ωtheory
- Strength of the light–atom coupling, µE/ħ in the paper’s convention (Ωp = µ₁₃Ẽ₁/ħ). It scales with √intensity.
- One-photon detuning Δtheory
- Laser frequency minus atomic transition frequency for each field: Δi = νi − ωi3.
- Two-photon detuning δtheory
- δ = Δ₁ − Δ₂ = ν₁ − ν₂ − ω₁₂: the mismatch between the probe–control frequency difference and the ground-state splitting. EIT is centred at δ = 0.
- Raman resonancetheory
- A two-photon transition between the ground states. With large one-photon detuning it appears as a narrow absorption line shifted by |Ωc|²/Δ₁. Far-detuned Raman memories are an alternative to EIT memories.
- Optical pumpingatom
- Using light plus spontaneous emission to move population into a particular state. In Zeeman EIT, the σ⁺ control pumps atoms toward the high-mF end of F=2 (mF=+1, +2 are dark to σ⁺ on F=2→F′=1).
- Susceptibility χtheory
- The medium’s linear response, P = ε₀χE. Im χ gives absorption and Re χ gives the refractive index (n ≈ 1 + Re χ/2 for a dilute gas; the paper writes n = 1 + Re χp).
- Kramers–Kronig relationstheory
- Causality links absorption and dispersion. A narrow transparency window must be accompanied by a steep refractive-index slope, which is the origin of slow light.
- Group index ng / group velocity vgtheory
- ng = n + ν dn/dν and vg = c/ng, the speed of a pulse envelope. Under EIT ng can be enormous.
- Slow lightmemory
- Pulse propagation with vg ≪ c inside the EIT window. The delay is τ ≈ ODEIT/γEIT.
- Stopped / stored lightmemory
- Turning the control off while the compressed pulse is inside the medium maps it completely onto atomic coherence. Turning the control back on regenerates the pulse.
- Dark-state polariton (DSP)memory
- A quasi-particle mixing the probe photon and the ground-state spin coherence. Its photonic fraction (and speed) is set by Ωc. With Ωc → 0 it becomes purely atomic.
- Spin wavememory
- The spatially distributed coherence ρ₁₂ left in the ensemble after storage. Its phase pattern follows the two-photon wavevector kp − kc.
- Optical depth (OD)vapour
- OD = 2α₀L, the resonant absorption without control: T = e−OD. ODEIT is how much of it the control removes. Storage inefficiency scales as 1/ODEIT.
- Doppler broadeningvapour
- Moving atoms see shifted frequencies (δ → δ − k·v). Averaging over Maxwell–Boltzmann velocities gives a Gaussian width σDop ≈ vthk, a few hundred MHz in warm Rb.
- Voigt profilevapour
- Convolution of the homogeneous Lorentzian with the Doppler Gaussian. A pseudo-Voigt is a linear mix of the two, often used for fitting.
- Transit-time broadeningvapour
- Atoms crossing a finite beam interact only for ~w₀/vth, broadening the EIT line by ~vth/w₀ (ballistic) or D/w₀² (diffusive). With mm beams this is tens of kHz.
- Buffer gasvapour
- An inert gas (He, Ne, N₂; a few to tens of Torr) that turns ballistic Rb motion into slow diffusion. Atoms stay in the beam far longer, at the cost of pressure broadening of the optical line (~10 MHz/Torr).
- Dicke narrowingvapour
- When the mean free path is shorter than the relevant wavelength, collisions suppress Doppler broadening. For Λ-EIT the two-photon wavelength is long, so the EIT line narrows strongly and becomes tolerant to small beam angles.
- Diffusion coefficient Dvapour
- Sets the diffusive time l²/D across a length l (≈10 cm²/s for Rb in 10 Torr buffer gas, per the paper).
- Wall (anti-relaxation) coatingvapour
- Paraffin (e.g. tetracontane) or OTS coatings that let atoms bounce off walls without losing spin coherence. They are temperature limited (paraffin breaks down around 60–80 °C).
- Power broadeningtheory
- The EIT width grows with control power: γEIT = γ₁₂ + |Ωc|²/γ₁₃ (stationary atoms), or |Ωc|²/σDop + γ₁₂ in Doppler-broadened vapour.
- Ground-state decoherence γ₁₂theory
- Decay rate of the ρ₁₂ coherence from transit, collisions (spin exchange, spin destruction), field gradients and so on. It sets the narrowest possible EIT line and the storage lifetime.
- Spin-exchange / spin-destruction collisionsvapour
- Rb–Rb collisions that redistribute (exchange) or destroy total spin. Their rate grows with density, which is a key trade-off against OD.
- Radiation trappingvapour
- Re-absorption of spontaneously emitted photons in a dense vapour. It shortens spin coherence and becomes significant at densities of about 5×10¹¹ cm⁻³ and above for mm-sized beams.
- Density matrix ρtheory
- Describes mixed states. Diagonals ρii are populations and off-diagonals ρij are coherences.
- Coherence ρ₁₂, ρ₁₃theory
- ρ₁₃ (optical coherence) radiates the probe’s response. ρ₁₂ (ground/spin coherence) is the long-lived memory. In the weak-probe limit ρ₂₁ = −ΩpΩc*/(Γ₁₂Γ₁₃ + |Ωc|²).
- Lindblad / master equationtheory
- dρ/dt = −(i/ħ)[H,ρ] + L[ρ]. The superoperator L adds decay and dephasing, and the paper uses it to derive EIT.
- Optical Bloch equationstheory
- The master equation written out element by element for a few-level atom driven by light (paper Eq. 7).
- RWA (rotating-wave approximation)theory
- Dropping terms oscillating at ~2ν, valid when Ω and Δ ≪ ν. It turns the Hamiltonian into time-independent form in the rotating frame.
- Autler–Townes splittingtheory
- A strong control splits the excited state into a doublet ±Ωc. It reduces absorption between the peaks without interference, so it is distinct from (but easily confused with) EIT.
- SAS (saturated absorption spectroscopy)lab
- A strong pump and a weak counter-propagating probe through a reference cell. Only atoms with v ≈ 0 see both, so narrow sub-Doppler features appear on the Doppler-broadened absorption.
- Lamb diplab
- The narrow transmission increase in SAS at an atomic resonance, caused by the pump saturating the v ≈ 0 atoms.
- Crossover resonancelab
- An SAS feature exactly midway between two transitions that share a lower level, from atoms whose Doppler shift puts pump and probe on different transitions. Often the strongest lock point.
- Error signallab
- A signal that is zero at the lock point and changes sign across it (e.g. a derivative of the SAS dip, from modulation plus lock-in detection). It drives the feedback loop.
- PID locklab
- Proportional-integral-derivative feedback that adjusts laser current (and/or temperature) to keep the error signal at zero.
- Servo (feedback loop)lab
- A loop that measures a deviation (error signal) and applies a correction to push it back to zero, as in the laser frequency lock.
- Lock boxlab
- The electronics that generate the error signal (e.g. lock-in demodulation) and apply PI/PID feedback, with adjustable slope sign, gain and integrator.
- Laser controller & current modulation inputlab
- A low-noise current source plus TEC controller for the diode. Its modulation input (typically a BNC) adds a voltage-proportional current change, which is how the lock box steers the DFB frequency quickly.
- Ditherlab
- A small, fast modulation (here of the laser current at tens of kHz) used with a lock-in to obtain a derivative error signal. It also frequency-modulates the light used elsewhere.
- DAVLLlab
- Dichroic atomic vapour laser lock: a magnetic field splits the σ⁺ and σ⁻ absorption of a reference cell, and the difference signal is dispersive. A modulation-free error signal.
- Polarization spectroscopylab
- A circularly polarized pump makes the vapour birefringent near sub-Doppler resonances. A probe analysed by a polarizer and balanced photodiodes gives a dispersive, modulation-free error signal.
- DFB laserlab
- Distributed-feedback diode laser with a grating in the gain chip. It is robust and mode-hop-resistant, with linewidth ~1–2 MHz (paper). Tuned by current and temperature.
- ECDLlab
- External-cavity diode laser with grating feedback. Typical linewidth is a few hundred kHz (paper), with a wider tuning range but more mechanical sensitivity.
- Laser linewidthlab
- Spectral width of the laser’s frequency noise. In Zeeman EIT, probe and control share one laser, so their common noise largely cancels in the two-photon detuning. This is why a 1–2 MHz DFB can still resolve kHz EIT lines.
- RIN (relative intensity noise)lab
- Fractional power fluctuations of a laser. It sets the noise floor of transmission measurements.
- Mode hoplab
- An abrupt jump of a diode laser to another longitudinal mode during tuning. It shows up as a discontinuity in SAS scans.
- Faraday optical isolatoroptics
- Input polariser, then a 45° Faraday rotator, then an output polariser at 45°. Light going forward passes. Back-reflected light is rotated a further 45° (non-reciprocally) and blocked, which protects the laser from feedback that destabilises its frequency. A dual-stage isolator puts two of these in series, so their isolation (in dB) adds. Our plan uses one free-space stage (Thorlabs I795P3D, centre 795 nm, at least 34 dB) after the collimator, on top of the micro-isolator inside the laser module.
- AOM (acousto-optic modulator)optics
- An RF-driven sound wave in a crystal (here TeO₂) acts as a moving grating. Light diffracts into orders m = 0, ±1 …, and order m is frequency-shifted by m·fRF. Switching the RF switches the diffracted beam in well under a microsecond.
- Bragg diffractionoptics
- Regime of thick acoustic gratings in which, at the Bragg angle, most power goes into a single order. It is what makes AOMs efficient.
- Diffraction ordersoptics
- The zeroth order is undeflected and unshifted. The ±1 orders are deflected by roughly λ fRF/vsound and shifted by ±fRF.
- Double-pass AOMoptics
- The diffracted beam is sent back through the AOM, so the total shift is 2fRF and beam steering cancels when fRF is scanned. A QWP in the return path rotates polarization by 90° so a PBS can separate the output.
- Cat’s-eye retro-reflectoroptics
- A lens one focal length from the AOM plus a mirror at its focus. The return beam retraces the input regardless of the small angle change, which is essential for double-pass scanning.
- RF driverlab
- Oscillator plus amplifier that powers the AOM transducer. Zeeman EIT needs twin, phase-locked channels whose difference can be set and scanned at the kHz level (paper: “twin phase-locked rf signals from the same dual-output waveform generator”).
- EOM (electro-optic modulator)optics
- A crystal whose index changes with voltage. It phase-modulates light to create sidebands at GHz frequencies. It is needed for hyperfine EIT (6.834 GHz) but not used in Zeeman EIT.
- PBS (polarizing beamsplitter)optics
- A cube that transmits p (here horizontal) and reflects s (vertical) polarization. Typical extinction is ~10³.
- NPBS (non-polarizing beamsplitter)optics
- Splits power in a fixed ratio (e.g. 50:50) almost independently of polarization.
- HWP (half-wave plate, λ/2)optics
- Retards one axis by π. It rotates linear polarization by 2θ, where θ is the angle between the input polarization and the fast axis. Used with a PBS as a variable power splitter.
- QWP (quarter-wave plate, λ/4)optics
- Retards by π/2. Linear light at 45° to its axis becomes circular, and vice versa. In Zeeman EIT it turns the orthogonal linear control and probe into opposite circular polarizations.
- Jones vector / matrixoptics
- A 2-component complex vector (EH, EV) for fully polarized light. Each element is a 2×2 matrix, and the simulator traces polarization this way.
- σ⁺, σ⁻, π polarizationoptics
- Circular light driving ΔmF = +1 or −1 relative to the quantization axis, and linear light along the axis driving ΔmF = 0. For a beam along B, circular light is σ±.
- Glan–Taylor polariseroptics
- A calcite prism polariser with an air gap. It transmits one linear polarization and rejects the other sideways with very high extinction (~10⁵, paper), which is why it is used to keep the strong control off the detector.
- Extinction ratiooptics
- Wanted-to-unwanted power ratio at a polarizing element (PBS ~10³, Glan–Taylor ~10⁵ per the paper).
- Mu-metal (µ-metal) shieldlab
- A nickel-iron alloy of very high magnetic permeability that diverts external fields around the cell. The paper uses a triple-layer shield.
- Degaussinglab
- Removing remanent magnetization of the shield with a decaying AC current in coils wound on the layers. It is done before taking data.
- Solenoid / Helmholtz coilslab
- Coils that produce a controlled uniform field. A long solenoid gives B along its axis (here the beam axis). Helmholtz pairs give a uniform field between two coils.
- Photodiodelab
- Converts optical power to current (responsivity roughly 0.5 A/W near 800 nm for silicon). Amplified photodetectors add a transimpedance stage.
- Transimpedance amplifierlab
- Converts photocurrent to voltage (V = I·Rf). Gain and bandwidth trade off, and must suit both µs pulses and slow sweeps.
- Lock-in amplifierlab
- Demodulates a signal at a reference frequency to extract tiny modulated signals. It is often used to produce the SAS derivative error signal.
- Oscilloscopelab
- Displays detector voltage vs time. It is used for EIT sweeps (triggered on the scan) and for storage pulse sequences (triggered by the function generator).
- Fabry–Pérot interferometerlab
- A two-mirror cavity whose transmission comb reveals the laser’s single-mode operation, mode hops and modulation sidebands.
- Function generator (burst mode)lab
- Emits a fixed number of pulses on a trigger. Two channels with programmable delays create the probe-pulse and control-switching sequence.
- TEC / temperature controllerlab
- A thermo-electric cooler or heater with a PID controller (e.g. the planned TC300B), used to hold the cell at fixed temperature and therefore fixed density.
- Retrieval efficiency ηmemory
- Energy (or photon number) of the retrieved pulse divided by that of the input pulse.
- Fidelitymemory
- Overlap between the input quantum state and the retrieved state (e.g. for polarization qubits). It is distinct from efficiency.
- Storage time / memory lifetimememory
- How long the stored coherence survives. It is usually quoted as the 1/e decay time of η vs storage duration and is limited by γ₁₂.
- Bandwidth B (EIT)memory
- The spectral range with high transmission. For large OD it narrows as B ~ γEIT/√ODEIT (“density narrowing”), which limits how short a stored pulse can be.
- Time–bandwidth productmemory
- Delay × bandwidth, Bτ ≈ √ODEIT. It counts how many pulses fit in the medium at once.
- Quantum memorymemory
- A device that stores a quantum state of light and releases it on demand with high efficiency and fidelity. It is a building block of quantum repeaters and networks.
- Flying qubitmemory
- A qubit carried by a travelling photon. In Objective 3 the α-MoO₃ single-photon emitters are intended as flying-qubit sources.
- Four-wave mixingmemory
- A nonlinear process enhanced at high OD that adds noise or gain to EIT memories.
- Thermal velocity vthvapour
- 1-D rms speed √(kBT/m). It is ~178 m/s for ⁸⁷Rb at 60 °C design estimate.
- Isotopically enriched cellvapour
- A cell filled with (nearly) pure ⁸⁷Rb rather than natural Rb (≈72 % ⁸⁵Rb). It avoids absorption by the other isotope. The paper’s example spectra use isotopically pure ⁸⁷Rb.
- Beam dumplab
- An absorbing target that safely terminates unwanted beams (rejected control, zeroth orders, leakage).
- Irisoptics
- An adjustable aperture, used to select one AOM diffraction order and to mark beam paths during alignment.
- ND filteroptics
- Neutral-density attenuator with transmission 10−OD, used to make the probe weak.
- Fibre collimatoroptics
- An aspheric lens package that turns the fibre output into a collimated Gaussian beam (planned: f = 11.07 mm FC/APC package, ~1.5 mm waist; it plugs onto the laser fibre and the free-space isolator follows it).
Physics from scratch
From the rubidium atom to stored light, step by step. Background lectures: two-level atom, dark states & EIT. Equation numbers in grey refer to Finkelstein et al., arXiv:2205.10959v2.
3a · The ⁸⁷Rb atom and the Zeeman Λ system
Rubidium is an alkali: one valence electron outside closed shells. Its ground configuration is 5S₁/₂. The first excited configuration splits by fine structure into 5P₁/₂ (reached by the D1 line near 795 nm) and 5P₃/₂ (D2, near 780 nm). The ⁸⁷Rb nucleus has spin I = 3/2. Coupling it to the electron gives hyperfine levels F = 1, 2 in both 5S₁/₂ and 5P₁/₂. In a magnetic field each F splits into 2F+1 Zeeman sublevels mF.
EIT needs three levels: two long-lived lower states and one excited state. Zeeman EIT takes all three from the D1 manifold (paper Fig. 9b):
- |1⟩ = 5S₁/₂, F=2, mF=+2
- |2⟩ = 5S₁/₂, F=2, mF=0
- |3⟩ = 5P₁/₂, F′=1, mF′=+1
The probe couples |1⟩→|3⟩ (Δm = −1, σ⁻) and the control couples |2⟩→|3⟩ (Δm = +1, σ⁺), with the quantization axis along the solenoid field, which is parallel to the beams. The σ⁺ control also optically pumps atoms toward the high-mF end of F=2. F′=1 has no mF′ = +2 or +3, so on this transition both mF=+1 and +2 are dark to σ⁺. The three-level theory below idealizes this as “all population in |1⟩”, the state the weak probe interrogates. Real multilevel pumping (including leakage to F=1) spreads population and reduces contrast, which is one reason measured numbers deviate from the three-level model.
Reference constants for ⁸⁷Rb D1 Steck · verify before citing
| Quantity | Value | Note |
|---|---|---|
| Vacuum wavelength λ (D1) | 794.978 850 9 nm | often rounded to 794.98 nm |
| Frequency ν (D1) | 377.107 463 5 THz | |
| Excited-state lifetime τ (5P₁/₂) | 27.70 ns | |
| Natural linewidth Γ/2π (D1) | 5.746 MHz | γ₁₃ ≈ Γ/2 for the optical coherence (stationary atoms, no collisions) |
| Ground hyperfine splitting (F=1↔2) | 6.834 682 610 904 GHz | the gap a hyperfine-Λ scheme must bridge |
| 5S₁/₂ Zeeman shift (F=2 / F=1) | ≈ +0.70 / −0.70 MHz/G per mF | gF ≈ ±1/2; paper: 0.7 kHz/mG |
| Nuclear spin I | 3/2 | |
| Natural abundance ⁸⁷Rb | 27.83 % | reason to buy an isotopically enriched cell |
| Atomic mass | 86.909 180 520 u | used for vth |
| D1 saturation intensity (far-detuned, π) | 4.484 mW/cm² | effective value; multilevel pumping changes this in practice |
| 5P₁/₂ hyperfine splitting (F′=1↔2) | not quoted here | revisions of Steck differ; read the current one |
Solid lines: sublevel shifts (kHz) up to 200 mG. The highlighted pair is the Zeeman EIT Λ (mF=+2 and 0). Their splitting is the two-photon resonance the AOM offset must match.
3b · Three levels, the Hamiltonian and the dark state
Treat the atom as three levels, |1⟩ and |2⟩ below and |3⟩ above, driven by a probe (field E₁, frequency ν₁) on |1⟩–|3⟩ and a control (E₂, ν₂) on |2⟩–|3⟩. After the rotating-wave approximation (drop terms oscillating at optical frequencies) and moving to a frame rotating with the fields, the Hamiltonian becomes time-independent:
This matrix has an eigenvector with eigenvalue zero, a state the light cannot touch. At two-photon resonance it is
Two ideas carry everything that follows:
- Interference, not depletion. The two excitation amplitudes |1⟩→|3⟩ and |2⟩→|3⟩ cancel exactly in |D⟩. With a strong control (Ωp ≪ Ωc) the dark state is almost entirely |1⟩. The atoms sit in the very state that should absorb the probe, yet they are transparent.
- The condition is a frequency difference. The dark state survives for any one-photon detuning as long as the two-photon detuning vanishes:
If δ ≠ 0 the relative phase drifts and the atoms slowly become absorbing. A coherence lifetime τcoh therefore gives a transparency width of order δ ≈ (π/2)/τcoh. This is the first hint that EIT linewidth measures ground-state coherence, which is exactly what a memory needs. It also explains why Zeeman EIT tolerates a 1–2 MHz DFB: probe and control come from the same laser, so laser frequency noise is common to both and largely drops out of δ.
Adding decay: the master equation
Real atoms decay and dephase, so we use the density matrix ρ and a Lindblad term LΓ:
Here γ₁₂ is the ground-state (spin) decoherence rate and γ₁₃ the optical-coherence decay rate. In the weak-probe limit all population is pumped into |1⟩ (ρ₁₁ ≈ 1), and in steady state only two linear equations survive. With Γ₁₂ = γ₁₂ − iδ and Γ₁₃ = γ₁₃ − iΔ₁:
3c · Susceptibility, transmission and the EIT linewidth
The probe sees the macroscopic polarization of N atoms per unit volume, i.e. the susceptibility. Writing α₀ for the unsaturated resonant field-absorption coefficient without EIT:
For a resonant probe (Δ₁ = 0) and small δ this takes the canonical EIT form:
Read this as a design rule. The window’s half-width γEIT starts at γ₁₂ and grows linearly with control intensity (power broadening). The residual absorption at line centre falls once |Ωc|² ≫ γ₁₂γ₁₃. A narrow line wants low control power; deep transparency wants high control power. The paper notes that the optimum is often where the two terms of γEIT are equal.
In warm vapour, motion broadens the optical transition by σDop (a few hundred MHz), and buffer-gas collisions add pressure broadening γ₁₃col. The power-broadening term is then divided by the whole optical width:
Formula used: f(δ) = W·Γ₁₂/(Γ₁₂Γ₁₃ + Ωc²) with Γ₁₂ = γ₁₂ − iδ, Γ₁₃ = W − iδ (all in units of 2π·kHz). T = exp[−OD·Re f], φ = −(OD/2)·Im f (field factor e−(OD/2)f). Replacing γ₁₃ by W ≈ γ₁₃ + γ₁₃col + σDop mimics Eq. 40. Default W = 300 MHz is a design estimate for warm Rb with buffer gas. Linewidths from this crude model can differ from measured ones by factors of order unity.
3d · Dispersion, slow light, dark-state polaritons and storage
Kramers–Kronig guarantees that the narrow absorption dip comes with a steep, positive refractive-index slope at δ = 0. Near the EIT peak (Δ₁ = 0):
Evaluating the slope gives a group index that grows as α₀|Ωc|²/(γ₁₃γEIT²) (paper Eq. 28; see the paper for the exact prefactor). In the useful regime γEIT ≈ |Ωc|²/γ₁₃, so weaker control means slower light, and so does higher density. The practical numbers are the delay and the bandwidth, both read straight from a measured spectrum:
From slow light to stored light
A pulse entering the EIT medium is spatially compressed by the ratio vg/c, because its front slows down on entry while its tail is still in free space. Inside, it travels as a dark-state polariton: a coherent mixture of the probe field and the spin coherence ρ₁₂. The control strength sets the mixing angle. Ramping Ωc to zero while the pulse is fully inside stops the polariton and converts it entirely into a spin wave, a stationary pattern of ρ₁₂ across the cell. Nothing is absorbed. The information is now in the relative phase and amplitude of mF=+2 and mF=0. Turning the control back on reverses the mapping and the pulse leaves the cell in the original direction.
- Storage time is limited by how long ρ₁₂ survives, i.e. by γ₁₂ from diffusion out of the beam, magnetic-field gradients (which dephase a Zeeman coherence), and collisions.
- Efficiency is limited by OD: for pulses within the bandwidth, the paper states that inefficiency scales as 1/ODEIT. A pulse that does not fit inside the medium leaks out before storage.
- The project’s planned storage protocol maps one-to-one: AOM 1 slices the attenuated probe into pulses; AOM 2 switches the control off mid-transit; switching it on retrieves the pulse; a final polarisation filter blocks the control before the detector.
3e · What changes in a hot vapour cell
Each motional effect is a time-of-flight T across a length l, giving spectral broadening σ ≈ 1/T. For ballistic motion T ∝ l; for diffusive motion T ∝ l².
Doppler and the co-propagating trick
One-photon Doppler broadening (a few hundred MHz) reduces the absorption cross-section and therefore the usable OD, but it does not by itself widen the EIT line. EIT is a two-photon process with effective wavevector keff = kp − kc for a Λ system. For Zeeman EIT the two frequencies differ by only kHz, so co-propagating beams give keff ≈ 0, and every velocity class shares the same transparency window. This is why Zeeman EIT sends probe and control along the same path. A small angle θ between them gives a residual broadening of about σDopθ, tens of kHz already for θ ~ 0.1 mrad without buffer gas.
Buffer gas and Dicke narrowing
A few Torr of inert gas makes Rb diffuse. Broadening over a length l becomes D/l², and when the mean free path is shorter than the two-photon wavelength 2π/|kp − kc| the residual Doppler width collapses to D|kp − kc|² (Dicke narrowing). In the paper’s data (Fig. 10c) the angular sensitivity becomes quadratic in θ rather than linear. The price is pressure broadening of the optical line (~10 MHz/Torr).
Transit time and beam size
A finite beam of waist w₀ is crossed in w₀/vth (ballistic) or w₀²/D (diffusive). Without buffer gas the EIT line takes a cusp shape with FWHM 2(vth/w₀)ln2, tens of kHz for mm beams. With a ~0.75 mm probe radius at 60 °C that is ≈52 kHz design estimate. Larger beams help, which is one reason the paper expands the control well beyond the probe (1/e² radii 2.55 mm vs 0.47 mm in Fig. 10c).
Walls, magnetic fields, collisions
Uncoated walls fully decohere atoms that reach them. Field inhomogeneity dephases a Zeeman coherence directly, which is why the cell sits in a solenoid inside a triple-layer µ-metal shield that is degaussed before data. Rb–Rb spin-exchange and spin-destruction collisions grow with density, and above ~5×10¹¹ cm⁻³ radiation trapping also shortens coherence.
3f · Decoherence budget, OD trade-offs and storage limits
Use this as a checklist when an EIT line is broader than expected or storage dies too fast. Numbers marked as estimates are for planning only.
| Mechanism | Scales as | Zeeman EIT planning value | Lever |
|---|---|---|---|
| Power broadening | Ωc²/(γ₁₃+γcol+σDop) | dominates in the paper’s data: 26 kHz at 5.5 mW/cm², 7.3 kHz at 1.3 mW/cm² paper | control intensity, beam expansion |
| Transit time (no buffer gas) | vth/w₀ | ≈50 kHz FWHM for w₀ ≈ 0.75 mm design estimate | buffer gas, larger beams, coatings |
| Diffusion out of beam (buffer gas) | D/w₀² | depends on pressure and w₀; small for mm beams at ~10 Torr design estimate | pressure, beam size |
| Residual Doppler (beam angle) | σDopθ (ballistic); ∝θ² (Dicke) | tens of kHz at 0.1 mrad without buffer gas paper | co-propagation, buffer gas |
| Magnetic inhomogeneity | 1.4 kHz/mG × ΔB across beam | a 1 mG gradient shifts the Λ resonance by 1.4 kHz design estimate | shield, degauss, uniform solenoid |
| Spin exchange / destruction | ∝ n | can reach kHz paper | temperature |
| Radiation trapping | n ≳ 5×10¹¹ cm⁻³ | sets in near the top of the heater range design estimate | temperature |
| Laser linewidth | common mode cancels | DFB 1–2 MHz is acceptable paper; residual from RF phase noise between channels | phase-locked RF channels |
Dots: the paper’s two measured FWHMs (7.3 kHz at 1.3 mW/cm², 26 kHz at 5.5 mW/cm²; isotopically pure ⁸⁷Rb, 10 Torr Ne, ~60 °C). Line: FWHM ≈ 1.5 kHz + 4.45 kHz/(mW cm⁻²) × I, a two-point linear fit design estimate also used by the simulator. Your cell will have its own slope and intercept: measure them in step O2.5.
The OD trade-off
OD is the resource. Efficiency improves as 1/ODEIT falls, delay grows as ODEIT/γEIT, and the time–bandwidth product as √ODEIT. Raising temperature raises density roughly exponentially, but it also raises spin-exchange decoherence, radiation trapping, four-wave-mixing noise, and the heater power needed. The paper also notes coating limits (if used) of ~50–100 °C. The planned polyimide foil heater is rated to 70 °C and the GCH25-75 assembly to 50 °C. Our vapour-pressure estimate gives OD ≈ 4 at 50 °C and ≈ 20 at 70 °C, scaled from the paper’s OD ~10 at ~60 °C design estimate.
What limits storage in practice
- ODEIT: too low and the pulse cannot be compressed into the cell, so its front leaks out before the control switches off.
- Bandwidth: pulses shorter than ~1/B are distorted and absorbed. Pulse length, OD and control power must be co-optimised.
- Coherence time: retrieved energy decays with storage time at a rate set by γ₁₂. Shielding and buffer gas dominate here.
- Control leakage and noise: at single-photon level, filtering (Glan–Taylor, and later spectral filtering) sets the signal-to-noise ratio.
- Switching: AOM rise times (beam size ÷ acoustic velocity) must be short compared with the pulse.
Zeeman EIT experimental architecture
One DFB, two double-pass AOMs, one shielded cell. Block by block, following paper Fig. 10 and the project plan.
1 · Source & isolation
A 795 nm DFB in a 14-pin butterfly (option: Yanban RB-795-DFB-BFW, 100–120 mW, linewidth 200 kHz typical, target 794.97 nm). Its packaging is pending the supplier reply. As a PM-fibre version with a built-in isolator it feeds the same f = 11.07 mm FC/APC collimator and one free-space isolator (Thorlabs I795P3D). As the listed free-space version its collimated beam (about 1.0 × 0.8 mm) goes straight into two isolator stages (two I795P3D, or one IOT-5-780-VLP tandem), because there is no isolator inside. With about ten times the power the paper needs, turn the beam down right after the isolation with a half-wave plate and a PBS into a rated beam dump, and treat the open 100 mW beam as Class 3B.
A PM-fibre-pigtailed 795 nm DFB (planned: Toptica Eagleyard EYP-DFB-0795-00015-1500-BFY12-0005, up to 15 mW, FC/APC, with a micro-isolator built into the module) feeds an f = 11.07 mm FC/APC collimator that gives a ~1.5 mm waist, followed by a free-space Faraday isolator (Thorlabs I795P3D: centre 795 nm, isolation at least 34 dB, transmission 90 %, beam up to Ø2.7 mm) with its input polarizer along the fibre’s slow axis. The paper notes that 20–40 mW is enough and that a DFB linewidth of 1–2 MHz is acceptable, so the 15 mW pigtailed laser is at the low end once isolator, AOM and polarization losses are counted: do a power budget with the power meter before ordering, or ask the vendor for a higher-power pigtailed version.
2 · SAS lock
A λ/2 + PBS pick-off sends a few percent to a saturated-absorption module (reference Rb cell, pump and probe, photodiode). The photodiode signal goes to a lock box, which makes an error signal and drives the laser controller’s current modulation input, closing the loop near F=2→F′=1 of D1 (paper; ≈794.98 nm). The double-pass AOMs shift the EIT beams by 2 × 80 MHz and the SAS light is not shifted: we lock on F = 2 → F′ = 1 and run the EIT beams 160 MHz off the one-photon resonance (−1 orders; the cell about 3 °C hotter), which needs no third AOM (see the AOM answer in section 09). See the frequency lock.
3 · Control & probe preparation
A λ/2 + PBS splits a weak probe from a strong control (paper). Each arm double-passes an AOM through a PBS + cat’s-eye with a λ/4 in the return path. The returning beam has rotated polarization and exits the other PBS port. The double pass gives 2fRF shift and no beam walk while scanning. The two AOMs are driven by twin phase-locked RF signals from the same dual-output generator (paper), so 2(fC − fP) is stable to Hz.
4 · Polarization & combining
A PBS recombines the arms (probe H transmitted, control V reflected) onto one co-propagating path. A λ/4 at 45° then makes them opposite circular: control σ⁺, probe σ⁻ relative to B. The paper also expands the control beam well beyond the probe for a uniform Rabi frequency (2.55 mm vs 0.47 mm radii in Fig. 10c). A telescope in the control arm is a recommended addition. design note
5 · Cell, heater, field, shield
Quartz ⁸⁷Rb cell (planned) with a polyimide foil heater (≤70 °C) or GCH25-75 assembly (≤50 °C) under a TC300B controller. Heat uniformly and non-magnetically (bifilar winding). Use a solenoid giving B along z (paper: typically 10–100 mG) inside a triple-layer µ-metal shield, degaussed before data. At 50 mG the Λ splitting is 70 kHz.
6 · Separation & detection
A second λ/4 converts the circular beams back to linear. A Glan–Taylor (~10⁵ extinction vs ~10³ for a PBS) passes the probe to a fast photodiode and sends the control to a dump (paper). The probe frequency is scanned around the fixed control by tuning AOM-P. A scan of less than ±100 kHz covers the EIT feature (paper).
The frequency lock: SAS → lock box → laser controller → DFB
The SAS module on its own only measures. A real lock is a feedback loop with four parts:
- SAS photodiode records the reference-cell transmission, with sub-Doppler dips at the atomic lines.
- Lock box (error-signal generation + PI/PID servo) turns that transmission into a dispersive error signal that crosses zero at the chosen feature and changes sign on either side. It then computes a correction.
- Laser controller (low-noise current source + TEC controller) adds the correction to the DFB injection current through its modulation input (usually a front-panel BNC).
- DFB: its frequency follows the current (fast) and the chip temperature (slow). A DFB has no piezo, so slow drifts are taken up by retuning the TEC setpoint (by hand or with a slow second loop), keeping the current correction inside its range.
Ways to make the error signal general background
| Method | How | Side effects for this experiment |
|---|---|---|
| (a) Current dither + lock-in | Dither the DFB current at tens of kHz through the controller’s modulation input, then demodulate the SAS photodiode at the dither frequency to get the derivative of the SAS spectrum. | The dither frequency-modulates all the light, including the EIT beams. In Zeeman EIT, control and probe come from the same laser, so this jitter is largely common-mode for the two-photon resonance. The one-photon detuning still wobbles by the dither depth, so keep the dither small compared with the optical line, or use (b) or (c). |
| (b) Modulation-free: DAVLL or polarization spectroscopy | DAVLL: a small magnetic field on the reference cell splits the σ⁺/σ⁻ absorption; the difference of two photodiodes is dispersive. Polarization spectroscopy: a circularly polarized pump makes the cell birefringent near the sub-Doppler lines, read out with a polarizer and balanced photodiodes. | No modulation on the laser. More optics in the SAS arm, and the zero point can drift with field, alignment and photodiode balance. |
| (c) Modulate only the SAS beam | Put an AOM or EOM in the SAS arm (e.g. frequency- or amplitude-modulate the pump) and demodulate as in (a). | The main beam stays clean. Needs an extra modulator and driver in the SAS arm. |
Timing for pulsed storage
Why Zeeman EIT rather than hyperfine EIT
The decision record for the chosen route is in Why Zeeman EIT? below. The table compares it with the other ways to build a Λ system in ⁸⁷Rb.
| Zeeman EIT: Λ system, 1 laser + 2 AOMs | Hyperfine Λ, 1 laser + EOM | Hyperfine Λ, 2 phase-locked lasers | Ladder (e.g. Rydberg) | |
|---|---|---|---|---|
| Lower states | F=2, mF=+2 and 0 | F=1 and F=2 | F=1 and F=2 | ground and highly excited |
| Probe–control offset | kHz (70 kHz at 50 mG) | 6.834 GHz | 6.834 GHz | different wavelengths |
| Frequency hardware | two 80–110 MHz AOMs + dual phase-locked RF planned | microwave synthesiser + EOM. AOM double-pass only practical below ≈3.5 GHz (paper) | optical phase lock at GHz offset | second laser + frequency lock |
| Separate, independently controllable beams | yes | no: carrier and sidebands overlap; needs filtering (paper) | yes | yes |
| Separating probe from control | by polarization (λ/4 + Glan–Taylor) | spectral filtering usually needed | polarization and/or spectral | wavelength |
| Magnetic sensitivity | first-order (1.4 kHz/mG), so shielding is critical | can use mF=0 clock pair (second-order) | same as EOM | n/a |
| Paper’s verdict | “least resource-intensive” | derive both fields from one laser by modulation; above ≈3.5 GHz “electro-optical modulators are the best choice” | “Hyperfine EIT requires two phase-locked lasers” (or modulation of one) | large k mismatch, residual Doppler |
| Fit to planned hardware | consistent | needs EOM + synthesiser (to procure) | needs second laser + GHz phase lock | out of scope |
Why Zeeman EIT?
The decision record for the single-laser Zeeman Λ-EIT route in ⁸⁷Rb D1.
| Criterion | Zeeman Λ (1 DFB + 2 AOMs) |
|---|---|
| Lower states | F=2, mF=+2 and 0 (same hyperfine level) |
| Hardware | two 80–110 MHz AOMs, dual phase-locked RF, PBSs, λ/4s, Glan–Taylor, solenoid, shield |
| Hardware readiness | planned AOMs and dual RF driver. To procure: shield, solenoid, Glan–Taylor, detector, scope. |
| Laser frequency lock | SAS → lock box → laser controller → DFB current. The lock holds the one-photon detuning (≈ MHz); the two-photon resonance comes from the phase-locked AOM RF. |
| How the two frequencies are made | Double-pass AOMs set a kHz relative offset (the Zeeman splitting) plus a common ~160 MHz shift |
| Probe/control separation | Separate beams with orthogonal circular polarizations, so λ/4 + Glan–Taylor (~10⁵) removes the control |
| Independent control of each field | Yes: each arm has its own AOM for intensity, switching and pulses |
| Magnetic sensitivity | First order: 1.40 kHz/mG for the mF=+2↔0 pair. Shielding and field stability are critical. |
| Linewidth expectations | paper 7.3–26 kHz measured (Zeeman, 10 Torr Ne, ~60 °C) |
| Pulsed storage at single-photon level | Good fit: independent switching plus polarization filtering, matching the planned storage protocol |
| Alignment difficulty | Higher: two arms, two double passes, recombination to ≪ 1 mrad |
| Main risks | AOM aperture vs beam size, RF phase coherence, shield and solenoid procurement |
3D optical-bench simulator
Build the Zeeman EIT bench on a 25 mm-pitch breadboard. Beams are traced with Jones calculus, AOM shifts and polarizing optics. The cell responds with a simplified EIT model.
Open the full-page 3D bench ↗ A larger view with the same features and more room for the 3D table. The simulated table is 2.4 m × 1.6 m, drawn larger than strictly needed so that the parts are not crowded; it is for illustration, and the lab’s own table is used for the real build.
How to use it. Drag a component from the palette onto the table, or click or tap it to drop it near the centre. Click a part to select it, then drag it to move it (it snaps to the grid). Rotate with R (Shift+R reverses) or the buttons. Delete with Del, nudge with the arrow keys while the table has focus. Orbit with the left mouse button or one finger, pan with the right button or two fingers, zoom with the wheel or a pinch. The bench opens with the complete Zeeman EIT reference layout, so take it apart and see what breaks.
Bring-up & audit protocol
An ordered commissioning sequence. Each step isolates one variable. Numeric pass criteria are design targets unless tagged otherwise.
Objective 1: locked laser and operating cell
- Laser characterisation. Mount the DFB with its current and TEC controller. Record power vs current. Collimate with the 11.07 mm package and measure the beam size before any optic.PM-fibre version: collimate with the 11.07 mm package; free-space version: the beam leaves the package collimated (about 1.0 × 0.8 mm). Measure the beam size before any optic, and run the arrival test of the Yanban answer in section 09 (power against current, the Rb D1 absorption dips and SAS features, polarization). Pass · single-mode output, stable power; waist close to the planned ~1.5 mm.
- Isolator first. Connect the laser fibre to the FC/APC collimator (PM fibre: keep the connector key on the slow axis), set it for a ~1.5 mm collimated beam, and put the free-space isolator (Thorlabs I795P3D) right after it, input polarizer along the fibre’s slow axis, arrow pointing away from the laser; turn it for the highest forward transmission.PM-fibre version: as for a fibre laser (FC/APC collimator, key on the slow axis, then one I795P3D, input polarizer along the slow axis). Free-space version: two isolator stages straight in front of the package window, input polarizer along the laser polarization, arrows away from the laser. Then a half-wave plate and a PBS send the power the bench does not need (about 90 mW) into a rated dump. Check that a deliberate back-reflection does not disturb the laser (watch the SAS or a Fabry–Pérot). Pass · forward transmission ≳ 70 % (isolator loss ≈ 1–1.5 dB plus connectors); no frequency jumps when a mirror retro-reflects the beam.
- Mode-hop map. Sweep current and temperature while watching a Fabry–Pérot or wavemeter (both procurement gaps; borrow if needed) and a Doppler-broadened Rb absorption signal. Pass · a continuous, mode-hop-free current scan covers the D1 F=2 lines with margin.
- SAS signal. Use λ/2 + PBS to pick off a few percent into the SAS module. Overlap pump and counter-propagating probe in the reference cell. Identify Doppler valleys and sub-Doppler dips and crossovers. Note that natural-abundance reference cells also show ⁸⁵Rb lines. Pass · sub-Doppler features clearly resolved; F=2→F′=1 identified unambiguously.
- Close the frequency lock. Cable SAS photodiode → lock box → laser controller modulation input. Then work in order:
- Open-loop scan: ramp the laser current slowly (loop open) and view the SAS transmission and the error-signal monitor on the scope.
- Find the lines: identify the Doppler valleys and the sub-Doppler features, and pick F=2→F′=1 (or a chosen crossover).
- Set slope and sign: adjust dither depth or modulation-free balance so the error signal crosses zero cleanly at the feature. Choose the sign so that feedback pushes the laser towards zero.
- Close the loop: stop the ramp with the laser parked near the zero crossing and engage the servo. Start with low gain, raise it until the lock is stiff, then back off from any oscillation.
- Check it holds: the error signal stays near zero, SAS transmission stays on the feature, and small taps on the table do not unlock it. Offload slow drift to the TEC setpoint.
- Cell thermal control. Install the ⁸⁷Rb cell with the foil heater and TC300B. Step 30 → 60 °C. Keep the cell stem or windows from being the coldest point, so Rb does not condense on the windows. Pass · setpoint held to ±0.1 °C; absorption increases with temperature as expected; no window deposits.
- Optical depth. With control blocked and a weak probe, scan the laser and fit the resonant absorption to obtain OD(T). Compare with the vapour-pressure estimate. Pass · OD reproducible to ~10 % at a fixed temperature; OD ≳ 5 reachable within the heater limit.
Objective 2: EIT and light storage
- Split and double-pass each arm. Set λ/2 for ~10 % probe. Build each AOM double pass (PBS, AOM, lens + mirror cat’s-eye, λ/4) and select the +1 order with an iris. Pass · double-pass efficiency ≳ 40–60 %; output position does not move when fRF is scanned ±1 MHz.
- RF coherence. Drive both AOMs from phase-locked channels with a shared clock. Beat the two arms on a fast photodiode (before the cell). Pass · beat note at 2(fC − fP) is stable and narrow at the Hz level on an RF spectrum or FFT.
- Overlap and polarization. Recombine on the PBS. Check co-propagation over ≥ 1 m (two irises). Set λ/4 at 45°, then verify circularity with a rotating polariser (power variation ≲ 5 %) for each arm separately. Pass · angle between beams well below 1 mrad; both beams circular, opposite handedness.
- Field control. Degauss the shield. Zero residual fields with the solenoid (and trim coils if available) by minimising EIT width with B ≈ 0. Then apply B ≈ 50 mG and confirm the resonance moves by 1.40 kHz/mG × B. Pass · resonance position vs solenoid current is linear with slope 1.40 kHz/mG paper: 0.7 kHz/mG per mF.
- First EIT spectrum. Scan AOM-P by ±50 kHz (optical ±100 kHz) around resonance. Separate the probe with λ/4 + Glan–Taylor. Then record FWHM vs control intensity. Pass · a narrow transmission peak at δ = 0 whose width falls roughly linearly with intensity; tens of kHz or below. paper example: 26 and 7.3 kHz
- Extract OD, ODEIT, γEIT. Take ln(I/Iin) of the spectrum (paper Fig. 8). Compute B and τdelay = ODEIT/γEIT. Pass · ODEIT/OD ≳ 0.5 (high-contrast EIT).
- Slow light. Send a probe pulse longer than 1/B (via AOM-P burst) with control on, and compare its arrival with a reference pulse (control and cell detuned). Pass · measured delay agrees with ODEIT/γEIT within ~30 %.
- Storage and retrieval. Switch the control off while the pulse is inside, wait τ, switch on. Record the retrieved energy vs τ and fit the decay. Pass · retrieved pulse clearly above control leakage and noise; decay curve recorded. milestone 2
Troubleshooting
| Symptom | Likely cause | Check |
|---|---|---|
| Laser frequency jumps when optics are touched | back-reflection into the diode | isolator orientation and throughput; tilt cube faces slightly; check fibre end-face |
| SAS shows only Doppler valleys | pump and probe not overlapped, or pump too weak | overlap inside the cell; increase pump fraction; check counter-propagation |
| Lock runs away the moment the loop closes | error-signal slope sign inverted | flip the sign switch on the lock box |
| Lock jumps to the wrong line | parked too far from the chosen zero crossing; neighbouring SAS features look alike | re-identify lines on an open-loop scan; park closer before engaging |
| Lock oscillates (ringing on the error monitor) | too much proportional or integral gain | reduce gain; check the modulation-input bandwidth |
| Lock lost periodically | mode hop near the operating current, or the correction hits its range limit | move the TEC setpoint so the operating point is mid-range and mode-hop-free |
| EIT width jitters although the lock holds | large current dither frequency-modulating the EIT beams | reduce dither; use a modulation-free lock or modulate only the SAS beam |
| Lock drops after minutes | mode hop near operating point, or thermal drift of the DFB | re-map mode-hop-free range; adjust TEC setpoint; integrator gain |
| No EIT peak at the expected AOM offset | wrong resonance sign or B magnitude, residual field, wrong helicity pair | scan wider (±300 kHz); reverse B; swap the λ/4 axis by 90°; verify the 1.4 kHz/mG slope |
| Several EIT peaks | unshielded or magnetised shield; field not along k; extra Λ systems from impure polarization | degauss; align solenoid with beams; check circular purity |
| EIT width plateaus far above expectation at low control power | transit time, field gradients, beam angle, RF phase noise | larger beams or buffer gas cell; gradient check; co-alignment; RF channel coherence |
| Peak transmission low although width is narrow | control too weak (|Ωc|² ≲ γ₁₂γopt) or poor optical pumping | increase control; check σ⁺ purity; check one-photon detuning |
| Large flat background on detector | control leakage | Glan–Taylor angle; second λ/4 angle; add spatial filtering or iris |
| Sweep distorts (beam walks) | single-pass AOM or misaligned cat’s-eye | double-pass alignment; lens focus on mirror |
| Retrieved pulse tiny, but slow light works | pulse not fully inside when control switches, or coherence lost | move t_off later; lengthen pulse or raise OD; shield and gradient checks; shorten τ |
| OD lower than expected at temperature | cold spot condenses Rb; thermometer not at cell | stem vs window temperatures; independent thermocouple |
Equipment list
What Zeeman EIT needs, and the status of each item.
Wiring diagram and cable schedule
Every electrical connection on the bench. The same cables are drawn in the 3D simulator (turn on “Cables”). Numbers in the circles match the schedule below.
BNC signalSMA RFTTL gate / syncpowercoilheater / sensorlaser diode cable
| # | From | To | Cable / connector | Signal | Note |
|---|---|---|---|---|---|
| W1 | SAS photodiode | Lock box (signal in) | BNC, 50 Ω coax, ≤ 1 m | sub-Doppler spectrum | Keep short and shielded; this signal is mV-level |
| W2 | Lock box (output) | Laser controller (modulation input) | BNC | correction voltage | Sets the fast current correction; mind the input range |
| W3 | Laser controller | DFB laser mount | manufacturer LD + TEC cable | injection current, TEC, thermistor | Use the cable made for the mount to avoid pin mismatches |
| W4 / W4b | RF source ch. A / ch. B | Attenuator / switch (control / probe) | SMA, 50 Ω | 80.000 / 79.965 MHz | Both channels from one clock keep the beat stable |
| W5 / W5b | Attenuator | RF amplifier | SMA | RF at the set level | Switch gates the arm for pulses |
| W6 / W6b | RF amplifier | AOM RF input | SMA | up to ~+30 dBm | Always connect the AOM (or a 50 Ω load) before powering the amplifier |
| W7 / W8 | Function generator ch. 1 / ch. 2 | Attenuator / switch gate input | BNC, TTL | burst gate | Times probe slicing and control off / on for storage |
| W9 | Probe photodiode | Oscilloscope CH1 | BNC | probe transmission | Terminate as the detector requires (1 MΩ or 50 Ω) |
| W10 | Lock box monitor out | Oscilloscope CH2 | BNC | error signal | Lets you see the lock state while scanning |
| W11 / W15 | Low-noise PSU | SAS and probe photodiodes | 2-core power lead | ±12 V | Linear supply; check rails before connecting |
| W12 | Function generator sync out | Oscilloscope EXT TRIG | BNC | trigger edge | Triggers sweeps and storage pulses |
| W13 | Coil current source | Solenoid | twisted pair, non-magnetic | DC current | Twist the leads to cancel stray field |
| W14 | Temperature controller | Heater + temperature sensor | heater lead + sensor lead | heater drive, sensor | Bifilar (non-magnetic) heater winding; keep leads inside the shield |
Equipment list: parts, quantities and why
Every item for the Zeeman EIT bench. Quantities for optics and instruments match the 3D reference bench above (a script checks this). Brands and part numbers are suggestions to start a quotation: confirm availability, 795 nm coatings and specifications with the vendor before ordering. Links go to the vendor, or to a Thorlabs search for the part number. Click a 3D picture to turn the item around. The same list is also on its own page, the Equipment tab.
| # | Look (3D) | Item | Qty | Suggested brand & spec | Why we need it | Link | Status |
|---|---|---|---|---|---|---|---|
| 1 · Laser, isolation and frequency lock | |||||||
| L01 | 795 nm single-frequency DFB laser, PM-fibre pigtailed, with built-in micro-isolator (14-pin butterfly) | 1 pc | Toptica Eagleyard EYP-DFB-0795-00015-1500-BFY12-0005: 5–15 mW from the PM fibre, 0.6–1 MHz linewidth, FC/APC (narrow key), PER 20 dB. Not the BFW11 type, which is a free-space collimated output without a fibre EYP-DFB-0795-00015-1500-BFY12-0005 | The single source for the control, the probe and the SAS reference. A DFB is narrow (~MHz), mode-hop free over its current range and tunes with current/temperature, which is exactly what the lock needs. The fibre pigtail removes the laser-to-fibre alignment, and the micro-isolator inside the module is a first line of defence. Up to 15 mW: do a power budget (isolator, AOM double-pass, polarization optics) before ordering; the vendor can quote a higher-power pigtailed version. | gophotonics.com ↗ | planned | |
| L01 | 795 nm single-frequency DFB laser, 14-pin butterfly, 100 mW class, free-space output (no isolator inside) | 1 pc | Yanban Laser RB-795-DFB-BFW, free-space version: 100–120 mW, linewidth 200 kHz typ (500 kHz max), SMSR ≥ 40 dB, target 794.97 nm, 0.06 nm/°C and 0.004 nm/mA, mode-hop free over 20 GHz, PER 20 dB, 150 mA typ / 175 mA max, NTC 10 kΩ (B 3950); collimated beam about 1.0 × 0.8 mm out of the package, no isolator inside RB-795-DFB-BFW | Same role as the Eagleyard: the single source for the control, the probe and the SAS reference. Ten times the power we need (turn it down with a half-wave plate and a PBS into a dump, or run a lower current), a narrower line, and no obsolescence notice. Mount it in the metal butterfly mount on a heat-sinked aluminium plate (not PETG). Get the test report of the actual unit and run the arrival test (Q&A: the Yanban entry) before building on it. | alibaba.com ↗ | to procure | |
| L02 | 14-pin butterfly laser mount with TEC and thermistor connections | 1 pc | Thorlabs LM14S2 (butterfly mount), matched to the laser pin-out LM14S2 | Holds the butterfly package, makes the electrical connections to the controller and conducts heat. Without a proper mount the TEC cannot stabilize the chip and the wavelength drifts. | Thorlabs search ↗ | to procure | |
| L03 | Laser diode current source + TEC temperature controller with analog modulation input | 1 pc | Thorlabs ITC502 benchtop controller: 0–200 mA laser current (noise < 1.5 µA rms, 10 Hz–10 MHz; compliance > 6 V), TEC ±2 A / 16 W, thermistor input (10 Ω–19.9 kΩ), analog current modulation 20 mA/V with 0–500 kHz bandwidth ITC502 | Drives the DFB with low-noise current and holds its temperature. Its modulation input is the actuator of the frequency lock (the lock box adds a correction to the current) and carries the dither for lock-in detection. Current noise here becomes laser frequency noise (about 1.4 GHz per mA), so < 1.5 µA rms is about 2 MHz. Set its current limit to 170 mA or lower before connecting the laser (maximum rating 170 mA, normal drive 160 mA). The modulation coefficient is 20 mA/V, about 28 GHz per volt: attenuate the lock-box output about 100:1 into the 10 kΩ input. The laser reads about 20 kΩ at 10 °C, so run the chip at 15 °C or warmer to stay inside the thermistor range. | Thorlabs search ↗ | in the lab ↗ | |
| L03 | Laser diode current source + TEC temperature controller with analog modulation input | 1 pc | Thorlabs ITC502 benchtop controller: 0–200 mA laser current (noise < 1.5 µA rms, 10 Hz–10 MHz; compliance > 6 V), TEC ±2 A / 16 W, thermistor ranges 10 Ω–19.99 kΩ and 100 Ω–199.9 kΩ, analog current modulation 20 mA/V with 0–500 kHz bandwidth ITC502 | Drives the DFB with low-noise current and holds its temperature; its modulation input is the actuator of the frequency lock. With this laser the current tuning is about 1.9 GHz per mA, so < 1.5 µA rms is about 3 MHz (common to control and probe). Set the current limit to 175 mA or lower before connecting (maximum 175 mA, typical 150 mA). 20 mA/V is about 38 GHz per volt: attenuate the lock-box output about 130:1 (DIY D6, 120 kΩ). The NTC reads about 20 kΩ at 10 °C: on the 20 kΩ range keep the chip above about 11 °C. | Thorlabs search ↗ | in the lab ↗ | |
| L04 | Digital lock box (error-signal generation + PI/PID servo) | 1 pc | Red Pitaya STEMlab 125-14 running the open-source Linien / PyRPL laser-lock software STEMlab 125-14 | Turns the SAS photodiode signal into an error signal (lock-in at the dither frequency) and closes the loop onto the laser controller. A programmable box is much cheaper than a commercial servo and gives slope-sign, gain and integrator control. Upgrade path: Vescent D2-125. | redpitaya.com ↗ | to procure | |
| L05 | Fibre collimator, FC/APC, f ≈ 11 mm (≈1.5 mm beam) | 1 pc | Thorlabs CFC11A-B (FC/APC, 650–1050 nm). It plugs straight onto the laser's FC/APC fibre and is followed by the free-space isolator (L06): match the APC connector and clock the key for the polarization you want. CFC11A-B | Turns the fibre output into a collimated ~1.5 mm beam, the size the AOM aperture and cell need. A mismatched connector (PC vs APC) damages the ferrule or causes back-reflection into the laser. | Thorlabs search ↗ | planned | |
| L05 | PM-fibre link after the isolators: fibre coupler, PM780 patch cable, output collimator, half-wave plate | 1 set | Coupler: Thorlabs PAF2-5B FiberPort (f 4.6 mm, made for a Ø1 mm beam into a 5 µm mode; the lab owns one). Fibre: PM780 patch cable, FC/APC both ends, 2 m (for example Thorlabs P5-780PM-FC-2). Output: a second PAF2-5B-type FiberPort (about Ø1 mm beam, 1.087 mrad) on the bench side, at the 100 mm beam height. Half-wave plate ؽ″ zero-order in a rotation mount before the coupler, to launch along the slow axis. The two steering mirrors and their mounts are counted in O01 and O02. PAF2-5B + P5-780PM-FC-2 | Our setup (decided 19 Oct 2026): the free-space beam is cleaned by a PM fibre. The output is then the same as a PM-pigtailed laser: a clean round Gaussian of about Ø1 mm (a good size for the AOMs, no reducing telescope needed), polarization fixed by the fibre axis, pointing fixed by the output collimator. Laser-side drift or a laser swap changes only the coupled power, never the alignment of the AOMs, the SAS and the cell. To buy: the patch cable, the second FiberPort and the half-wave plate (the coupler is in the lab). | thorlabs.com ↗ | to procure | |
| L06 | Free-space Faraday optical isolator, 795 nm, single stage (Thorlabs I795P3D) | 1 pc | Thorlabs I795P3D: fixed narrowband, centre 795 nm (operating range 775–815 nm), isolation ≥ 34 dB and transmission 90 % at the centre wavelength, max beam Ø2.7 mm, max 0.7 W. Mounting adapters listed by Thorlabs: H1C, SM1B2, SM087RC(/M). I795P3D | First element after the collimator, with its input polarizer along the fibre's slow axis. It stops reflections from the AOM double-passes and cell windows from re-entering the DFB (even 10⁻⁴ feedback can cause mode hops) and adds to the micro-isolator inside the laser: together about −95 dB or better at the chip (estimate). The ~1.5 mm collimated beam fits the Ø2.7 mm aperture. | thorlabs.com ↗ | to procure | |
| L06 | Free-space Faraday optical isolators, 795 nm: two stages right after the laser window | 2 pc | Thorlabs I795P3D: fixed narrowband, centre 795 nm (775–815 nm), isolation ≥ 34 dB and transmission 90 % at the centre wavelength, max beam Ø2.7 mm, max 0.7 W. Instead of two I795P3D: one Thorlabs IOT-5-780-VLP tandem isolator (55 dB min, 760–800 nm, Ø4.7 mm). I795P3D | The laser has no isolator inside, and its notes warn that a retro-reflected beam can damage the chip. One stage leaves about −67 dB at the chip, at the edge of mode hopping; two stages about −100 dB (estimate). Nothing reflective may stand between the laser and the first stage. Turn each isolator about the beam for maximum transmission (its input polarizer then lies along the laser polarization); the output polarization is at 45°, so a half-wave plate follows. | thorlabs.com ↗ | to procure | |
| 2 · Optics for the two double-pass arms, SAS and cell line (counts match the 3D bench) | |||||||
| O01 | Steering / retro mirror, protected silver, Ø25.4 mm | 13 pc | Thorlabs PF10-03-P01 (protected silver, 450 nm–20 µm), or the catalogue OQAg-25.4 (Ø25.4 × 5 mm, 450–2000 nm, > 95 %; ask flatness, scratch-dig, protected coating, reflectance at 795 nm at 45°). 13 = 11 on the bench (2 master axis, 3 SAS, 2 control, 2 probe, 2 retro) + 2 for the free-space Yanban laser (steering into the PM-fibre coupler; not needed with the fibre-pigtailed Eagleyard). Order 1–2 spares PF10-03-P01 | Fold the beams so the control and probe arms fit the table and arrive at the recombiner together. Two mirrors per beam give the two degrees of freedom needed to walk a beam onto an axis. The two retro mirrors return the diffracted order in each double pass. | Thorlabs search ↗ | planned | |
| O02 | Kinematic mirror mount, Ø1″, 2-axis | 13 pc | Thorlabs KM100 (or KM100T for the retro mirrors). 13 = 11 on the bench + 2 for the Yanban laser's fibre coupling (same count as the mirrors, O01) KM100 | Gives each mirror the fine tilt adjustment for alignment to a fraction of a milliradian. Without it the mirrors cannot be aligned, and the cat’s-eye returns drift when the RF frequency changes. | Thorlabs search ↗ | planned | |
| O03 | Polarizing beamsplitter cube, cage-mounted, 620–1000 nm | 7 pc | Thorlabs CCM1-PBS252/M (1″ cube in a 30 mm cage cube, metric taps; replaces the discontinued CM1-PBS252): Tp:Ts > 1000:1, Rs:Rp about 20:1 to 100:1, Tp > 90 %. Pick-off, splitter, 2 SAS cubes, 2 double-pass separators, recombiner CCM1-PBS252/M | The PBSs route light by polarization: they split control from probe, separate each double-pass output from its input, recombine the arms, and inject/extract the SAS pump. The reference layout needs seven. Use the transmitted port where purity matters (1000:1); the reflected port is only 20:1 to 100:1. Cheaper option: unmounted ½″ cubes in printed PETG holders (DIY Section, part D12). | Thorlabs search ↗ | planned | |
| O04 | Non-polarizing 50:50 beamsplitter cube, cage-mounted, 700–1100 nm | 1 pc | Thorlabs CCM1-BS014/M (30 mm cage cube, metric taps; replaces the discontinued CM1-BS014) CCM1-BS014/M | Divides the SAS beam into a strong pump and a weak probe independent of polarization. | Thorlabs search ↗ | planned | |
| O05 | Zero-order half-wave plate, 780 nm design, ؽ″ | 4 pc | Thorlabs WPH05E-780 (usable at 795 nm). Pick-off ratio, probe/control split, SAS probe, control trim WPH05E-780 | Sets how much light goes to the SAS (~5 %) and the control/probe power ratio (~12 % probe), turns the SAS probe horizontal, and trims the control polarization. Rotating by θ rotates the polarization by 2θ. | Thorlabs search ↗ | planned | |
| O06 | Zero-order quarter-wave plate, 780 nm design, ؽ″ | 4 pc | Thorlabs WPQ05E-780. 2 in the double passes, 2 either side of the cell WPQ05E-780 | In each double pass the plate is crossed twice, turning the returning beam’s polarization by 90° so the PBS can separate it. At the cell, one plate makes σ⁺/σ⁻ for the Λ system and the second returns the light to linear for the Glan–Taylor. | Thorlabs search ↗ | planned | |
| O07 | Rotation mount for waveplates, 360° with vernier | 8 pc | Thorlabs RSP05/M (ؽ″) RSP05/M | Plate angles must be set to a fraction of a degree: the split ratio, circular polarization purity and double-pass return all depend on it. | Thorlabs search ↗ | planned | |
| O08 | Achromatic doublet f = 100 mm (AR 650–1050 nm) | 3 pc | Thorlabs AC254-100-B. 2 cat’s-eye lenses, 1 expander output lens AC254-100-B | The cat’s-eye lens focuses the diffracted beam onto the retro mirror, so a change of RF frequency (which changes the deflection angle) does not walk the returning beam. The third forms the control beam expander. | Thorlabs search ↗ | planned | |
| O09 | Achromatic doublet f = 50 mm (AR 650–1050 nm) | 2 pc | Thorlabs AC254-050-B. Expander input lens, probe collection lens AC254-050-B | With the f = 100 mm lens it expands the control beam ×2 so it overfills the probe in the cell (control intensity sets the EIT width). The second collects the probe onto the small photodiode area. | Thorlabs search ↗ | planned | |
| O10 | Lens mount, Ø1″ | 5 pc | Thorlabs LMR1/M LMR1/M | Holds each lens on a post with a centred, repeatable position. | Thorlabs search ↗ | planned | |
| O11 | Alignment iris, Ø12 mm | 5 pc | Thorlabs ID12/M. 2 master axis, 1 SAS, 1 before and 1 after the cell ID12/M | Define a repeatable beam axis: centre the beam on two irises and every optic between them is on axis. Essential for walking the beams through the double passes and the shield. | Thorlabs search ↗ | planned | |
| O12 | Beam dump / beam trap | 12 pc | Thorlabs BT610 beam trap or anodised blocks (4 AOM 0th orders, 1 Glan reject, 1 SAS pump, 6 PBS leakage ports) BT610 | Absorb every unused beam: undiffracted AOM orders, the control rejected by the Glan–Taylor and the ~0.1 % PBS leakage. Stray 795 nm light is invisible and a hazard, and scatters onto the detector. | Thorlabs search ↗ | to procure | |
| O13 | Neutral-density filter, OD 0.3 and OD 2.0 (absorptive) | 2 pc | Thorlabs NE03A-B (OD 0.3, SAS probe) and NE20A-B (OD 2.0, probe arm) NE03A-B / NE20A-B | Keeps the probe weak (Ω_p ≪ Ω_c) so EIT is not power-broadened, and makes the SAS probe weaker than its pump. | Thorlabs search ↗ | planned | |
| O14 | Filter holder with post | 2 pc | Thorlabs FH2D or FH1 FH2D | Holds the ND filters on the table. | Thorlabs search ↗ | planned | |
| O15 | Glan–Taylor polarizer, 650–1050 nm, extinction ~10⁵ | 1 pc | Thorlabs GT10-B GT10-B | Removes the strong control after the cell far better than a PBS (10⁵ vs 10³), leaving only the probe on the detector. Without it the control leaks onto the photodiode and hides the EIT peak. | Thorlabs search ↗ | to procure | |
| O16 | Rotation mount for the Glan–Taylor | 1 pc | Thorlabs RSP1X15/M or PRM1/M RSP1X15/M | Sets the transmission axis to the probe polarization and to maximum extinction. | Thorlabs search ↗ | to procure | |
| O17 | Acousto-optic modulator, TeO₂, 415–900 nm, 80 MHz, 2 mm aperture | 2 pc | Gooch & Housego AOMO 3080-125 (quote) 3080-125 | One per arm. Each shifts its beam by 2 × f_RF in a double pass, so a few-tens-of-kHz RF difference gives the 70 kHz two-photon offset at 50 mG, and each can switch its beam for storage pulses. The 2 mm aperture takes a collimated beam of up to about 1.5 mm; a smaller beam gives a faster rise time (about 160 ns per mm of beam diameter). G&H outline drawing 97-01598-01 rev D: SMB snap-on RF input (needs an SMB-to-SMA cable to our amplifiers), housing 2.00 × 1.00 × 0.53 in, polarization 90° to the mounting plane, contrast 1000:1, AR coating 442–633 nm on that drawing: ask for the unit to be coated for 795 nm. | gophotonics.com ↗ | planned | |
| 3 · Mounting, table and hardware | |||||||
| M03 | Post + post holder + clamping fork (+ base) set, Ø1/2″ posts | 60 set | Thorlabs TR75/M + PH75/M + CF125 (or BA1S base) TR75/M + PH75/M + CF125 | Every optic sits on a post at the 100 mm beam height, which the magnetic shield and its cradle set. Sets are counted for 55 optics plus spares. | Thorlabs search ↗ | planned | |
| M04 | Mounts for the two AOMs and the Ø25 mm EIT-cell holder (custom or kinematic platforms) | 3 pc | Thorlabs KM200? / machined aluminium plates custom | The AOMs need a tilt-adjustable stage for the Bragg angle; the cell holder keeps the cell, heater and sensor aligned on the axis. | Thorlabs search ↗ | to procure | |
| M05 | Black hardboard enclosure / beam tubes for the beam path | 1 set | Thorlabs TB4 hardboard panels (covers 160 mm high inside for the 100 mm beam, DIY D10) + SM1 beam tubes to the shield end caps and the detector TB4 | Blocks room light and air currents, and contains stray beams (laser safety). | Thorlabs search ↗ | to procure | |
| M06 | Shield cradle: 3D-printed PETG, holds the shield with its axis at the 100 mm beam height (DIY Section D1). No purchase: printed in the lab | 1 pc | Print d1-shield-cradle.stl (base 210 × 90 × 8, two saddles for the Ø68 outer layer, M6 slots on the 25 mm grid); add 1 mm felt pads and two Velcro straps. Files and notes: DIY Section D1 diy-stl/d1-shield-cradle.stl | Holds the 1.3 kg shield level and on the beam axis, touching it only between the outside degaussing groups. Non-magnetic, at room temperature. | ruxxzif89.github.io ↗ | print in the lab | |
| 4 · SAS reference | |||||||
| S01 | Rb reference cell for SAS, quartz Ø19 × 75 mm, natural Rb, no buffer gas, room temperature | 1 pc | Precision Glassblowing stock cell AB-RB-Q-UV-19X75-AW (quartz, 19 mm OD, 75 mm path, natural Rb, no buffer gas, uncoated windows), stock item AB-RB-Q-UV-19X75-AW | Provides the sub-Doppler lines the laser is locked to. The published Zeeman-EIT set-up (DeRose et al. 2023) locks to a room-temperature cell of natural-abundance Rb with no buffer gas and uncoated walls, so no enrichment is needed. A pump crosses it against the weak probe; where they overlap, atoms near zero velocity give a narrow feature on the photodiode. | precisionglassblowing.com ↗ | planned | |
| S02 | Reference cell holder: 3D-printed PETG cradle, two straps and a light cover (DIY Section D11). No purchase: printed in the lab | 1 set | Print from the STL files: sas-cell-cradle.stl (1), sas-cell-strap.stl (2), sas-cell-cover.stl (1), in matte black PETG; add 4 nylon M3 screws and nuts and 1 mm felt pads. Files and steps: DIY Section D11 diy-stl/sas-cell-*.stl | Keeps the SAS cell level and on the axis without stressing the glass, and covers it against room light and draughts (the cell temperature moves the line slightly). The cell is at room temperature and outside the shield, so PETG is suitable. | ruxxzif89.github.io ↗ | print in the lab | |
| 5 · Rb cell, heating, magnetic field and shielding | |||||||
| C01 | Quartz ⁸⁷Rb vapour cell with 10 Torr neon, Ø25 mm, 25 mm vapour path (about 28 mm long with two 1.6 mm windows), uncoated, custom | 1 pc | Precision Glassblowing custom quartz cell with the geometry and fill of the published Zeeman-EIT cell (DeRose et al. 2023, which is Pyrex): Ø25 mm, 25 mm vapour path, enriched ⁸⁷Rb, 10 Torr Ne, windows uncoated. Torch-sealed stem (tip-off) on the side at mid-length, at most 4 mm above the glass and Ø8 at its base: the wrapped cell must slide into the Ø34 bore of the wound solenoid former (DIY D2). Needs a quote: the stock Ø19 × 75 mm cell is only a reference custom (quote) | The EIT medium, copying the published cell to avoid errors: 25 mm path, pure ⁸⁷Rb (no absorption by ⁸⁵Rb) and 10 Torr neon, which slows atoms diffusing out of the beam and gives Zeeman-EIT lines a few kHz wide. The paper runs it at 55-65 °C with a 50 mG field inside a shield that keeps stray fields below 0.2 mG. Price is our estimate for a custom cell until the vendor quotes. | precisionglassblowing.com ↗ | planned | |
| C02 | Polyimide foil heater with Pt100/NTC sensor, non-magnetic bifilar winding, sized for the Ø25 × 25 mm EIT cell | 2 pc | Minco / Omega polyimide heater, about 80 × 25 mm to wrap a Ø25 mm cell; Pt100 sensors KHLV-103/10 | Warms the cell to ~60 °C (OD ≈ 10). Bifilar winding cancels the heater’s own magnetic field, which would otherwise broaden the Zeeman resonance. | omega.com ↗ | planned | |
| C03 | Cell heater assembly, up to 50 °C (alternative) | 1 pc | Thorlabs GCH25 series heater for Ø25 mm cells, in the length variant that matches the cell GCH25-75 | Ready-made option for a Ø25 mm cell; the 50 °C limit gives OD ≈ 4. Use if building the foil heater is delayed (the paper runs 55-65 °C, so the foil heater is the main route). | Thorlabs search ↗ | optional | |
| C04 | Temperature controller for the cell heater | 1 pc | Thorlabs TC300B TC300B | Holds the cell temperature (OD changes steeply with T) and drives the heater from the sensor reading. | Thorlabs search ↗ | planned | |
| C05 | µ-metal magnetic shield, 3 concentric layers, Ø~70 × 250 mm, with end caps: Ø14 beam hole on the axis, Ø12 cable hole 16 mm off the axis (all caps, both ends) | 1 set | MuShield custom cylinder (alternative: Twinleaf MS-1L 4-layer) custom | Zeeman EIT is first-order sensitive to magnetic field (1.4 kHz/mG), so stray fields must be reduced to the mG level. Without it the line is broad, shifted and irreproducible. Critical-path item. | twinleaf.com ↗ | to procure | |
| C06 | Degaussing coil + variable AC supply (variac) | 1 set | Wound from enamelled copper + 1 A variac custom | Demagnetizes the shield after assembly and any time it is knocked; remanent magnetization dominates the residual field otherwise. | Thorlabs search ↗ | to procure | |
| C07 | Solenoid: non-magnetic former + 0.5 mm enamelled copper wire | 1 set | Machined PEEK/Delrin former (about Ø35 mm, to slide over the Ø25 mm cell and its heater) + 1 kg magnet wire custom | Produces the uniform bias field along the beams inside the shield; its field sets the Zeeman splitting and the two-photon resonance. | mcmaster.com ↗ | to procure | |
| C08 | Low-noise DC supply for the solenoid | 1 pc | Rigol DP832A (3-channel). Upgrade path: battery or Keysight E36312A for lower noise DP832A | Powers the solenoid. Current noise appears as two-photon detuning noise, so noise and stability matter. | int.rigol.com ↗ | to procure | |
| C09 | Fluxgate magnetometer (mG resolution) with probe | 1 pc | Stefan Mayer Instruments FLC100 (or Bartington Mag-01H) FLC100 | Measures the residual field inside the shield and calibrates B against solenoid current. It is the only way to know the mG-level field the experiment depends on. A lower-cost listing of the FLC100 (single axis, range ±100 µT, noise below 5 nT peak-to-peak, DC to 1 kHz) was found: check that the seller is genuine, ask for the zero offset and the calibration sheet, and measure the three axes one after another. | stefan-mayer.com ↗ | to procure | |
| 6 · RF chain for the AOMs | |||||||
| R01 | Dual-channel RF synthesizer, 54 MHz–13.6 GHz, shared clock | 1 pc | Windfreak SynthHD (via Saelig) SynthHD | Generates both AOM drive frequencies (80.000 MHz and 79.965 MHz) from one clock, so the RF phase relation (and probe-control beat) is stable and tunable in Hz steps. Fixed VCO drivers cannot do this. | windfreaktech.com ↗ | planned | |
| R02 | RF power amplifier, 5–500 MHz, 29 dB, +33 dBm | 2 pc | Mini-Circuits ZHL-1-2W-S+ (the SMA model of the ZHL-1-2W+) ZHL-1-2W-S+ | Lifts the synthesizer output to the ~+30 dBm an AOM needs for good diffraction efficiency. One per arm. | minicircuits.com ↗ | to procure | |
| R03 | Digital step attenuator, DC–2.4 GHz, 0–31.5 dB (RF level) | 2 pc | Mini-Circuits ZX76-31R5-PN-S+ ZX76-31R5-PN-S+ | Sets the RF level, so the diffraction efficiency, and so each arm’s power, can be adjusted without touching the optics. | minicircuits.com ↗ | to procure | |
| R04 | RF switch, DC–5 GHz, TTL controlled, fast | 2 pc | Mini-Circuits ZASWA-2-50DR+ ZASWA-2-50DR+ | Gates each RF channel in nanoseconds-to-microseconds: slices the probe pulse and switches the control off and on for storage. The attenuator alone is too slow. | minicircuits.com ↗ | to procure | |
| R05 | Linear DC supply +24 V / 3 A for the amplifiers | 1 pc | Rigol DP832A is already bought for the coil: use channel 2/3, or a small bench supply DP832A | The ZHL-1-2W-S+ amplifiers need +24 V. Use a clean linear source to avoid ripple on the RF. The ±5 V and ±3 V rails of the switch and the attenuator come from the DIY bias box (DIY Section, D8). | int.rigol.com ↗ | to procure | |
| R06 | Directional coupler (20 dB) for RF monitoring | 2 pc | Mini-Circuits ZFDC-20-4-S+ (the SMA model of the ZFDC-20-4+, optional) ZFDC-20-4-S+ | Lets you check the RF power and frequency at the AOM on the scope or a spectrum analyzer without breaking the line. | minicircuits.com ↗ | optional | |
| 7 · Detection, timing and measurement electronics | |||||||
| E01 | Dual-channel function / arbitrary waveform generator, burst + sync output | 1 pc | Siglent SDG2042X (40 MHz, 2 ch) SDG2042X | Provides the gate pulses (TTL) for the two RF switches and the sync that triggers the scope. Needed for the pulsed storage sequence. | siglentna.com ↗ | planned | |
| E02 | Digital oscilloscope, 4-channel, ≥ 50 MHz, with probes | 1 pc | Rigol DS1054Z (or Siglent SDS1104X-E) DS1054Z | Records the probe photodiode (CH1) and the lock-box monitor (CH2) while sweeping, triggered by the generator sync. Shows the EIT peak, the error signal and the retrieved pulse. | int.rigol.com ↗ | to procure | |
| E03 | Amplified photodetector, Si, 350–1100 nm, switchable gain | 2 pc | Thorlabs PDA36A2 (probe detector and SAS photodiode) PDA36A2 | Converts the weak probe light (µW) and the SAS signal to volts with adjustable gain and bandwidth. One for the EIT probe, one for the SAS. | Thorlabs search ↗ | to procure | |
| E04 | Low-noise linear ±12 V power supply for the photodiodes | 1 pc | Thorlabs LDS12B (check whether bundled with the PDA36A2) LDS12B | Supply ripple lands directly on the detected probe signal. A linear supply keeps the EIT peak clean. | Thorlabs search ↗ | to procure | |
| E05 | Optical power meter console + Si sensor head | 1 set | Thorlabs PM100D + S120C PM100D + S120C | Measures absolute power at each stage so the split ratios and the control intensity (mW/cm²) are known, not assumed. Also the calibration for the photodiode. | Thorlabs search ↗ | to procure | |
| E06 | Digital multimeter (6½ digit) | 1 pc | Siglent SDM3065X or Keysight 34461A SDM3065X | Checks supply rails, heater and coil currents and cable continuity. | siglentna.com ↗ | to procure | |
| 8 · Cables and adapters | |||||||
| K01 | BNC cable RG58, 1 m | 12 pc | Pomona / any 50 Ω RG58 1 m | Signals: photodiodes → scope/lock box, lock box → laser controller, generator gates and sync. | digikey.com ↗ | to procure | |
| K02 | SMA male–male cable, 50 Ω, 0.5–1 m | 8 pc | Mini-Circuits CBL-1FT-SMSM+ or similar CBL-1FT-SMSM+ | RF chain: synthesizer → switch → attenuator → amplifier → AOM. Low-loss, well-shielded cables avoid pick-up. | minicircuits.com ↗ | to procure | |
| K03 | SMA–BNC adapters, BNC T-pieces, 50 Ω SMA/BNC terminators | 1 kit | Pomona / Mini-Circuits adapter kit adapter kit | Joins the BNC and SMA parts of the chain and terminates unused ports. | digikey.com ↗ | to procure | |
| K04 | Coil and heater leads, twisted pair, cable ties, Velcro | 1 set | Any non-magnetic twisted pair — | Twisting cancels stray field from the solenoid and heater leads. | digikey.com ↗ | to procure | |
| 9 · Optional / shared | |||||||
| X01 | Scanning Fabry–Pérot interferometer with controller | 1 set | Thorlabs SA200-5B + SA201 (≈ 1.5 GHz FSR) SA200-5B | Checks the laser for mode hops and shows the AOM-shifted components; useful for diagnosing the lock. | Thorlabs search ↗ | optional | |
| X02 | Wavemeter (shared instrument) | 1 pc | HighFinesse WS-series or shared WS | Absolute frequency check of the DFB near 795 nm. Borrow rather than buy if possible. | highfinesse.com ↗ | optional | |
| X03 | Spectrum analyzer or RF power meter for the RF chain | 1 pc | Siglent SSA1015X or similar SSA1015X | Verifies the AOM drive frequency, power and spurs. | siglentna.com ↗ | optional | |
Recommended reading
Only two kinds of entry: links the researcher collected, and references printed in the Finkelstein et al. bibliography (copied as printed). Where a link’s title could not be confirmed it is labelled descriptively.
Start here: foundational & tutorial
- Ran Finkelstein, Samir Bali, Ofer Firstenberg, and Irina Novikova. A practical guide to electromagnetically induced transparency in atomic vapor. arXiv:2205.10959v2 (2022)The reference design for Zeeman EIT (Fig. 10). Read §II–V in full.
- S. E. Harris. Electromagnetically induced transparency. Physics Today, 50(7):36, 1997. Paper ref. [1]: short conceptual introduction.
- Michael Fleischhauer, Atac Imamoglu, and Jonathan P. Marangos. Electromagnetically induced transparency: Optics in coherent media. Rev. Mod. Phys., 77:633–673, Jul 2005. Paper ref. [2]: the standard review.
- K.-J. Boller, A. Imamoğlu, and S. E. Harris. Observation of electromagnetically induced transparency. Phys. Rev. Lett., 66:2593–2596, May 1991. Paper ref. [13]: the first observation.
- Petr M. Anisimov, Jonathan P. Dowling, and Barry C. Sanders. Objectively discerning autler-townes splitting from electromagnetically induced transparency. Phys. Rev. Lett., 107:163604, Oct 2011. Paper ref. [29]: EIT vs Autler–Townes.
- Wikipedia: Electromagnetically induced transparencyQuick orientation only.
- physlab.org: “Electromagnetically induced transparency” (PDF)Teaching-lab style document (title from file name).
- AAPT Advanced Labs wiki: file 2370Advanced-lab resource page (content not confirmed).
- RGN Publications (JAMCNP journal), article 323Title not confirmed.
- dokumen.pub: “Photonic Quantum Technologies: Science and Applications” (book, as named in the URL)Third-party copy. Prefer the publisher or your library.
- Video (YouTube) ykWIOBJZ0OE · Video (YouTube) OVIwu10N5lMCollected lecture or demo videos (titles not confirmed).
Rubidium data
- Daniel A. Steck, “Rubidium 87 D Line Data” (PDF, rev. 1.6)Source for the constants table. Check steck.us/alkalidata for the current revision before citing. Paper ref. [95] is “Daniel A. Steck. Alkali d line data. Dec 2010.”
- Scribd copy of rubidium87numbers 1.6Third-party mirror. Prefer steck.us.
- NIST publication 919036 (PDF)Title not confirmed.
- ResearchGate figure: the D1 absorption spectrum of ⁸⁷Rb at 795 nmUseful for recognising your SAS and absorption scans.
- ResearchGate figure: energy-level diagram of ⁸⁷Rb D1 line and CPT spectroscopy
Lasers, locking & vendors
- K. B. MacAdam, A. Steinbach, and C. Wieman. A narrow-band tunable diode laser system with grating feedback, and a saturated absorption spectrometer for cs and rb. American Journal of Physics, 60(12):1098–1111, 1992. Paper ref. [75]: the classic SAS reference.
- Alberto M. Marino and C. R. Stroud. Phase-locked laser system for use in atomic coherence experiments. Review of Scientific Instruments, 79(1):013104, 2008. Paper ref. [78]: the two-laser alternative to Zeeman EIT.
- Guoqing Yang et al., “Laser frequency locking with subnatural linewidth spectroscopy”, JOSA B 37(2), 574–578 (2020)Title and authors confirmed from the Optica page.
- Guochao Wang et al., “In situ probing and stabilizing the power ratio of electro-optic-modulated laser pairs based on VIPA etalon for quantum sensing”, Optics Letters (2022)EOM-sideband diagnostics, i.e. the hyperfine route Zeeman EIT avoids.
- Toptica eagleyard datasheet: EYP-DFB-0795-00080-1500-BFW01-0005 (PDF)
- Agiltron: 795 nm DFB butterfly laser diode, 15 mW
- Innolume: fibre-coupled DFB laser diode at 795 nm, 5 mW
- Sintec Optronics: laser product page 435
- Thorlabs: low-noise turnkey laser systems, 780 or 795 nm · Thorlabs: single-frequency ultra-low-noise lasers, extended butterfly package
EIT in warm vapour: physics & experiments
- Kenneth DeRose, Kefeng Jiang, Jianqiao Li, Linzhao Zhuo, Hong Cai, and S. Bali. Producing slow light in warm alkali vapor using electromagnetically induced transparency, 2020. Paper ref. [38]: the paper points to it for further experimental details of the Fig. 10 setup. Read this next.
- O. Firstenberg, M. Shuker, R. Pugatch, D. R. Fredkin, N. Davidson, and A. Ron. Theory of thermal motion in electromagnetically induced transparency: Effects of diffusion, doppler broadening, and dicke and ramsey narrowing. Phys. Rev. A, 77:043830, Apr 2008. Paper ref. [48].
- M Shuker, Ofer Firstenberg, Rami Pugatch, A Ben-Kish, A Ron, and Nir Davidson. Angular dependence of dicke-narrowed electromagnetically induced transparency resonances. Physical Review A, 76(2):023813, 2007. Paper ref. [53].
- Yanhong Xiao. Spectral line narrowing in electromagnetically induced transparency. Modern Physics Letters B, 23(05):661–680, 2009. Paper ref. [23].
- A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch. Radiation trapping in coherent media. Phys. Rev. Lett., 87:133601, Sep 2001. Paper ref. [96].
- Nathan Belcher, Eugeniy E. Mikhailov, and Irina Novikova. Atomic clocks and coherent population trapping: Experiments for undergraduate laboratories. American Journal of Physics, 77(11):988–998, 2009. Paper ref. [85].
- ResearchGate: “Electromagnetically induced transparency in rubidium” (publication 253348984)
- ResearchGate figure: EIT spectra of room-temperature ⁸⁷Rb atoms
- arXiv:2104.10613Experimental EIT in Rb vapour (from the abstract; title not confirmed).
- arXiv:2401.13350v1Rubidium spectroscopy (from the abstract; title not confirmed).
- arXiv:1409.3598 (PDF)EIT with Laguerre–Gaussian modes (from the abstract; title not confirmed).
- PubMed Central article PMC5562294 · PMC3989522 · PMC13170533Titles could not be retrieved (access check).
- Photonics 11(12):1165 (2024), PDF hosted by Shanxi University IOECitation as given in the file name.
- Shanxi University IOE publication PDF (16.pdf) · Proc. SPIE 8773, 877311 (2013), PDF
- IJAERD paper 1482 (PDF)
Storage & quantum memory
- M Fleischhauer and MD Lukin. Dark-state polaritons in electromagnetically induced transparency. Phys. Rev. Lett., 84(22):5094–5097, MAY 29 2000. Paper ref. [11].
- M. D. Lukin. Colloquium: Trapping and manipulating photon states in atomic ensembles. Rev. Mod. Phys., 75:457, April 2003. Paper ref. [12].
- D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin. Storage of light in atomic vapor. Phys. Rev. Lett., 86(5):783–786, JAN 2001. Paper ref. [43]: warm-vapour storage, the template for Objective 2.
- I. Novikova, R. L. Walsworth, and Y. Xiao. Electromagnetically induced transparency-based slow and stored light in warm atoms. Laser & Photonics Reviews, 6(3):333–353, 2012. Paper ref. [37].
- Alexey V. Gorshkov, Axel André, Michael Fleischhauer, Anders S. Sørensen, and Mikhail D. Lukin. Universal approach to optimal photon storage in atomic media. Phys. Rev. Lett., 98:123601, Mar 2007. Paper ref. [70]: why inefficiency ∝ 1/OD.
- Irina Novikova, Nathaniel B. Phillips, and Alexey V. Gorshkov. Optimal light storage with full pulse-shape control. Phys. Rev. A, 78:021802, Aug 2008. Paper ref. [83].
- Nathaniel B. Phillips, Alexey V. Gorshkov, and Irina Novikova. Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing. Phys. Rev. A, 83:063823, Jun 2011. Paper ref. [73].
- Or Katz and Ofer Firstenberg. Light storage for one second in room-temperature alkali vapor. Nat. Commun., 9(1):2074, dec 2018. Paper ref. [72].
- Lijun Ma, Oliver Slattery, and Xiao Tang. Optical quantum memory based on electromagnetically induced transparency. Journal of Optics, 19(4):043001, feb 2017. Paper ref. [7].
- Ya-Fen Hsiao, Pin-Ju Tsai, Hung-Shiue Chen, Sheng-Xiang Lin, Chih-Chiao Hung, Chih-Hsi Lee, Yi-Hsin Chen, Yong-Fan Chen, Ite A. Yu, and Ying-Cheng Chen. Highly efficient coherent optical memory based on electromagnetically induced transparency. Phys. Rev. Lett., 120:183602, May 2018. Paper ref. [114].
- Ran Finkelstein, Eilon Poem, Ohad Michel, Ohr Lahad, and Ofer Firstenberg. Fast, noise-free memory for photon synchronization at room temperature. Science Advances, 4:1, jan 2018. Paper ref. [115].
- Quantum technology group @Zagreb (Institute of Physics): rubidium-vapour EIT quantum memoriesGroup page on a bilateral project building Rb-vapour quantum memories.
- Quantum master Barcelona: advanced quantum physics laboratory (course page)Teaching-lab page. Specific setup claims about it were not verified.
Theses
- University of Bonn (bonndoc) thesis PDF, handle 20.500.11811/13451
- grahamgreve.com: thesis (PDF)
- LMU München (edoc) dissertation PDF, Zhou_Yiru.pdf
- Open University (ORO) thesis PDF, Final_Thesis_Tim_Leese.pdf
- University of Amsterdam (UvA) thesis PDF
- MIT RLE, Ketterle group: “Streed thesis” (PDF)
- dspace.cus.ac.in: PhD thesis PDF (Physics), file “Indra Hang Subba-Physics-PhD.pdf”The collected link had another file name appended; this is the cleaned link.
Related (other EIT regimes)
- Matthew Cloutman et al., “EIT Spectroscopy of Rydberg Levels Dressed by Linearly Polarized RF fields: Complementary Angular Response for Two Types of Transition Ladders”, arXiv:2503.17997
- Yuanbin Chen et al., “Harnessing Rydberg Atomic Receivers: From Quantum Physics to Wireless Communications”, arXiv:2501.11842
- arXiv:1706.07666v2Cold Rydberg atoms in a hollow-core fibre and Rydberg EIT (from the abstract; title not confirmed).
Questions and answers
The questions asked while the bench was being specified, with short answers and the numbers behind them. Working notes, not a specification: check each figure against the vendor document. A readable copy is in QA.md on GitHub. No prices here.
The laser and its controller
Q1 Is our 795 nm DFB laser the right specification, and is 5–15 mW enough?
Yes on both counts. It is the manufacturer's Rb D1 spectroscopy part, and its 5–15 mW is the right size: about 1 mW of control light at the cell and under 1 µW of probe need only 5–15 mW at the laser fibre. The part is the Toptica Eagleyard EYP-DFB-0795-00015-1500-BFY12-0005 (datasheet revision 0.93, 5 Feb 2025). Nothing in the datasheet rules it out, and a 40 mW laser would be wasted.
| Our need | Datasheet | Fit |
|---|---|---|
| Rb-87 D1 line, 794.978 nm | target 794.98 nm reachable at 10–45 °C chip temperature at 15 mW; 0.06 nm/K | yes |
| About 1 mW at the cell | 5–15 mW out of the fibre; 160 mA typical for 15 mW | yes, about 5× margin |
| Linewidth well below about 100 MHz | 0.6 typical, 1.0 MHz at 15 mW | yes |
| Lock range | mode-hop-free over more than 10 GHz; current tuning about 1.4 GHz/mA | yes |
| Single mode | side-mode suppression 30 dB minimum, 45 typical | yes |
| Clean polarization | 20 dB extinction, PM fibre, FC/APC narrow key | yes |
| Protection | built-in micro-isolator (no figure given) plus our free-space isolator (Thorlabs I795P3D) | yes |
What keeps it from perfect
- Thin current margin: 15 mW needs 160 mA and the absolute maximum is 170 mA. Set the controller limit to 165–170 mA and run near 10–12 mW for lifetime.
- The ITC502 20 kΩ thermistor range reads up to 19.99 kΩ and this thermistor is about 20 kΩ at 10 °C: keep the chip at 15 °C or warmer, or switch to the 200 kΩ range (coarser, 10 Ω steps).
- Toptica Eagleyard lists the part as about to become obsolete (replacement "on request"): consider a spare.
- The datasheet is a preliminary revision (below 1.0), all figures at beginning of life; the individual test protocol that ships with each laser is what counts.
- The label says Class 4 (20 mW, IEC 60825-1).
- Not stated: isolation of the micro-isolator in dB, the fibre type, how the linewidth was measured.
How much power we actually need
| Beam | Intensity in the papers | Power needed at the cell |
|---|---|---|
| Control (1/e² radius 2.55 mm) | 1.3–5.5 mW/cm² | 0.13–0.56 mW if that is the peak intensity, 0.27–1.1 mW if it is power over area (the paper does not say) |
| Probe (radius 0.47 mm) | about 0.12 mW/cm² | under 1 µW |
| SAS lock | the simulator gets 0.09 mW on the photodiode | about 0.2–0.5 mW picked off |
More control power only broadens the line: the EIT width grows by about 4.5 kHz per extra mW/cm². The DeRose experiment ran with about 7 mW out of its fibre.
Where the light goes (10 mW laser): free-space isolator ×0.9 (Thorlabs I795P3D, 90 % transmission), 5 % pick-off to the SAS, about 88 % to the control arm, then the double-pass AOM and optics. With realistic AOMs (about 70 % per pass) the control at the cell is about 3.4 mW, so even a 5 mW laser gives about 1.8 mW. The simulator is pessimistic (35 % per pass): 10 mW gives about 0.8 mW and 15 mW about 1.2 mW, still enough.
So: minimum about 5 mW, comfortable 10–15 mW, not needed 20–40 mW. Measure the double-pass AOM efficiency (the biggest unknown) and the power at the cell with the power meter; turn the control down with the half-wave plate or the AOM RF level if it exceeds about 1 mW.
Specification for any 795 nm DFB we buy (for quotes):
| Item | Requirement | Why |
|---|---|---|
| Type | single-frequency DFB laser diode | narrow, mode-hop free, tuned by current and temperature (no piezo) |
| Wavelength | must reach 794.978 nm (Rb-87 D1, vacuum) at a chip temperature of about 15–35 °C and a current below the maximum | the lock line; outside the TEC/thermistor range it cannot be reached |
| Output power | at least 20 mW from the package (at least 10 mW after a fibre and isolator) | we need 5–15 mW at the bench; margin for AOM and polarization losses |
| Linewidth | ≤ 1 MHz (≤ 2 MHz acceptable) | common to control and probe; the SAS features are 6–12 MHz wide |
| Side-mode suppression | ≥ 30 dB (≥ 40 dB preferred) | single mode on the Rb line |
| Mode-hop-free tuning | ≥ 10 GHz around 794.98 nm | scan across the Rb D1 lines (ground splitting 6.8 GHz) |
| Tuning coefficients | about 0.06 nm/K, 0.003–0.005 nm/mA (state them) | sets the lock-box divider (DIY D6) |
| Operating current / voltage | ≤ 190 mA, ≤ 5 V | ITC502: 0–200 mA, compliance > 6 V |
| Package | 14-pin butterfly, built-in TEC, NTC thermistor, monitor photodiode | ITC502 + butterfly mount (LDM-4980 / LM14S2) |
| TEC | ≤ 1.5 A, ≤ 4 V | ITC502 TEC ±2 A, 16 W |
| Thermistor | 10 kΩ NTC at 25 °C (state B value) | ITC502 20 kΩ range: chip above about 10 °C |
| Pin-out | standard type-1 butterfly (1 TEC+, 2/5 thermistor, 3/4 PD, 10 LD anode, 11 LD cathode, 13 case, 14 TEC−); laser floating from the case | ITC502 wiring (AG or CG) |
| Output (preferred) | PM fibre (PM780, slow axis), FC/APC, about 1 m, built-in isolator ≥ 30 dB | robust pointing, protects the chip |
| Output (accepted) | free-space collimated, about 1 mm beam, with two external isolator stages | the chip must not see the back-reflections |
| Polarization extinction | ≥ 20 dB | clean split at the first PBS |
| Documents | test report of the actual unit: temperature and current at 794.978 nm, P–I curve, spectrum with SMSR, PER; drawing; pin-out | acceptance test on arrival |
| Other | lead time, warranty, laser class, availability of the part (not near obsolescence) |
On arrival check: the test protocol (wavelength against temperature at 15 mW, operating current, extinction ratio), single-mode operation on the spectrum analyser, that the wavelength lands on the Rb D1 line on the SAS signal, and the fibre key alignment.
Sources: Eagleyard datasheet · Steck, Rb-87 D line data
Q2 Is an isolator mandatory, even though most of the bench is free space?
Yes. Free space does not remove the need for an isolator: the returning light comes from the free-space part. Our laser has a micro-isolator inside, and a free-space Faraday isolator right after the collimator (Thorlabs I795P3D, BOM L06) is the second stage. For a laser with no isolator inside, a second stage would be mandatory.
Why a DFB laser needs one
- It reacts to very little returned light. In the classic measurements on a DFB laser (Tkach and Chraplyvy, 1986, summarised in section 2.6 of F. Rogister's thesis) mode hopping began near −70 dB of returned power, and from −45 dB to −10 dB the line broke up (coherence collapse, 100 MHz to 25 GHz wide). Those figures belong to that laser and are only a guide for ours, but the lesson holds: the line stays as narrow as the data sheet says (about 1 MHz) only if almost nothing comes back.
- Our own bench sends light back. Each double-pass AOM arm ends in a cat's-eye mirror that returns the beam exactly along itself. The wave plate and the PBS cube are meant to steer the returning beam out sideways, but no wave plate is perfect: a retardance error of 2° (a plate designed for 780 nm and used at 795 nm is about 1.7° off) or a plate set 1° off its axis lets about 10⁻³ of the returning light (−29 dB) pass the PBS and travel back towards the laser. With the AOM losses and the share of power in the arm, that is about −33 dB at the laser, far inside the coherence-collapse range if nothing blocks it. The 3D simulator uses perfect wave plates, so it shows almost nothing returning and hides this.
- Flat surfaces add more, and alignment makes it worse. An uncoated quartz window returns about 3.4 % per surface (−15 dB), a bare silicon detector about a third of the light, an AR-coated optic about 0.25 %. The collimator and single-mode fibre accept only light coming back within about 0.3 mrad (0.02°) of the beam, so a surface has to be square to the beam within about 0.01° to count. That is rare by accident, but it is exactly what happens when a beam is aligned by watching its back-reflection, or when a mirror or card is left square to the beam.
| What protects the laser chip | Returned light at the chip (about −33 dB with nothing in front) | Against the −70 dB and −45 dB marks |
|---|---|---|
| nothing | −33 dB | inside coherence collapse |
| the micro-isolator inside the Eagleyard alone (one stage, typically about 30 dB; its data sheet gives no figure) | about −63 dB | in the mode-hopping band |
| the Thorlabs I795P3D alone (at least 34 dB at 795 nm) | about −67 dB or better | at the edge of the mode-hopping band |
| both, as in our design | about −97 dB or better | far below |
These are estimates (about ±10 dB), not measurements. They show the order of magnitude and why either stage alone is marginal.
What we do
- Put the I795P3D right after the FC/APC collimator. Thorlabs lists it as a fixed narrowband isolator centred at 795 nm (operating range 775–815 nm), isolation at least 34 dB and transmission 90 % at the centre wavelength, beams up to Ø2.7 mm (our ~1.5 mm beam fits), 0.7 W maximum. Set its input polarizer along the slow axis of the laser fibre, turn it for the highest forward power, and dump both rejected-beam ports.
- Keep the short gap between the collimator and the isolator clear: nothing in between. The angled FC/APC fibre end and the AR-coated collimator return very little themselves.
- Check the replacement of the laser. The vendor lists the Eagleyard part in our list as about to become obsolete. If its replacement has no isolator inside, the I795P3D alone gives only about −67 dB: then add a second stage (a second isolator in series, or a dual-stage isolator).
- Habits that cost nothing: tilt the cell and the detector by a degree or two, dump every unused port, set each double-pass wave plate for the least light in its leak port (not by the scale on the mount), and never leave a mirror or card square to the beam while the laser is on.
Verdict: keep both the micro-isolator inside the laser and the free-space I795P3D. One free-space stage is enough while the laser has its own isolator. A feedback fault shows up as a lock that drifts or a line that is wider than the data sheet says, which is slow to trace afterwards, so the isolator goes in before the first alignment.
Sources: Rogister, Nonlinear dynamics of semiconductor lasers subject to optical feedback (thesis, section 2.6) · Eagleyard data sheet EYP-DFB-0795-00015-1500-BFY12-0005 (micro-isolator inside, no isolation figure given) · Thorlabs I795P3D and Thorlabs NIR free-space isolators (specification table)
Q3 Is the Yanban RB-795-DFB-BFW DFB laser (Alibaba listing) suitable for our bench, and can our ITC502 drive it?
Yes as a laser, on paper, but not in the version listed. The listed RB-795-DFB-BFW is a free-space butterfly with no isolator inside, so we have asked the vendor for a PM-fibre-pigtailed version with a built-in isolator. Until the answer arrives, the Eagleyard BFY12 stays in our plan. Use the laser switch at the bottom left of the guide, Equipment, 3D Bench and DIY pages to see them with this laser instead (equipment rows L01, L03, L05, L06, the source card and first build steps, the simulator texts, the D6 divider and the D10 dumps). The figures below are from the vendor's data sheet (sent to us, not online) and the Alibaba listing.
| Our need | RB-795-DFB-BFW data sheet | Fit |
|---|---|---|
| Rb D1 line, 794.978 nm | target 794.97 nm (794–796 nm), 0.06 nm/°C and 0.004 nm/mA; "guaranteed to hit the Rb D1 line" | yes |
| 5–15 mW usable | 100 mW minimum, 120 mW typical | yes, about 10× margin: turn it down with a half-wave plate and a PBS, or run at a lower current |
| Narrow line | 200 kHz typical, 500 kHz maximum (over 100 µs, with a very low-noise driver) | yes, narrower than the BFY12 (about 1 MHz) |
| Single mode | side-mode suppression 40 dB minimum, 45 dB typical; mode-hop free over 20 GHz | yes |
| Polarization | 20 dB extinction | yes, the first PBS cleans it up |
| Laser current on the ITC502 (0–200 mA, compliance above 6 V) | 150 mA typical, 175 mA maximum, 2.0 V | yes: set the current limit at 175 mA or below |
| TEC on the ITC502 (±2 A, 16 W) | 0.4 A, 1.3 V at 120 mW | yes |
| Thermistor on the ITC502 (reads up to 19.99 kΩ) | 10 kΩ at 25 °C, B = 3950 K, so about 20 kΩ at 10 °C | yes: keep the chip above about 11 °C |
| Pin-out | 1 TEC+, 2 and 5 thermistor, 3 and 4 photodiode, 10 and 11 laser anode and cathode, 13 ground, 14 TEC−; the laser floats | looks like the usual 14-pin butterfly layout: check it against the LDM-4980 pin table before connecting |
| Isolator inside | none listed; the safety notes say "Do not retro-reflect beam! This can cause Catastrophic Optical Damage" | no |
What to watch
- Isolation. With about −33 dB of light returning from the bench (see the isolator answer), one Thorlabs I795P3D (at least 34 dB) leaves about −67 dB at the chip, at the edge of the mode-hopping band, and at 100 mW a strong return can damage the chip. A free-space version would need two stages: two I795P3D in series (about −100 dB) or one Thorlabs IOT-5-780-VLP tandem isolator (55 dB minimum, tunable 760–800 nm, 4.7 mm aperture; about −88 dB). A built-in isolator in a fibre version removes most of this worry.
- Free-space beam. About 1.0 × 0.8 mm, divergence 0.1° (about 1.7 mrad; the data sheet does not say whether this is the full or half angle). Over a 1.5 m path the beam grows by about 2.5 mm, so the telescopes we already plan for the arms set the beam sizes. The window centre is about 5.1–5.45 mm above the package base; the mount must leave that end open and be raised to the 100 mm beam height.
- The 200 kHz needs a very low-noise driver. With 0.004 nm/mA (about 1.9 GHz/mA) and the ITC502 current noise of 1.5 µA rms, we estimate MHz-level broadening with our controller. That is acceptable: the control and the probe come from the same laser, so most of it cancels in the two-photon detuning, and the SAS lock needs only MHz.
- Safety. 100–140 mW is Class 3B (the label also shows a 0.2 W Class IV sticker): goggles rated for 795 nm, rated beam dumps, and the ITC502 interlock.
- Data-sheet quality. The mode-hop range is printed in "Pm" (the comment says 20 GHz), and the two wavelength plots do not state their test conditions (about 795.3 nm at 25 °C in one, 794.92 nm at 135 mA in the other). Both suggest the D1 line is reached near 18–25 °C, but only the test report of the actual unit counts.
What we asked the vendor
- A PM-fibre-pigtailed version (PM780 fibre, slow axis aligned, FC/APC) with a built-in isolator, its isolation in dB and the power after the fibre and isolator.
- The test report of the actual unit: temperature and current at 794.978 nm, power, side-mode suppression, polarization extinction.
- How the linewidth is measured, whether the divergence is a full or half angle, warranty and lead time.
What it would change
- PM-fibre version with built-in isolator: it drops into our design in place of the BFY12 (BOM L01). The FC/APC collimator (L05) and the free-space I795P3D (L06) stay as they are, and the two isolators together give about −95 dB or better.
- Free-space version only: L01 becomes the RB-795-DFB-BFW, the fibre collimator L05 is dropped, L06 becomes two I795P3D or one IOT-5-780-VLP, and the butterfly mount is checked for a free-space output.
- Either way the obsolescence problem of the BFY12 goes away.
Free space or a PM-fibre version? Both work. If the data sheet is right, the laser itself meets every need of our bench; the choice is about protection and robustness:
| Free-space RB-795-DFB-BFW (as listed) | PM-fibre version with a built-in isolator (custom, asked) | |
|---|---|---|
| Isolation | none inside: two stages outside (two I795P3D in series, or one IOT-5-780-VLP tandem) | the built-in stage plus our I795P3D after the collimator |
| Beam | about 1.0 × 0.8 mm collimated, straight into the isolator; the fibre collimator (L05) is not needed | round, from our FC/APC collimator (L05); fibre coupling costs part of the 100 mW, still far more than the 5–15 mW we need |
| Pointing | the laser sits on the bench: mount it rigidly on a heat sink, because its pointing drift reaches the SAS and the AOMs (Bragg acceptance about 0.5 mrad) | decoupled by the fibre: the laser can sit off the board, and a replacement does not need realignment |
| Polarization | 20 dB from the chip | 20 dB or what the vendor guarantees after the fibre |
| Mount | butterfly mount that leaves the window end open, raised so the beam is at 100 mm | any 14-pin butterfly mount (fibre exit) |
| Safety | 100 mW open beam right at the package | the beam first appears after the collimator |
Our view: if the vendor offers the PM-fibre version with an isolator inside at a similar price and lead time, take it (more robust, less alignment, the internal isolator protects the chip). If only the free-space version is possible, it is manageable: two isolator stages, a rigid heat-sinked mount, and the same alignment as any free-space diode laser.
Is a free-space DFB normal in published work? Yes: it is how our reference design does it. In the guide we follow (Finkelstein, Bali, Firstenberg and Novikova, New J. Phys. 25, 035001 (2023), Sec. V.1 and Fig. 10), the laser is a free-space diode laser (an ECDL in their figure; they state that DFB lasers with 1–2 MHz linewidth also satisfy all the requirements and are widely used in EIT experiments). Its beam goes through a free-space optical isolator and is then coupled by the experimenters into a polarization-maintaining fibre, only to clean the beam profile and polarization; the fibre output is then split at a PBS. A free-space Yanban can follow exactly this route: isolator stages straight after the package, then (optionally) a FiberPort coupler into a PM patch cord, and from there the bench is the same as with a pigtailed laser. The lab already owns FiberPort couplers (PAF2-5B, PAF-X-18-B in the Lab Inventory). Another example: Mottola, Buser and Treutlein (arXiv:2307.08545) use a commercial 795 nm DFB as the D1 probe in a Rb vapour experiment.
Since we cannot fully check the data sheet: ask for the test report of the actual unit, and test it on arrival before anything else: threshold and power against current (power meter), the four Rb D1 absorption dips and the saturated-absorption features in the reference cell while scanning the current (this proves it reaches the line and stays single-mode across the scan), and the polarization extinction with a polarizer. A laser that shows the SAS features cleanly at a chip temperature inside the 20 kΩ thermistor range is fit for our bench.
Can our Thorlabs ITC502 drive it? Yes. Every figure of the laser is inside the ITC502 ranges (ITC500 operation manual, technical data 1.5.1):
| The laser needs | ITC502 gives | Fit |
|---|---|---|
| 150 mA typical, 175 mA maximum | 0 to ±200 mA; hardware limit ILD LIM 0 to ≥ 200 mA | yes: set ILD LIM at about 170 mA before the first switch-on |
| 2.0 V | compliance above 6 V | yes |
| Monitor photodiode 5 µA/mW (about 0.5 mA at 100 mW) | monitor current range 5 µA to 2 mA | yes (only needed for constant-power mode; the lock uses constant current) |
| TEC 0.4 A, 1.3 V at 120 mW | ±2 A, 16 W, compliance above 8 V | yes: start with I TEC LIM at about 0.5 A, because the data sheet gives no TEC maximum |
| NTC 10 kΩ at 25 °C, B = 3950 K | thermistor ranges 10 Ω–19.99 kΩ (100 µA) and 100 Ω–199.9 kΩ (10 µA) | yes: the 20 kΩ range works down to about 10 °C (20.2 kΩ); the D1 line is expected near 18–25 °C |
| Current tuning for the lock (0.004 nm/mA, about 1.9 GHz/mA) | modulation input 20 mA/V, DC to 500 kHz | yes; see the divider note below |
Wiring (ITC502 9-pin laser jack from the manual, section 1.9.1; the laser floats, so either polarity works):
- Polarity CG: ITC pin 8 → laser anode (butterfly pin 10), ITC pin 3 → laser cathode (pin 11); voltage sense pin 9 to pin 10 and pin 6 to pin 11. (With AG instead: pin 7 → cathode, pin 3 → anode.)
- Monitor diode: ITC pin 4 (input) and pin 2 (ground) to butterfly pins 3 and 4, in the polarity the manual's monitor-diode section asks for.
- Interlock: pins 1 and 5. TEC jack (15-pin): TEC+ (pins 5, 6, 7) → butterfly pin 1, TEC− (pins 13, 14, 15) → pin 14, thermistor (pins 3, 4) → pins 2 and 5. Case ground (pin 13) to the shield and ITC ground.
- In practice the butterfly sits in a mount (the lab's ILX LDM-4980 or a Thorlabs LM14S2), and the cables go to the mount: check the mount's pin table against these before switching on, and run the dummy-load test of DIY part D3 first.
Lock-box divider (DIY part D6). The divider was sized for the BFY12 (about 1.4 GHz/mA): 91 kΩ over 1 kΩ gives about 0.28 GHz per volt and a 0.55 GHz swing. With this laser (about 1.9 GHz/mA) the same 91 kΩ gives a 0.75 GHz swing, which still works; about 120 kΩ restores the same scale.
The 200 kHz line needs a very low-noise driver: the ITC502 current noise (1.5 µA rms, 10 Hz–10 MHz) times 1.9 GHz/mA is about 3 MHz of frequency noise, so expect a MHz-level line with our controller. That is acceptable for Zeeman EIT (common to control and probe) and for the SAS lock.
Sources: RB-795-DFB-BFW data sheet (Yanban Laser, from the vendor) · Alibaba listing · Thorlabs NIR free-space isolators (I795P3D, IOT-5-780-VLP) · Thorlabs ITC500 operation manual (ITC502 technical data and laser-jack pin assignment)
Q4 How do we make the free-space Yanban beam equal to a PM-fibre-pigtailed laser (profile, polarization, pointing)?
Couple it into a polarization-maintaining single-mode fibre ourselves. A PM-pigtailed laser is the same chip with an isolator, a lens and a PM fibre built into the package. The fibre is what makes its output a clean round Gaussian with a fixed polarization axis and a fixed pointing, so the only way to get exactly that output from a free-space laser is to put the same fibre in the path. This is also what our reference design does: Finkelstein et al. (New J. Phys. 25, 035001 (2023), Sec. V.1 and Fig. 10) send their free-space laser through an isolator and then into a PM fibre, to clean the beam profile and the polarization. Free-space optics alone (lenses, prisms, a pinhole) only come close.
Our setup: through the PM fibre (decided 19 Oct 2026). The equipment list (Yanban option) now has the fibre link (row L05) to buy; its two steering mirrors and mounts are counted in the mirror rows O01 and O02 (13 = 11 on the bench + 2). Was the fibre strictly needed? No. The free-space beam could go straight from the two isolators into the bench (half-wave plate, PBS, AOM arms). The laser already gives a single-frequency, nearly round 1.0 × 0.8 mm beam (a good size for the AOMs) with 20 dB polarization, and the first PBS cleans the polarization. What the direct beam does not give:
- Pointing decoupling: drift of the laser mount or the isolators (temperature, screws settling) moves the beam on the AOMs (Bragg acceptance about 0.5 mrad), the SAS and the cell; a laser swap means realigning the bench. With the fibre, such drift changes only the coupled power.
- A guaranteed clean mode: the data sheet gives no beam-quality figure (M²); the fibre passes only its own Gaussian mode.
We chose the fibre for exactly these reasons: a guaranteed clean Ø1 mm beam at the AOMs (the direct beam would need a reducing telescope), and a bench that stays aligned whatever happens on the laser side.
Direct or through the fibre: which is better?
| Direct into the bench | Through the PM fibre | |
|---|---|---|
| Parts after the isolators | none extra | half-wave plate, 2 steering mirrors, coupler, patch cable, output collimator |
| Alignment work | the laser-to-bench alignment once | the same plus fibre coupling and the polarization launch (a few hours, a practised skill) |
| Power at the bench | about 80 mW (two isolators at 90 %) | tens of mW (coupling losses), still far more than the 5–15 mW needed |
| Beam profile | whatever the chip gives (no M² on the data sheet) | a clean round Gaussian, guaranteed by the fibre |
| Beam 1 m after the source (at the AOMs) | Ø2.3 mm if the data-sheet 0.1° is the full angle, Ø4.4 mm if it is the half angle: larger than the 2 mm AOM aperture, so a lens or a reducing telescope is needed before the AOMs (the data sheet implies M² ≈ 1.7 or 3.4) | Ø1.5 mm from a Ø1 mm FiberPort output (1.087 mrad) |
| Polarization | 20 dB from the chip, cleaned by the first PBS | set by the fibre axis; can wander a little with temperature if the launch is off |
| Pointing on the AOMs, SAS, cell | follows any drift of the laser mount and isolators | fixed by the output collimator; laser-side drift only changes the power |
| Laser swap or repair | realign the bench | realign only the coupling |
| Extra maintenance | none | an occasional touch-up of the coupler |
See both in 3D: the laser-source simulation shows the two layouts at the 100 mm beam height with the alignment steps, the data-sheet values, and the power, isolation and beam-size budgets.
For EIT itself the two give the same result: the experiment needs a stable single-frequency beam of a few mW in a known polarization, and the PBS and the cell do not care about a slightly non-ideal profile. The fibre buys long-term stability and an ideal beam at the price of one more alignment stage. We chose the fibre (19 Oct 2026); the direct beam remains the fallback if the fibre coupling ever becomes a problem.
The sequence, from the chip to the bench
| # | Part | Why there | Our part |
|---|---|---|---|
| 1 | Butterfly laser in a metal, heat-sinked mount, driven by the ITC502 | the chip's TEC pumps its heat into the mount; current limit 170 mA | lab ILX LDM-4980 (check its pin table first) |
| 2 | No extra lens | the data sheet gives a collimated beam of about 1.0 × 0.8 mm (check it on arrival: same size at 0.2 m and 2 m) | none |
| 3 | Isolator, stage 1, right at the laser window | no isolator inside the laser; nothing reflective may come before it | Thorlabs I795P3D (≥ 34 dB) |
| 4 | Isolator, stage 2 | one stage leaves about −67 dB at the chip; two give about −100 dB | a second I795P3D, or one IOT-5-780-VLP tandem (55 dB) |
| 5 | Half-wave plate | the isolator output is linear at 45° to its input; this plate turns it onto the slow axis of the fibre | ؽ″ zero-order HWP in a rotation mount |
| 6 | Two steering mirrors | the two degrees of freedom of beam walking into the coupler | mirrors in kinematic mounts |
| 7 | Fibre coupler (input) | focuses the beam onto the fibre core; its tip, tilt and focus are adjustable | lab Thorlabs PAF2-5B FiberPort (f 4.6 mm, made for a Ø1 mm beam with a 5 µm mode, so it matches our 1.0 × 0.8 mm beam) |
| 8 | PM single-mode fibre | the mode and polarization filter: everything after it behaves like a pigtail | PM780 patch cable, FC/APC both ends (for example Thorlabs P5-780PM-FC-2) |
| 9 | Output collimator | the bench beam starts here, at 100 mm, exactly as with a pigtailed laser | a second FiberPort (about Ø1 mm beam, good for the AOMs) or the planned FC/APC collimator |
After step 9 the bench is the one already designed (wave plate, PBS, AOM arms, cell); the isolation now sits before the fibre, so returns from the bench travel back through the fibre and are stopped by stages 1 and 2.
Alignment, in order 1. Laser on, low power: set the ITC502 current limit and the TEC first; check that the laser reaches the Rb line (absorption and saturated-absorption features in the reference cell while scanning the current). 2. Isolators: turn each isolator about the beam until the transmitted power is maximum (its input polarizer is then along the laser polarization); keep the beam centred in the aperture. 3. Wave plate: set roughly at first; it is fixed in step 5. 4. Fibre coupling: with both mirrors, walk the beam into the coupler while reading the power at the fibre output with the power meter (first mirror for position, second for angle, alternately), then optimise the focus of the coupler, and repeat. Expect a good part of the power to be coupled when the modes match; measure it rather than assume it. 5. Polarization: put a polarizer and the power meter after the output collimator. Turn the half-wave plate for the deepest minimum (the input is then on a fibre axis). Then warm or gently bend the fibre: if the output power through the polarizer changes, the input is not on the axis yet; turn the plate until warming and bending change nothing. That is the standard way to launch into a PM fibre. 6. Lock it down: tighten the locking screws of the mounts and the coupler, write down the coupled power, and check it again the next day.
Power: 100 mW from the laser, about 90 % through each isolator stage, then the fibre coupling: tens of milliwatts at the output, still far more than the 5–15 mW we need. Run the laser at a lower current or turn the power down after the fibre.
The fixed mount: metal, not PETG.
- Heat: the butterfly's TEC pushes the chip's heat into its base; a PETG base insulates (several times worse than aluminium), so the TEC cannot hold the temperature, and PETG softens not far above 60 °C.
- Stability: coupling into a 5 µm fibre core needs micrometre stability. PETG creeps under screw load and expands several times more than aluminium with temperature, so the coupling would drift.
- What works: a flat aluminium base plate (a casting is fine if its mounting faces are machined flat), the laser mount and the optics on short, low posts, locking screws on every mount, and a cover against air currents. PETG is fine for that cover.
- What the fibre does for stability: it does not remove all alignment (the free-space coupling can drift slowly and need a touch-up of the coupler), but it fixes everything after it: a touch-up changes only the coupled power, never the beam position on the bench.
Sources: Finkelstein et al., New J. Phys. 25, 035001 (2023), Sec. V.1, Fig. 10 · Yanban RB-795-DFB-BFW data sheet (from the vendor) · Thorlabs PAF2-5B FiberPort and I795P3D specifications · Thorlabs PM780-HP fibre (MFD 5.3 µm at 850 nm)
Q5 DFB or ECDL? Why not an ECDL, why do the reference papers use one, and is a narrow linewidth crucial?
A DFB is good enough for this experiment and much cheaper and simpler. An ECDL would be a luxury, not a requirement. The reason is that the laser's own linewidth is not what sets the EIT line.
Two linewidths that get mixed up
- The EIT linewidth is the narrow one (7.3 kHz at 1.3 mW/cm², 26 kHz at 5.5 mW/cm²). It is set by control intensity, magnetic field, buffer-gas diffusion and coherence time, not by the laser.
- The laser linewidth only has to be well below the optical width of the atoms (Doppler about 500 MHz, wider with buffer gas). Our 0.6–1 MHz is 100× below.
What matters more (my reasoning)
- Relative phase of control and probe. Both come from the same laser through phase-locked RF, so the laser's phase noise is common to both and cancels. A 1 m path difference (about 3 ns) at 1 MHz linewidth gives a relative phase variance of only about 0.02 rad² (0.14 rad rms), so about 98 % of the two-photon drive stays narrow (calculator 4 of the distance calculator). What reaches the atoms is noise from the RF source and drift in the arm lengths.
- Lock stability. The laser must stay within a fraction of the optical width; the DeRose paper reports drift of about 10 MHz per hour and negligible drift during data taking.
DFB against ECDL
| DFB (our choice) | ECDL | |
|---|---|---|
| Linewidth | 0.6–1 MHz | a few hundred kHz |
| Tuning | mode-hop-free over more than 10 GHz by current and temperature | wide, but piezo and grating alignment |
| Build | one sealed, fibre-pigtailed butterfly with isolator | open cavity, more sensitive to vibration, mode hops |
| Lock actuator | laser current (fast and simple) | piezo plus current feed-forward |
| Cost | the lower one | typically several times more |
Why a DFB is enough
- The papers only ask for a linewidth far below the Doppler width (about 500 MHz), and 1 MHz passes easily.
- The 10 Torr Ne buffer gas makes the optical line wider still (order 100 MHz).
- The narrow 7–26 kHz EIT line depends on the control–probe phase relation, not on the laser's own linewidth; both beams share the laser's noise (my reasoning, not quoted from a paper).
- We need only about 1 mW at the cell.
- A narrower laser helps only with a very noisy driver or sub-Doppler spectroscopy at the few-MHz level; the SAS features are 6–12 MHz wide (the D1 natural width is 5.75 MHz), which a 1–2 MHz laser resolves.
Why the reference papers use ECDLs. No sentence in either paper says why, so this is partly inference. What they do say: ECDLs have a linewidth of a few hundred kHz, DFBs about 1–2 MHz, and either is fine for EIT. Likely reasons (my judgment):
- Installed base: atomic-physics labs have used ECDLs for decades and these groups already own several.
- Reuse: an ECDL covers other wavelengths and atoms and scans over several GHz.
- Narrower line: more margin for sub-Doppler spectroscopy, not needed for EIT.
- Wavelength availability: DFB diodes exactly on the Rb D1 line used to be less common.
- Teaching setup: the DeRose paper is an undergraduate set-up where students scan the laser by hand.
None applies strongly to us: one fixed target line, no existing ECDL, and a budget. For a real answer, ask the authors.
When an ECDL would be better: driver current noise turning into linewidth (1 µA is about 1.4 MHz), scanning several GHz or other lines, a replacement if the DFB is no longer available, or an ECDL already in the building.
Q6 What specification do the AOMs and their RF driver need (for a quote)?
Two identical 80 MHz TeO₂ AOMs for 795 nm (one per arm, each in double pass), driven by one two-channel RF source with a common clock, an amplifier, an attenuator and a fast switch per channel. Two are enough: the 160 MHz lock offset is handled without a third AOM (see the end). Our planned parts are BOM O17 (Gooch & Housego 3080-125) and R01–R06; the table is what any alternative must meet.
AOM (2 pieces)
| Item | Requirement | Why |
|---|---|---|
| Wavelength | 795 nm, AR coated (≤ 0.5 % per surface) | Rb D1 line; each surface reflection is lost light and feedback |
| Material, frequency | TeO₂ longitudinal mode, 80 MHz centre, bandwidth ±10 MHz or more | we tune only about ±1 MHz around 80 MHz |
| Aperture | ≥ 1.5 mm (2 mm preferred) | our beam is 1.0–1.5 mm |
| Diffraction efficiency | ≥ 80 % single pass at 795 nm (ask for the figure at our beam size) | double pass squares it: 80 % gives 64 % |
| Rise time | ≤ 200 ns for a 1 mm beam | about 0.64 × D / v = 150 ns per mm in TeO₂ (v ≈ 4.2 mm/µs); storage pulses are microseconds |
| RF power | ask the figure at 795 nm; expect about 1.5–2 W; maximum input ≥ 2 W | the power for full efficiency grows as λ²: 1 W at 633 nm becomes about 1.6 W at 795 nm |
| Extinction (on/off) | ≥ 1000:1 | the control light must be off during storage |
| Separation angle | about 15 mrad (0.87°) at 80 MHz | λ·f/v; sets the cat's-eye and iris geometry |
| RF input | 50 Ω, SMA, VSWR ≤ 1.5:1; ask whether DC is blocked | matches the amplifiers; DC on the line is an open item |
| Mechanics | flat base, tapped holes, drawing; conduction cooling | mounted on the DIY D9 platform at 100 mm beam height |
RF driver (2 phase-locked channels)
| Item | Requirement | Why |
|---|---|---|
| Channels | 2 from one reference clock (10 MHz in/out) | the control–probe difference (35 kHz in RF, 70 kHz in light) must not drift; separate fixed drivers cannot do this |
| Frequency | 70–90 MHz, resolution ≤ 1 Hz | working points 80.000 and 79.965 MHz; the EIT line is a few to tens of kHz wide |
| Power | 0 to +33 dBm (2 W) per channel into 50 Ω, ≥ 30 dB adjustment | sets each arm's power without touching the optics |
| Gating | TTL per channel, rise/fall ≤ 50 ns, on/off isolation ≥ 60 dB | slices the probe pulse and turns the control off for storage |
| Amplitude modulation | optional analog input, ≥ 1 MHz | pulse shaping for better storage efficiency |
| Purity, protection | spurs ≤ −50 dBc, harmonics ≤ −20 dBc; survives an open or shorted output | clean sidebands; an unplugged AOM must not kill the amplifier |
Our planned build meets this from separate parts: Windfreak SynthHD (two channels, one clock), two Mini-Circuits ZHL-1-2W-S+ amplifiers (+33 dBm), ZX76-31R5-PN-S+ attenuators, ZASWA-2-50DR+ switches and ZFDC-20-4-S+ couplers. An integrated driver from an AOM maker is fine only if both channels share one clock.
The 160 MHz lock offset without a third AOM. Both EIT arms are shifted by 160 MHz (double pass at 80 MHz) and the SAS light is not, and no SAS feature of the F = 2 line lies 160 MHz from F = 2 → F′ = 1 (the nearest, the F′ = 1/F′ = 2 crossover, is 407 MHz away). Two free solutions:
- Lock on F = 2 → F′ = 1 and run the EIT beams 160 MHz off the one-photon resonance (recommended). EIT in Zeeman Λ depends on the two-photon detuning (the kHz difference of the two AOMs), not on the one-photon detuning, and in a warm cell the Doppler profile is wide: about 530 MHz FWHM at 60 °C (σ ≈ 225 MHz). At 160 MHz off the line centre the absorption is about 78 % of the peak, so the cell needs about 3 °C more for the same optical depth (the Rb density rises about 8 % per °C near 60 °C). Use the −1 order in both AOMs (−160 MHz): F′ = 2 is then 974 MHz away instead of 654 MHz, so its contribution becomes negligible. Expect a slightly asymmetric EIT line at this detuning in a buffer-gas cell; contrast and width are still measured the same way.
- Take the SAS light from the control arm after its AOM (a small pick-off after the double pass), so the lock sees the shifted light and the control sits exactly on the line. The catch: when the control is switched off for storage, the lock light disappears too, so the lock box must hold its output during the off time (microseconds, much shorter than the lock response).
A third AOM in the SAS arm would also work, but it is not needed and is not in the budget.
Status and decision path (16 Oct 2026). An AOM supplier can make the AOM to this specification; the RF driver is the open item. Before confirming the AOM, get in writing: RF connector (SMB or SMA), maximum RF input power, diffraction efficiency at 795 nm and the RF power for it, AR coating covering 795 nm, input polarization, and a drawing. For the driver, three routes are compared:
- A, our planned build from parts: two-channel synthesizer (SynthHD), per channel an RF switch, a step attenuator, a 2 W amplifier and a monitor coupler, plus the DIY D8 bias box.
- B, a two-channel box from the AOM supplier built to our block diagram (two tunable channels from one clock, fast TTL gates, analog amplitude inputs, monitor ports, about 1 W per channel, 2 W maximum, a frequency sweep on the probe channel).
- C, a budget fallback: a four-channel DDS board based on the Analog Devices AD9959 (all channels from one clock, sub-hertz steps) in place of the synthesizer, with the same RF parts, a low-pass filter per channel, and our own control software.
B is taken if it meets the specification and costs less than A; C only if the budget forces it. Whatever the route, a fixed-frequency driver (its own oscillator per channel) is never accepted: the 35 kHz difference must come from one clock and stay tunable.
Reading an AOM data sheet or listing: check these, in this order. 1. Wavelength and AR coating. It must cover 795 nm (for example 780–850 nm, or 700–1100 nm). A 633 nm, 532 nm or 1064 nm part is the wrong coating. 2. Centre frequency. 80 MHz is what our RF chain and frequencies are built around. A 110 MHz part also works, but then both AOMs must be 110 MHz and the beams sit 220 MHz off the line instead of 160 MHz. 3. Material and mode. TeO₂ longitudinal mode. Avoid shear-mode TeO₂ (slow acoustic wave, about 0.6 mm/µs, so switching is several times slower and the angles are large) and quartz or fused-silica parts (much more RF power). 4. Active aperture. At least 1.5 mm; a 1 mm aperture clips our beam. 5. Diffraction efficiency at our wavelength. At least 80 %. Many listings quote it at 633 or 1064 nm only: ask for the figure near 795 nm. 6. RF power for that efficiency. It must be reachable with our amplifiers (up to about 2 W): about 1–2 W at 795 nm is right; a part that needs 3–4 W is not. 7. Rise time. Usually given per mm of beam: about 150 ns per mm (TeO₂ longitudinal). Under 200 ns for a 1 mm beam. 8. RF input. 50 Ω, SMA, VSWR at most 1.5:1, maximum RF power at least 2 W. 9. Size and mounting. A drawing with the housing, the hole pattern and the height of the aperture above the base. 10. The driver. Buy the AOM alone, or with a driver that accepts an external RF input. A fixed-frequency driver (its own oscillator) cannot be phase-locked to the other arm, so it is no use for the control and the probe.
Our planned part, the Gooch & Housego AOMO 3080-125, against this list (G&H outline drawing 97-01598-01, rev D):
| Check | 3080-125 drawing | Verdict |
|---|---|---|
| Material, mode | TeO₂, 4.2 mm/µs (longitudinal) | yes |
| Centre frequency, bandwidth | 80 MHz, 25 MHz | yes |
| Active aperture | 2.5 mm × 2 mm | yes, takes our 1–1.5 mm beam |
| Contrast ratio | 1000:1 minimum | yes |
| Rise time | 23 / 34 / 65 ns for 125 / 200 / 400 µm beams (about 160 ns per mm) | yes, about 160–240 ns for 1–1.5 mm |
| Saturation RF power | 0.65 W at 515 nm, 1.0 W at 633 nm, so about 1.6 W at 795 nm (λ² scaling, an estimate) | yes, inside our 2 W amplifiers; at our typical 1.05 W about 90 % of the peak efficiency |
| Wavelength, AR coating | 442–633 nm on this drawing, reflectivity ≤ 1 % per surface there; the web listing gives 450–850 nm | check: ask G&H for the unit to be coated for 795 nm and for the efficiency at 795 nm |
| Polarization | 90° to the mounting plane (vertical) | set each arm's polarization with a half-wave plate before the AOM, or mount the AOM on its side |
| RF input | SMB snap-on jack | an SMB-to-SMA cable to our SMA amplifiers (one per AOM) |
| Housing | 2.00 × 1.00 × 0.53 in, holes on the base | fits the D9 platform; measure the unit before drilling |
So it works for our bench, provided the coating covers 795 nm. With the visible coating it still diffracts, but each surface may reflect a few percent at 795 nm: more loss, and more light back towards the isolator.
Driver: no G&H driver needed. The "driver" of our bench is the planned RF chain: the two-channel Windfreak SynthHD (one clock for both arms), then per arm a ZASWA-2-50DR+ switch, a ZX76-31R5-PN-S+ attenuator and a ZHL-1-2W-S+ amplifier (about +30 dBm, up to 2 W), with a ZFDC-20-4-S+ coupler to monitor (BOM R01–R06). A G&H fixed-frequency driver has its own oscillator and cannot be phase-locked to the other arm, so it is not suitable for the control and probe pair.
Has the RF chain (BOM R01–R06) been checked against our AOMs? Yes, part by part; one number was corrected on 14 Oct 2026.
| Part | What its data sheet says | With our AOMs |
|---|---|---|
| Windfreak SynthHD (R01) | two channels, 54 MHz–13.6 GHz, about −50 to +20 dBm, 0.1 Hz steps, phase between the channels settable (one reference) | 80.000 and 79.965 MHz from one clock: the 35 kHz difference cannot drift |
| ZASWA-2-50DR+ switch (R04) | DC–5 GHz, TTL, ±5 V, insertion loss 1.3 dB typ | gates each arm for the storage pulses |
| ZX76-31R5-PN-S+ attenuator (R03) | DC–2.4 GHz, 0–31.5 dB in 0.5 dB steps, +3 / −3 V | sets each arm's power; 31.5 dB at every power-up |
| ZHL-1-2W-S+ amplifier (R02) | 5–500 MHz, gain 29 dB min / 32 dB typ, +33 dBm at 1 dB compression, +24 V 0.9 A, at most +10 dBm in, never an open output | with the synthesizer at +1 dBm: about +30 dBm (1.05 W) at the AOM, about 90 % of the peak efficiency of the 3080-125 at 795 nm (saturation about 1.6 W, estimate); a minimum-gain unit gives +27 dBm: raise the synthesizer by up to 3 dB |
| ZFDC-20-4-S+ coupler (R06) | 19.5 dB coupling, 2 W | reads the drive level on the scope |
Corrected: the DIY page gave the amplifier gain as "29 to 34 dB, typical 33"; the data sheet (REV G) gives 29 dB minimum and 32 dB typical, with no maximum. The synthesizer setting is now +1 dBm (never above +5 dBm), which keeps the AOM drive at about +30 dBm.
Not yet confirmed, and how to close each:
- The harmonics of the SynthHD at 80 MHz (near the bottom of its range; no figure found). Look at its output on a spectrum analyser or a fast scope first; if the harmonics are strong, put a low-pass filter with a cut-off near 100 MHz after each channel. The AOM's 25 MHz bandwidth already rejects most of them, but the amplifier would still spend power on them.
- The AOM connector: the 3080-125 has an SMB jack: two SMB-to-SMA cables.
- DC on the RF lines: the switch and the attenuator need 0 V; measure the synthesizer output and the AOM input with the multimeter, and add a DC block if needed.
- Supplies: +24 V at about 1.8 A for the two amplifiers (R05), and ±5 V and ±3 V from the DIY bias box (D8), which is not yet a BOM row.
Red flags: efficiency quoted only at another wavelength, no AR coating stated, aperture under 1.5 mm, shear mode, "driver included" with a fixed frequency only, no RF power figure.
Ask the vendor: the diffraction efficiency at 795 nm for a 1.0 and a 1.5 mm beam and the RF power for it, the rise time for 1 mm, the input polarization, whether the RF input is DC-blocked, a housing drawing, and the lead time.
Q7 What mirrors do we use, and what is their specification?
Equipment row O01: 11 Thorlabs PF10-03-P01 protected-silver mirrors, Ø1″, in KM100 kinematic mounts (row O02). Two on the master axis, three in the SAS, two per EIT arm, and one retro mirror in each double pass. The laser-source fibre option adds two more (the steering pair before the coupler).
| Item | PF10-03-P01 (Thorlabs drawing) | What we need |
|---|---|---|
| Size | Ø25.4 mm, 6.0 ± 0.2 mm thick, clear aperture > 22.9 mm | fits the KM100 mount; beams are 1–5 mm |
| Coating | protected silver | broadband, insensitive to the angle |
| Reflectance | average > 97.5 % from 450 nm to 2 µm, at 0–45° incidence | high at 795 nm; each mirror loses about 2–3 % |
| Flatness | λ/10 at 633 nm | λ/4 would do for steering; λ/10 keeps the cat's-eye return clean |
| Surface quality | 40-20 scratch-dig | less scatter onto the detectors |
| Substrate, parallelism | fused silica, < 3 arcmin | not critical (only the front surface is used) |
Things to watch
- Polarization: at 45° a metal mirror keeps a linear polarization unchanged only if it is s or p (perpendicular or parallel to the plane of incidence); anything in between becomes slightly elliptical. On our bench the beams are linear and horizontal or vertical before the quarter-wave plate, so this holds; there should be no 45° mirror between the quarter-wave plate that makes σ⁺/σ⁻ and the cell.
- Losses add up: about seven mirrors in a path at 97.5 % each leave about 84 %. That is fine with milliwatts to spare. A broadband dielectric mirror (for example Thorlabs BB1-E03, 750–1100 nm) reflects more but costs more and is more sensitive to the angle and polarization: check its data sheet if a path is short of power.
- A cheaper supplier is fine if the data sheet gives the same: Ø25.4 mm, protected silver (or a dielectric coating covering 795 nm), reflectance at 795 nm, λ/10 (or λ/4 for steering only), 0–45° incidence.
A cheaper catalogue (silver mirror table, part "OQAg"): which one? The OQAg-25.4 (Ø25.4 mm, 5 mm thick, 450–2000 nm, reflectivity > 95 %, clear aperture > 90 %) is the one that matches: the right diameter for the Ø1″ mounts and thick enough to stay flat. Not the OQAg-25 (Ø25.0 mm sits loose in a Ø1″ mount) and not the 3 mm versions if the thicker one is available. Its > 95 % against > 97.5 % costs about 2.5 % more per mirror: seven mirrors leave about 70 % instead of 84 %, still far more than we need. Before ordering, ask what the table does not give: flatness (λ/10 at 633 nm wanted, λ/4 the least for steering), surface quality (60-40 or better), whether the silver is protected (overcoated, so it does not tarnish), the reflectance at 795 nm at 45° for s and p, and the substrate.
Sources: Thorlabs PF10-03-P01 specification (GoPhotonics listing) · Thorlabs drawing of the PF10-03-P01
Q8 What specification do the polarizing beamsplitter cubes (PBS) need?
Seven broadband cemented PBS cubes (620–1000 nm coating) with a transmitted extinction of at least 1000:1 are enough; laser-line cubes (3000:1) are not needed, because the Glan–Taylor does the final separation after the cell. Our listed part, the Thorlabs CM1-PBS252, was discontinued in 2016: the replacement is the CCM1-PBS252/M (the /M version has metric taps), now in BOM O03. The non-polarizing SAS cube CM1-BS014 was discontinued too; it is replaced by the CCM1-BS014/M (BOM O04).
| Item | Requirement | Why |
|---|---|---|
| Wavelength | 795 nm inside the coating band (620–1000 nm broadband is fine); AR-coated faces | Rb D1; every bare face would reflect about 4 % |
| Transmitted extinction Tp:Ts | ≥ 1000:1 | this is the clean port: use it wherever purity matters |
| Reflected extinction Rs:Rp | about 20:1 to 100:1 (what cube PBSs give) | acceptable: each beam has already been cleaned by an earlier cube, and the Glan–Taylor (10⁵) cleans the probe at the end |
| Transmission | Tp > 90 % (Thorlabs figure) | the control makes four cube passes; losses multiply |
| Aperture | cube ≥ ½″ (12.7 mm); the Thorlabs part is 1″ | beams are 1–1.5 mm, the expanded control about 5 mm |
| Damage | any catalogue cube | even 100 mW in a 1 mm beam is far below the rating |
| Mount | 30 mm cage cube with metric taps, or an unmounted cube on a kinematic platform | the cage version holds the cube square, with SM1 ports for wave plates and irises |
| Quantity | 7 | pick-off to the SAS, control/probe splitter, 2 SAS cubes, 2 double-pass separators, recombiner |
Where the extinction matters
- Double-pass separators. The returning beam must leave by the other port; whatever passes back goes towards the laser. The 1000:1 cube plus the wave-plate error give about 10⁻³ returned, which is why the isolator is needed (see the isolator answer).
- Recombiner. Control and probe meet here in orthogonal polarizations. Control light in the probe polarization would reach the detector, because the Glan–Taylor cannot remove light that already has the probe polarization. With clean beams arriving (each from an earlier cube), the leak is of order 10⁻⁶ of the control, a few nW against a probe of about 0.5 µW: acceptable.
- Pick-off and splitter. Here the cube only sets a power ratio with the half-wave plate in front, so the extinction does not matter.
Cheaper option: unmounted cubes from a general optics supplier. The cage housing is most of the cost; the cube itself is a standard part. The Spain-style bench does the same: its videos show uncaged cubes on the boards. Search terms: "polarizing beam splitter cube 780nm", "PBS cube 12.7mm 700-900nm", "polarization beamsplitter cube extinction ratio 1000:1". What to ask for:
- cemented cube polarizing beamsplitter, 12.7 × 12.7 × 12.7 mm (10 mm or 25.4 mm also fine), N-BK7 or equivalent;
- design wavelength 795 nm (a 780–800 nm laser-line or a 700–900 nm broadband coating);
- transmitted extinction Tp:Ts ≥ 1000:1 measured at 795 nm (listings often quote the best point of a broad band; reject 500:1 parts);
- Tp ≥ 90 %, Rs ≥ 99 %;
- AR coating on all four faces at 795 nm (R ≤ 0.5 %); cheap cubes are sometimes uncoated;
- beam deviation ≤ 5 arcmin, flatness λ/4 at 633 nm, scratch-dig 60-40, clear aperture ≥ 85 %;
- 7 pieces plus 1 spare, with the measured extinction and transmission at 795 nm.
K9 or N-BK7? Either. K9 (CDGM H-K9L) is the Chinese equivalent of Schott N-BK7: the same borosilicate crown glass, refractive index about 1.517 and Abbe number about 64, fully transparent at 795 nm. At our milliwatt powers absorption does not matter. What decides the cube is the coating (made for 795 nm), the extinction measured at 795 nm, and a well-annealed, bubble-free glass (stress in the glass is birefringent and lowers the extinction): ask the supplier for the glass grade or the measured extinction, not for N-BK7 by name. The same holds for the non-polarizing cube. A promise is not a data sheet. "We can follow your spec" counts only when the vendor's data sheet or test report states the figures at 795 nm: coating design wavelength, Tp, Ts (or Tp:Ts), AR reflectance per face, size and tolerance, beam deviation. Ask for the measured curve or the batch test data, and check one cube on arrival with our own laser: transmitted power with and without the cube (Tp), then a polarizer after the transmitted port turned for the minimum (extinction), using the power meter. Watch the design wavelength. A supplier sheet that says "@1064 nm" (or 532, 633 nm) describes a cube whose polarizing and AR coatings are made for that line. Its geometry figures (±0.2 mm, λ/10, beam deviation under 3 arcmin) may be excellent, but at 795 nm the extinction and transmission of a laser-line coating fall off and the faces reflect more: ask for the same cube coated for 795 nm (or 780 nm, or 700–900 nm broadband) with the extinction measured at 795 nm. For the SAS 50:50 cube ask: non-polarizing cube, 12.7 mm, 700–900 nm, R/T = 50/50 ± 5 % for both s and p at 795 nm.
Mounting an unmounted cube: a kinematic prism platform on a post, or a 3D-printed PETG cube holder on a ½″ (Ø12.7 mm) post at the 100 mm beam height: now DIY part D12, with STL files, a drawing and the build steps. The holder must hold the cube square to the beam (within a degree) and allow rotation about the vertical axis for alignment; fix the cube with a nylon-tipped screw or a drop of removable adhesive, never by clamping the faces.
Is a printed holder precise enough? Yes, for a cube PBS, with three conditions. A PBS needs far less precision than its price suggests:
- Squareness. An FDM print on the Bambu A1 is typically within about 0.1 mm (to be confirmed with a test print and a calliper). Over a 15 mm seat that is about 0.4°. The cube is pushed by a light spring or nylon screw against two printed reference walls, so the angle comes from those walls, not from the clearance of the pocket. A cube a fraction of a degree off normal still separates the polarizations; the reflected beam turns by twice the error, about 0.8°, and the next mirror takes that out during alignment.
- Height and rotation. The beam height is set by the post in its post holder, and the rotation about the vertical axis by turning the post, so print tolerance in height does not matter.
- Drift is what matters, not the starting angle. A lever of 0.3 m from the recombiner to the cell turns 0.1 mrad of creep into 30 µm at the cell, small next to the 0.47 mm probe and 2.55 mm control radii. To keep creep that small: a firm joint at the post (an M4 screw through the print into the post, as in the D11 holder, with a steel washer under the head so the plastic is not crushed), and a light load on the cube. Heat is not an issue here: all PBS positions are well away from the heated cell (PETG softens near 80 °C).
- Where we would still buy a metal mount: nowhere in the PBS positions. The places that need fine tip and tilt are the mirrors and the double-pass retro mirrors, which stay commercial kinematic mounts.
Alternative: the lab's resin (MSLA/SLA) printer. Resin gives sharper corners, smoother walls and finer detail than FDM, so the reference walls and a small flexure spring for the cube come out cleaner; layer lines and anisotropy are not an issue. Its weak points are mechanical, not dimensional:
- Brittleness at the screw. Standard resins crack when an M4 screw is tightened into or onto them. Use a tough or ABS-like resin, a through-hole with a large steel washer, and hand-tight torque; do not use heat-set inserts in resin.
- Creep, moisture and ageing. Many resins creep under a constant clamp load, take up moisture and keep curing under UV light, which can change a dimension slowly. Wash and fully post-cure, let the part rest a day, then measure it with a calliper before fitting the cube.
- Supports and shrinkage. Orient the part so the reference walls and the base are not on supports (support marks spoil a datum), and allow for the resin's cure shrinkage when sizing the pocket (measure a test pocket first).
- Heat. Standard resins soften at lower temperatures than PETG; this does not matter at the PBS positions, which are away from the heated cell.
Decided (14 Oct 2026): PETG on the Bambu A1. Our judgement: PETG on the Bambu A1 is the first choice for the cube holders, because it is tough at the screw and already proven on the bench parts. Resin is a good alternative for the seat when a sharper fit is wanted, best in a tough resin; a hybrid (resin seat glued onto a PETG base that takes the screw) combines both. Either way the acceptance test below decides; for resin, repeat it after a week to catch slow creep.
Acceptance test before printing seven: print one holder, mount a cube, send the laser (or a red pointer) through it and mark the reflected spot on a wall about 2 m away; check it again after a day and after gently tapping the post. A drift under about 0.5 mm (0.25 mrad) is good enough for every PBS position on our bench. Printed optomechanics has been compared with commercial parts before: a printed kinematic mount behaved like a Thorlabs KM100 in Salazar-Serrano, Torres and Valencia, PLoS ONE 2017 (ICFO).
Sources: Thorlabs broadband PBS cubes in 30 mm cage cubes (CCM1-PBS252/M) · Thorlabs CM1-PBS252 (discontinued, replaced by CCM1-PBS252)
Q9 Is a double-pass AOM practical on our table, how is it arranged, and who uses it?
Yes. It is the standard way to shift and switch a laser beam with an AOM in atomic physics labs. The classic description is Donley et al. (NIST), "Double-pass acousto-optic modulator system", Rev. Sci. Instrum. 76, 063112 (2005), who report 75 % double-pass diffraction efficiency and a 60 MHz tuning bandwidth. The reference guide we follow (Finkelstein et al., New J. Phys. 25, 035001 (2023), Fig. 10) uses one double-pass AOM per beam for Zeeman EIT and notes that "the double-pass AOM configuration suppresses spatial misalignment of the beam during the scanning".
Why double pass
- Twice the shift: the light is shifted by 2 × f_RF (160 MHz at 80 MHz).
- The beam does not move when the frequency changes: a single pass deflects the beam by an angle that depends on the RF frequency; on the way back the cat's eye sends the beam through the same point, so the output direction stays fixed while the probe is scanned. This is the main reason for using it.
- Better on/off: the light is diffracted twice, so leakage when the RF is off is squared, which helps the storage pulses.
How it is arranged (one arm, about 25–30 cm of table) 1. Half-wave plate, then the PBS: the incoming beam passes the PBS (p-polarized). 2. The AOM on its yaw platform (DIY D9), turned to the Bragg angle (7.6 mrad at 80 MHz and 795 nm). 3. A lens (f = 100 mm, BOM O08) one focal length after the AOM. 4. A quarter-wave plate, then a flat mirror at the focus, one focal length after the lens: lens and mirror form a "cat's eye" that sends every ray back along itself. 5. At the mirror the diffracted beam and the undiffracted (0th order) beam are about 1.5 mm apart (100 mm × 15 mrad): a razor blade or iris there blocks the 0th order. 6. The returning beam is recollimated by the lens, diffracted by the AOM a second time (another +f_RF), and arrives at the PBS turned to s-polarization (it crossed the quarter-wave plate twice), so the PBS reflects it out sideways: this is the arm's output.
Alignment, in order 1. Single pass first: set the Bragg angle with the D9 micrometer for the strongest first order (RF at the working level). 2. Place the lens at f and the mirror at its focus; steer the mirror so the beam returns on itself through the AOM. 3. Block the 0th order at the mirror. 4. Turn the quarter-wave plate for the most power out of the PBS side port. 5. Check: change the RF by ±1 MHz; the output beam must not move. Expect about 50–60 % double-pass efficiency with a good AOM (about 70–80 % per pass).
All parts are in the equipment list (AOMs O17, lenses O08, mirrors and mounts O01/O02, quarter-wave plates O06, PBS O03) and the D9 platform in the DIY Section. The 3D bench shows both double-pass arms.
Sources: Donley et al., Rev. Sci. Instrum. 76, 063112 (2005), NIST PDF · Finkelstein et al., arXiv:2205.10959
Q10 What linewidths and frequencies do we have to set?
| Item | Value |
|---|---|
| Rb-87 D1 line | 794.978851 nm in vacuum (about 377.107 THz) |
| Control AOM | 80.000 MHz, double pass, so +160.000 MHz |
| Probe AOM | 79.965 MHz, double pass, so +159.930 MHz |
| Control–probe difference | 70 kHz, the ground-state splitting at 50 mG (1.4 kHz per mG) |
| Solenoid field | about 50 mG (the photographed COILS supply showed about 80 mA) |
| Lock dither | about 10–100 kHz on the laser current (the ITC502 modulation covers 0–500 kHz) |
| Excited-state splitting | 814.5 MHz (F′=1 to F′=2) |
| Ground-state splitting | 6.8347 GHz, never needed by the AOMs |
| EIT linewidth target | 30 kHz or narrower, approaching 10 kHz at low power |
| Laser linewidth | 0.6–1.0 MHz (needs only to be below about 100 MHz) |
| SAS feature width | about 6–12 MHz |
80 MHz in the RF, 160 MHz in the light. 80.000 and 79.965 MHz are the RF frequencies of the two AOMs. Each beam passes its AOM twice (double pass), so its light is shifted by twice the RF: 160.000 MHz for the control and 159.930 MHz for the probe. The two beams differ by 70 kHz, which is what EIT needs. The 160 MHz that both share is the offset from the laser, which is locked to the F = 2 → F′ = 1 line through the SAS cell (no AOM there): both EIT beams therefore sit 160 MHz off that line. We use the −1 order in both AOMs, so they sit 160 MHz below it, away from F′ = 2. EIT depends only on the 70 kHz difference; the common 160 MHz only costs some absorption (the cell runs about 3 °C warmer).
Is the doubling real or only theory? Real, and exact. Each pass through the AOM scatters the light off the moving sound wave: the photon gains or loses exactly one RF quantum, so its frequency changes by exactly f_RF (+1 or −1 order). In the double pass the cat's eye sends the diffracted beam back into the same order, so it is shifted a second time: exactly 2 × f_RF. The shift is as exact as the synthesizer (both channels come from one clock), not an approximation. This is routine in atomic physics labs (Donley et al., Rev. Sci. Instrum. 76, 063112 (2005), measured it with a beat note). What is not perfect is the power: only the light diffracted twice carries 2 × f_RF (40 to 60 % of the input), the rest (unshifted, or shifted once) leaves at other angles and is stopped by the razor blade and the irises. Check it on our bench: overlap the arm output with a little unshifted laser light on a fast photodiode and look for the 160 MHz beat on the oscilloscope (it needs well over 160 MHz of bandwidth); between the two arms the beat is 70 kHz, visible on any photodiode.
What the two RF frequencies do (and do not do). 80.000 MHz drives the control AOM and 79.965 MHz drives the probe AOM (megahertz, not kilohertz). They are our design choice: 80 MHz is the centre frequency of the AOMs, and the 35 kHz between them follows the Zeeman splitting we set. An RF frequency only shifts the light frequency; as long as the RF is on, the light is continuous (CW EIT). Pulses come from switching the RF on and off with the TTL gate of each channel: the probe gate cuts a short probe pulse, and the control gate turns the control off and on for storage. So the frequencies decide where the light sits, the gates decide when it is there.
Where the numbers come from. The reference guide (Finkelstein et al., New J. Phys. 25, 035001 (2023), Sec. V) gives the method and the scale, not our RF values: double-pass AOMs "driven by twin phase-locked rf signals from the same dual-output waveform generator", Zeeman shifts of 0.7 kHz per mG between adjacent F = 2 sub-levels, a 50 mG solenoid field as the example (adjacent sub-levels 35 kHz apart), and a probe scan of less than ±100 kHz around a fixed control frequency. It gives no AOM centre frequency. The 80 MHz is the centre frequency of the AOMs we buy, and 79.965 MHz follows from our Λ (m = −1 and m = +1, two steps apart: 70 kHz in the light at 50 mG, halved by the double pass). The Spain-style bench does not show its frequencies.
Finkelstein's 0.7 kHz per mG and our 1.4 kHz per mG: the same constant. For Rb-87 F = 2 the Zeeman shift is g_F μ_B B m with g_F = ½ and μ_B/h = 1.40 MHz per gauss, so each step of one in m moves by 0.7 kHz per mG: the guide's number, the gap between neighbouring sub-levels. Our Λ spans two steps (σ⁺ control and σ⁻ probe meet at one excited sub-level, for example m = −1 and m = +1 through F′ = 1, m = 0), so the gap the two beams must match is 2 × 0.7 = 1.4 kHz per mG. The other Λ pairs (m = −2 with 0, and 0 with +2) are also two steps apart, so they all meet at the same value and add up to one EIT peak. The double pass then halves it again on the driver:
| Per mG | At 50 mG | |
|---|---|---|
| neighbouring sub-levels (the guide's number) | 0.7 kHz | 35 kHz |
| our Λ ground states (Δm = 2): light difference needed | 1.4 kHz | 70 kHz |
| RF difference between the two AOMs (double pass, ÷ 2) | 0.7 kHz | 35 kHz |
Try it with sliders: the interactive flow page moves the solenoid current, redraws the sub-levels and the Λ gap, updates both RF channels, and shows the EIT peak appear only when the RF difference matches the field.
Why do the two RF channels differ by 35 kHz?
- EIT needs two-photon resonance. In our Λ system the control (σ⁺) connects F = 2, m = −1 to the excited state F′ = 1, m = 0, and the probe (σ⁻) connects F = 2, m = +1 to the same excited state. The probe passes (EIT) only when the frequency difference of the two beams equals the energy difference of the two lower states.
- The lower states are split by the solenoid field. For F = 2 of Rb-87 the Zeeman shift is g_F μ_B B / h = 0.70 MHz per gauss for each step in m (g_F = 1/2). The two states differ by Δm = 2, so the splitting is 1.40 MHz per gauss, that is 1.4 kHz per mG. At our working field of about 50 mG: 1.4 × 50 = 70 kHz.
- Each AOM is passed twice. A double pass shifts the light by 2 × f_RF, so the light frequencies differ by 2 × (f₁ − f₂). To get 70 kHz in the light, the RF channels differ by 70 / 2 = 35 kHz: 80.000 MHz and 79.965 MHz.
- Why a field at all, instead of 0 G and equal frequencies? The solenoid field along the beam sets the quantization axis, so that "σ⁺" and "σ⁻" are well defined, and it is about 50 mG, far above what the shield leaves (well below a milligauss), so stray fields cannot move the resonance. The AOM difference is then simply matched to the splitting that this field produces.
- Physics or our design? Both. The 1.4 kHz per mG is a constant of the Rb-87 atom (it cannot change). The field is our choice: the solenoid gives 3.39 mG per mA (DIY D1), so 50 mG needs about 14.7 mA from the ITC502. The RF difference is then 0.7 kHz per mG × the field we set.
- No risk of "missing" the condition with the AOMs we buy. We can always meet it from either side: change the solenoid current until the splitting matches the RF difference, or change the RF difference (the driver is tunable in 1 Hz steps over 70–90 MHz on each channel) until it matches the splitting. Even 0 G with equal frequencies works. The only purchase that would trap us is a fixed-frequency driver, which is exactly why the specification asks for two tunable channels from one clock. The AOMs themselves (80 MHz, 25 MHz bandwidth) do not care about a difference of a few tens of kHz.
- It is not a magic number. If the field is set differently, the RF difference follows it (35 kHz for 50 mG, 0.7 kHz per mG of RF difference). For the EIT spectrum, the probe channel is swept a little around 79.965 MHz, and the transparency peak appears where the two-photon condition is met. Which channel is higher depends on the field direction and on which beam is σ⁺; if no peak appears, swap the sign of the difference.
Because the offset between the two beams is only kHz, a generator with 1 Hz resolution is far more than precise enough. The control–probe difference must stay steady to well under the EIT width (a few kHz): use one two-channel source, or sources sharing a clock.
Q11 Is a DFB with a TEC and the Thorlabs ITC502 good enough? How do the controllers compare?
Yes, if the current noise is low, and the ITC502 is the best match we have. The rule: the laser tunes at about 1.4 GHz per mA, so every 1 µA rms of driver noise can become about 1.4 MHz of linewidth.
| Controller | Noise | Verdict |
|---|---|---|
| G&H EM595 | 5 µA rms (10 Hz–10 MHz) | usable, up to about 7 MHz worst case, the noisiest |
| Thorlabs ITC502 | under 1.5 µA rms | about 2 MHz worst case: best match |
| ILX LDX-3220 | not found | current source only, needs a separate TEC controller |
| Thorlabs ITC4001 | not found | no proven advantage |
A 5 µA driver does not harm EIT (the optical line is about 100 MHz wide and both beams share the noise) but it blurs the 6–12 MHz SAS features and makes the lock noisier. Ask vendors for "rms current noise, 10 Hz to 10 MHz" (target about 1 µA or better) and "temperature stability over 24 h"; also check the modulation bandwidth against the lock dither. The laser's temperature tuning is about 28 GHz per kelvin, so the temperature must be stable to a few mK; the lock removes the slow remainder.
The ITC502 against our laser
| Spec | ITC502 | Our laser needs | Verdict |
|---|---|---|---|
| Laser current | 0–200 mA | 160 mA (absolute maximum 170 mA) | fits |
| Compliance voltage | above 6 V | about 2 V | fits |
| Noise (10 Hz–10 MHz) | under 1.5 µA rms | as low as possible | about 2 MHz worst case |
| 24 h drift | under 10 µA (about 14 MHz) | within lock range | fine, the lock removes it |
| Modulation | 0–500 kHz | lock dither 10–100 kHz | fits |
| TEC | ±2 A, 16 W | about 0.4 A | plenty |
| Thermistor | 10 Ω–19.9 kΩ | 10 kΩ NTC | fits, chip at 15 °C or warmer |
Four things to design for
- The modulation input is 20 mA/V, about 28 GHz per volt. Put a 100:1 divider between the lock box and the controller: one DAC step of the Red Pitaya would otherwise move the laser by 3–7 MHz (3.4 MHz into 50 Ω, 6.8 MHz into a high impedance) and the DAC noise adds linewidth. Use 91 kΩ in series and 1 kΩ to ground (DIY Section, part D6): the source impedance stays near 0.9 kΩ, so the 500 kHz modulation bandwidth is kept (corner above 1 MHz with 150 pF of cable). A single 1 MΩ series resistor into the 10 kΩ input gives the same ratio, but its corner is only about 100 kHz, too close to the lock dither.
- Front-panel steps are coarse (10 µA is about 14 MHz, 1 Ω is about 2 mK or 65 MHz): tune coarsely by hand and let the lock do the fine tuning.
- Set the current limit to 170 mA or below before connecting the laser.
- Check the output polarity (anode ground) and the cable to the butterfly mount.
Equipment found in the lab
Q12 Are the extra lab items useful? (second ITC502, LDM-4980 mounts, TCLDM9 mounts)
| Item | Useful? | Why |
|---|---|---|
| 2 × ITC502 | yes, both | one drives the laser and its TEC; the second can run the cell heater and the solenoid (see the answers below) or a second laser |
| 2 × LDM-4980 (14-pin butterfly mount) | yes, likely | ILX's 14-pin telecom mount family fits a 14-pin butterfly like our DFB and can replace the Thorlabs LM14S2; check the pinout first |
| 2 × TCLDM9 | not for the DFB | a mount for 5.6 and 9 mm TO-can diodes, not butterfly packages; useful for a home-built ECDL or a practice diode |
| Cable set label LCM-39425 | unknown | no listing found; read the label |
Before connecting: the mounts are ILX wiring (9-pin D-sub, configurable pins; ILX cables are DB9–DB9 for the laser and DB15–DB9 for an ILX temperature controller) and the ITC502 is Thorlabs, so compare the ITC502 laser and TEC pinout with the mount's pin table; the cables may need rewiring. Our laser: anode pin 10, cathode 11, TEC 1 and 14, thermistor 2 and 5, monitor diode 3 and 4.
The second ITC502 has better uses than a spare laser controller: its TEC half can regulate the cell heater and its laser half can be a very quiet solenoid supply. They are described in the three answers about the second ITC502 below.
Sources: ILX LDM-4984 · Thorlabs TCLDM9 catalogue
Q13 Which of the loose mounts and stages in the photographs are useful?
Identified from five photographs of the lab shelves and added to the Lab Inventory with a drawing of each (the drawings follow the photographs, with the markings that are legible).
| Item | Status | Use in the bench |
|---|---|---|
| Melles Griot kinematic mounts (yellow mG knobs) | use | mirror and beamsplitter mounts (BOM O02): measure the aperture |
| Thorlabs PR01/M rotation stage | use | Glan-Taylor analyser or waveplate angle; also an option for the AOM yaw (DIY Section, D9) |
| Micrometer XY stages | use | cell holder, AOM and collimator positioning |
| XY lens positioners | check | cat-eye and expander lenses |
| Brass rotation holders, degree scale | check | possible waveplate or polarizer rotators: measure the bore |
| Navitron TV zoom lenses | check | beam or cell imaging with an IR camera (none listed yet) |
| Printed grid target cards | use | beam centring |
Left out as not needed: the ball-screw stepper stage, aluminium rails, the V-block, brackets, loose screws and the box of cables.
Q14 Is the Credix SG-1710 signal generator useful?
Yes, as an AOM driver. It is a single-channel synthesizer, 200 kHz to 1000 MHz, 1 Hz resolution, 0.5 ppm accuracy, up to +13 dBm, with AM, FM and GPIB (figures from a third-party listing, not a Credix datasheet).
- It can drive one AOM at 80 MHz through an RF amplifier (+13 dBm alone is not enough), for example the AOM in the SAS arm that moves the lock by 160 MHz.
- Two independent generators share no phase, which is acceptable for CW EIT because the offset stays within a few Hz, far below the 7–26 kHz EIT width.
- It is not a gate: switch the RF with a proper RF switch (AM is not a clean off).
- It cannot reach 6.8 GHz.
Source: SG-1710 listing
Q15 Which bench power supplies can do which job? (Aditeg PS-3030DD, Multicomp Pro 72-2710)
The Aditeg PS-3030DD is the main supply of the RF chain and, if wished, of the cell heater. The Multicomp Pro 72-2710 is not needed now. Neither is for the solenoid or the photodiodes.
Aditeg PS-3030DD. From the front panel: two adjustable channels with a tracking switch (independent, series, parallel) and a fixed 5 V / 3 A output; the model name suggests 0–30 V and 0–3 A per channel. No datasheet was found, so the ripple is unverified (similar linear supplies quote about 0.5–1 mV rms in voltage mode and about 3 mA rms in current mode). It is in the lab inventory with a 3D picture.
Multicomp Pro 72-2710. From the datasheet: one channel, 0–30 V and 0–5 A (150 W), voltage and current ripple at most 2 mVrms and 3 mArms (20 Hz–20 MHz), setting resolution 10 mV and 1 mA, setting accuracy 0.5 % + 20 mV and 0.5 % + 10 mA, USB and RS-232, 110 × 156 × 260 mm. The datasheet does not say whether it is linear or switching.
| Job | Aditeg PS-3030DD | Multicomp 72-2710 |
|---|---|---|
| RF amplifiers (+24 V) and RF switches (±5 V) | yes, primary: channel 1 at +24 V; the fixed 5 V and channel 2 give the two rails; millivolts of ripple do not matter for RF parts; check that the outputs are isolated first | yes: 2 mV ripple is harmless for RF parts; but one channel only, so two supplies are needed for the ± rails |
| Cell heater | yes: constant-current mode, about 0.3–0.5 A, but no temperature loop: add a thermistor and adjust by hand, or let the second ITC502 regulate the heater and keep this supply for the RF parts | yes: constant-current mode, 0.3–0.5 A, controlled over USB; no temperature loop (a thermistor read-out is still needed). A DC heater makes a magnetic field: wind the heater wire as twisted pairs (bifilar) and, if possible, switch it off while measuring |
| Solenoid | no: a few mA of ripple is too much against a 7–26 kHz EIT line; use the ITC502 laser section | no: the solenoid current is only milliamps, and 3 mArms ripple with 1 mA steps and 10 mA accuracy is larger than the current itself; a 7 kHz line is about 5 mG wide (1.4 kHz per mG), so the field must stay stable to about 0.1 mG (0.2 % of 50 mG), which needs a low-noise source |
| Photodiodes, lock electronics | no: millivolts of ripple | no: millivolts of ripple |
Verdict: the PS-3030DD covers the RF chain and the Multicomp is a good general bench supply that nothing in the bench needs today. Buy it only if the PS-3030DD is occupied by the RF chain and the heater needs its own supply. The small ±5 V and ±3 V rails of the RF switches and attenuators can be made by the home-built bias box (DIY Section, part D8) from a ±12 V supply, so the +24 V for the amplifiers is the only high-current need.
Q16 Which of our optical power meters and heads can measure 795 nm? (ILX OMM-6810B, PM100USB with S140C, S144C and S120VC, Newport 818-SL)
The working set is the Thorlabs PM100USB with the S120VC (probe) and the S140C (control and fibre). The S144C and the ILX OMH-6745B head do not cover 795 nm, and the Newport 818-SL needs a Newport meter.
| Item | At 795 nm? | Notes |
|---|---|---|
| PM100USB console | yes | reads any C-series head; no display, so it needs a PC with the Thorlabs Optical Power Monitor software |
| S140C (silicon, 350–1100 nm, 1 µW–500 mW) | yes | reads the fibre output (5–15 mW) and the control (about 1 mW); polarization and beam shape do not matter; the 1 µW floor reads the 2 µW probe poorly |
| S120VC (silicon, 200–1100 nm, 50 nW–50 mW) | yes, best for the probe | 9.5 mm aperture, 1 nW resolution, uncertainty 3 % from 451 nm; plugs into the PM100USB |
| S144C (InGaAs, 800–1700 nm) | no | 795 nm is below its 800 nm limit, so the calibration is not valid; keep it for infrared work |
| ILX OMM-6810B meter with the OMH-6745B head | no, with this head | the head reads 950–1650 nm; the meter is useful only if a silicon head (OMH-6703B or OMH-6742B) is found |
| Newport 818-SL head | maybe | covers 795 nm but has no display: needs a working Newport meter; the PM100USB cannot read it |
Thorlabs PM100USB, S140C and S144C. Figures are from the Thorlabs spec sheets. The S140C floor is 1 µW (1 nW resolution), so the probe at about 2 µW is read poorly: measure the probe before the attenuating optics, or read it with the S120VC.
S120VC. It fills the gap of the S140C. Figures are from reseller and catalogue pages (the Thorlabs datasheet was not found; the product is listed as discontinued). Use it for the probe (about 2 µW), the SAS beams and the control (about 1 mW). Keep the beam inside the 9.5 mm aperture and enter 795 nm on the console. With the PM100USB, the S120VC and the S140C the lab has the complete power-meter set.
ILX OMM-6810B and OMH-6745B. The OMM-6810B is ILX's optical power and wavelength meter for the OMH-6700B heads (5-digit LED display, GPIB, no longer sold); its power range, wavelength range and accuracy come from the head. The head in the lab, the OMH-6745B, reads 950 to 1650 nm (confirmed from its label), so it cannot measure our 795 nm laser. It is not in the silicon-head brochure I could read, which lists:
| Head | Covers |
|---|---|
| OMH-6703B | power only, 400–1100 nm |
| OMH-6742B | power and wavelength, 350–1100 nm |
| OMH-6790B | 830–1100 nm only (does not cover 795 nm) |
What a silicon head (OMH-6703B or OMH-6742B) would give:
- Power budget: 100 nW to 1 W, spanning the fibre output (about 5–15 mW), the control (about 1 mW) and the probe (about 2 µW); the integrating sphere makes the reading independent of polarization.
- Wavelength: a power/wavelength head reads a power-averaged wavelength to about 1 nm with at least 10 µW. That only confirms the diode is near 795 nm; it cannot find the Rb line or resolve MHz shifts.
- Cautions: the detectors are temperature controlled (about one hour of warm-up), accuracy is about 3.5–5 %, the calibration date matters, and the readout is GPIB only.
Until a silicon head turns up, use the Thorlabs set for the power budget. Check whether the lab has other OMH heads.
Newport 818-SL. A passive silicon photodiode head (400–1100 nm, 10.3 mm clear aperture, removable OD3 attenuator that adds three decades of range). Its power limits depend on the meter and the attenuator, so the exact numbers are in the 818-series datasheet. Status in the inventory: check. 1. Find which Newport meter goes with it, and test whether that meter still works (power on, zero, a known source). 2. Until it works, the Thorlabs set above is the working power-meter set, so nothing is blocked. 3. Without a meter it can still be a photodiode: about 0.5 A/W at 795 nm, so 1 mW gives about 0.5 mA. Check whether the head needs a bias first.
Sources: ILX 6700B silicon heads brochure · Newport 818-SL/DB
Q17 Which instruments record the result, and which photodetectors do we need? (PDA36A2, PDB210A balanced detector, AD-300/DC)
The result comes from a photodetector read on the oscilloscope. The power meter is a setup tool. The EIT signal is the probe transmission while the two-photon detuning is scanned, and the window is only about 7–30 kHz wide. A USB or benchtop power meter updates far too slowly to follow a scan, shows only a number, and the S140C floor (1 µW) is close to the probe power (about 2 µW).
| Instrument | Job |
|---|---|
| Signal photodetector + oscilloscope | EIT transmission: the result |
| SAS photodiode (+ ITC502) | laser lock signal |
| Power meter (PM100USB + S140C) | fibre, control and AOM-efficiency checks before the run |
| Fabry-Perot or wavemeter | single-mode and mode-hop check (missing from the budget) |
| Fluxgate or gaussmeter | shield and 50 mG field check (the FLC100 answer below) |
| Beam profiler or camera, IR card | beam size (sets the intensity) and alignment |
| Fast detector (AD-300/DC) | control and probe beat note, AOM pulse shapes |
Signal detector: the Thorlabs PDA36A2, two needed, a third optional. It is an amplified silicon detector (350–1100 nm, 8 switchable gain steps, 0–70 dB, 3.6 × 3.6 mm chip).
- One for the probe signal after the Glan-Taylor (the EIT result).
- One for the SAS lock signal.
- Optional third: the control beam monitor or a reference channel. The AD-300/DC we own can serve as a diagnostic channel.
Gain: the probe is only about 2 µW, so use about 50–60 dB. At 70 dB the bandwidth falls to a few kHz, which is marginal for a 7–30 kHz window. The SAS detector can use a lower gain. The PDA36A2 normally ships with its ±12 V supply; check before buying a separate LDS12B. The 3D bench, the Spain-style bench and the equipment table show the PDA36A2 drawn from the Thorlabs outline drawing (approximate dimensions).
The Thorlabs PDB210A balanced detector: not needed, it is overkill. A balanced detector subtracts the laser intensity noise with a second reference beam. The reference papers do without it:
- Finkelstein et al. 2022: the probe passes a Glan-Taylor and is focused on "a fast photodiode"; the probe is scanned and the EIT spectrum is recorded.
- DeRose et al.: one New Focus 1621 photodiode on a digital oscilloscope (low detector impedance to avoid cable reflections); the pump leakage was reduced with a Glan polariser, not a better detector.
The EIT window is slow (7–30 kHz), so averaging on the oscilloscope recovers any noise. Use the two PDA36A2 detectors. Try balanced detection only if the probe is still too noisy after the Glan-Taylor, scope averaging and a lock-in. The PDB210A datasheet could not be retrieved, so its price and bandwidth are unverified.
The Newport AD-300/DC fast detector: a good diagnostic, not the main probe detector. No datasheet was found for this number; the closest Newport parts are the 818-BB amplified detectors (rise time under 400 ps).
- Use it to watch AOM switching and pulse shapes on the oscilloscope, the control–probe beat note, or the strong SAS beam.
- For the weak probe (about 2 µW at the cell) a gain-adjustable low-noise detector such as the Thorlabs PDA36A2 is better: EIT pulses last microseconds, so 300 ps speed only adds noise.
- Check the responsivity at 795 nm, the supply it needs and its output into 50 Ω before use.
Sources: Finkelstein et al. 2022, DeRose et al.
Solenoid, heater and fluxgate (the magnetic field)
Q18 What can the second ITC502 be used for, besides a laser?
Three jobs. An ITC502 is a laser current source (0–200 mA, noise under 1.5 µA rms, drift under 10 µA per 24 h) plus a TEC controller (±2 A, 16 W, thermistor input), and the two halves are independent. The lab has two units, so after the first runs the DFB the second is free.
| Job | Which half | Notes |
|---|---|---|
| Cell heater with a temperature loop | TEC | needs a 10 kΩ NTC thermistor on the cell (not a Pt100); a foil heater of about 10–20 Ω fits the 8 V and 2 A limit; the output is DC, so use twisted pairs and switch it off while measuring |
| Solenoid current source | laser | needs about 0.2 % stability (0.1 mG = 10 nT out of 50 mG = 5 µT, a 140 Hz shift against a 7 kHz line); at 20 mA that is 40 µA, well above the 1.5 µA noise and 10 µA drift; check that the solenoid resistance is below about 300 Ω at 20 mA and set a low current limit first |
| Spare or second laser | both | for a repump or a backup if the DFB is discontinued |
If both work on the bench, the separate cell-heater controller (BOM C04) and the solenoid current source (C08) could be dropped. This has not been applied to the BOM yet. The next two answers give the wiring; the plugs, the heater and the coil are built step by step in the DIY Section (parts D1 to D3).
Q19 How do I use the second ITC502 as the cell-heater controller (connection and set-up)?
Assignment: the first ITC502 with an LDM-4980 mount is reserved for the DFB laser; the second ITC502 runs the cell heater with its TEC half and, if wished, the solenoid with its laser half. Everything below is from the ITC500 operation manual. The plug, the heater and the dummy-load test are drawn and built step by step in the DIY Section (parts D2 and D3).
TEC output (15-pin D-sub, rear). TEC (+) is pins 5, 6 and 7, TEC (−) is pins 13, 14 and 15; all three pins of each must be connected. Pins 2 and 9 sense the heater voltage (optional). The output is ±2 A, 16 W, compliance above 8 V, and the (−) side is at ground. Thermistor: pins 3 and 4 (if one lead of the thermistor is grounded, it goes to pin 3). Use shielded cable and connect the shield to pins 13–15. Pin 12 is a supply for Thorlabs mounts: leave it alone.
Heater wiring. 1. TEC (+) → a series power diode (for example 1N5400, 3 A) → the foil heater → TEC (−). 2. A 10 kΩ NTC glued to the cell wall next to the heater, with Kapton tape or thermal epoxy, on a twisted shielded pair away from the heater leads. 3. Twist the two heater leads together along their whole length (and wind the foil bifilar) so that the DC current makes almost no field in the shield.
Why the diode. The controller reverses its current when the temperature is above the set-point. A resistor heats for either polarity, so without a diode an overshoot would make it heat more: a thermal runaway (the manual warns that a TEC with wrong polarity can run away and destroy the parts). The diode blocks the reverse current; the 0.8 V drop is small against 8 V.
Front panel and DIP switches.
- Sensor: DIP switches SW7/SW8 to "TH < 20 kΩ" (100 µA measurement current; the setting range is 10 Ω to 19.99 kΩ), and the SENSOR button to thermistor. The display shows the thermistor resistance in ohms, so convert: R = R0·exp[B(1/T − 1/T0)] (temperatures in kelvin; R0 and B from the thermistor datasheet). A 10 kΩ NTC with B ≈ 3900 K reads about 2.1 kΩ at 65 °C. Select the display T SET and dial the value in with the TEC knob.
- TEC current limit: select the display I TEC LIM and set it with the small screwdriver pot beside its LED; use 0.3 A for the dummy-load test and 0.50 A for the real heater on the open bench and 0.33 A once it is inside the closed shield (so even a runaway stays below about 85 °C), and keep heater resistance × current under about 7 V (a 12 Ω heater at 0.6 A gives about 4 W).
- Temperature window protection: select T WIN, set about ±200 Ω (a few degrees), and switch SW5 down (WIN on). If the temperature leaves the window the output switches off.
- PID: start from the factory values (chapter 2.15.4 of the manual), raise P until the temperature oscillates a little, then back off. Raise the set-point in steps of 10 °C. Warm-up for rated accuracy is up to 10 minutes.
First switch-on (diode direction). Start with the cell at room temperature and T SET warmer than the cell. Press TEC ON. If I TEC reads a current and T ACT rises towards T SET, the diode is the right way round. If I TEC stays at about 0 mA and nothing heats, reverse the diode. Never start with T SET below the cell temperature, and never remove the diode. (The dummy-load test of the DIY Section settles the direction before the cell is connected.)
Check the field. With the fluxgate inside the shield, switch the heater on and off: the change should be small compared with 1 mG (the DIY test uses 0.1 mG). If not, twist the leads tighter.
Q20 Is it safe to wrap the bifilar heater directly round the rubidium cell?
Yes, if the heater stays on the barrel and the controller's current limit is set so that even a runaway stays cool.
- Glass: 1 to 2 W spread over the 68 × 24 mm heater is about 0.1 W per cm², so the wire runs only a little warmer than the glass. Quartz takes the slow warm-up easily. The heater never covers a window, and no wire crosses one: the runs are 22 mm long on the 24.8 mm barrel between the windows (corrected on 19 Oct 2026; the earlier 25 mm runs would have reached the window joints).
- Electrical: 12 Ω at under 0.42 A is a few volts. The two Kapton films insulate it (check heater to NTC above 10 MΩ), and the diode of D3 stops the controller from driving the heater backwards.
- Magnetic: the bifilar pairing cancels the heater's own field. The on-and-off test in the shield must show less than 0.1 mG.
- Rubidium: keep the windows a little warmer than the stem, so the metal condenses in the stem and not on the windows.
- Runaway: if the NTC comes off the glass, the ITC502 drives its full limit. So set I TEC LIM to 0.50 A on the open bench (worst case about 84 °C) and 0.33 A inside the closed shield (also about 84 °C). Both still give the power needed at 65 °C, and both stay below the 100 °C rating of the foam and the epoxy. The earlier figure of 0.6 A was too high for a runaway inside the shield.
What is the foam sleeve made of, and will silicone foam survive the heater? The sleeve is not printed: it is 3 mm melamine foam or silicone foam, cut from sheet and wrapped on (ID 25.6, OD 31.6, 34 long, a Ø10 hole for the stem). PETG would sit directly on the heater, close to its softening range, and solid plastic insulates several times worse than foam. The rules: no metal at all (no aluminium-foil facing), a temperature rating of at least 100 °C, and exactly 3 mm (the radial room to the former bore is 1.2 mm).
| Melamine foam | Silicone sponge sheet | |
|---|---|---|
| Insulation | better | less good: more heat needed |
| Handling | crumbly, sheds dust: wrap it in polyimide tape | tough, easy to cut, no dust |
| Temperature | far above our 84 °C worst case | commonly rated to about 200 °C (check the data sheet) |
Silicone does not burn or melt here: the worst case with the current limits is about 84 °C. Buy a sheet that states "silicone" and a temperature rating (some cheap sponge sheets are polyurethane or neoprene), and hold a scrap on the heater during the open-bench test at 0.50 A for an hour: no smell, no darkening, no shrinking. Because silicone insulates less, check that the cell still reaches 65 °C inside the closed shield at 0.33 A; if not, use melamine (a thicker sleeve does not fit).
Q21 Can we heat the cell the Duke way (heaters and insulation wrapped in aluminium foil)?
Partly. The foil itself is fine and can be added as an outer layer, but the Duke heater cannot be copied as it is: their experiment does not need a milligauss-quiet field, and ours does. The Duke page shows a cell inside "a collection of heating elements and insulation" with aluminium foil wrapped round the outside, held at about 72 °C, inside Helmholtz coils that only cancel the axial part of the Earth's field. No shield, and nothing about how the heater is wound.
| Part of their method | For our Zeeman EIT | Why |
|---|---|---|
| Aluminium foil as the outer wrap | yes, optional | aluminium is not magnetic; at DC it makes no field. It reflects heat radiation, but inside our closed stack most heat leaves by conduction, so the gain is small. |
| Unspecified heating elements | no, use our bifilar heater (DIY D2) | an ordinary heater wire or tape carries about 1 A; one loop of it near the cell makes far more than our 0.1 mG budget. The bifilar winding cancels its own field; we test it with the fluxgate before use. |
| 72 °C | close to ours (55–65 °C) | the temperature sets the vapour density; the target comes from the paper, not from Duke. |
| Helmholtz coils only, no shield | no | 1.4 kHz per mG: we need the three-layer shield and the solenoid. |
If you add foil
- One layer (about 20 µm) over the foam sleeve: it fits in the former bore (radial room about 1 mm).
- Keep it off the beam: leave both window ends open.
- Insulate it from the heater leads and the thermistor (it conducts) and do not let it touch the solenoid winding.
- Do not close it into a loop round the cell with a soldered or overlapping conductive joint if the heater is ever driven with AC or PWM: a closed ring is a one-turn coil. With DC from the ITC502 it does not matter, but leave a small gap anyway.
- Keep the windows a few degrees warmer than the stem, or rubidium condenses on the windows. The foil should not cover the windows more than the heater does.
Accuracy does not depend on the foil: it depends on where the thermistor sits (on the glass, near the beam) and on the controller. With the ITC502 and a 10 kΩ NTC the setting is stable to well below 0.1 K.
Verdict: keep our bifilar heater, foam and tubes (DIY D2); an outer foil layer is allowed and harmless, but it is not a replacement for a non-magnetic heater.
Q22 Can the solenoid former be 3D-printed in PETG on a Bambu Lab A1 with a 0.2 mm nozzle?
Yes. Print it upright, cable end on the plate, and print the 50 mm test coupon first. The STL files and the slicer settings are in the DIY Section, part D1 (“3D-printed former”).
| Requirement | With the A1 and a 0.2 mm nozzle |
|---|---|
| Size Ø38 × 160 mm | fits the 256 mm build height |
| Ten pitches 36.0 ± 0.2 mm, ± 0.05 per pitch | the helix comes from the Z axis; 0.08 mm layers give steps of ± 0.04 mm |
| Wire seat 0.60 wide × 0.40 deep | 7 to 8 layers high, about two line widths deep; the upper flank is 45° so no support is needed |
| Bore Ø34.0 for the Delrin tubes (Ø33.7) | set the X-Y hole compensation from the coupon |
| Non-magnetic | natural or plain PETG, no metal or “magnetic” filler; check with a compass |
| Temperature | PETG softens near 75 °C; the former sits outside the foam sleeve of the 55–65 °C cell |
Accuracy: PETG shrinks about 0.2 to 0.5 %. A uniform shrinkage changes the field per mA by the same fraction and leaves the uniformity unchanged, and the in-shield calibration takes it out; correct the Z scale from the coupon if ten pitches are off by more than 0.1 mm.
Is the groove right for the winding? Yes. Checked on the STL by axial sections at several angles: 42 seats, each 0.600 mm wide at a radius of 18.600 mm (0.40 deep), centred on the design helix to better than 0.01 mm, ten main pitches 36.000 mm. The enamelled wire (Ø0.55) has 0.05 mm of side clearance and its centre lands on the design winding radius of 18.875 mm. Printed slots usually come out a little narrower, so if the wire does not drop into the coupon's seat, print the 0.65 mm seat version (same pitch, same field).
Slicer: select the A1 0.2 mm nozzle preset first (the 0.4 mm defaults of 0.2 mm layers and 0.42 mm lines are too coarse), then 0.08 mm layers, 0.22 mm line widths, 10 wall loops, scarf seam off, outer wall 50 mm/s, Precise Z height on, no support, 5 mm brim. The full field-by-field list is in D1.
The STL files: the former, the test coupon, the two spacer rings (with the lead notch and the recess for the degaussing bundle) and the winding as a reference model, not for printing: the wire is wound by hand in the printed groove.
Q23 Can we 3D-print the holder for the SAS reference cell in PETG?
Yes, and it is the right material for this part. The SAS cell (BOM S01, Ø19 × 75 mm) works at room temperature and sits outside the shield, so PETG is not near its softening point, and the lock does not need a milligauss-quiet field (no metal fillers anyway). The STL files and the steps are in the DIY Section, part D11; the equipment list row S02 now points to them.
| Part | What it does |
|---|---|
| Cradle (base 110 × 44 × 6 with two saddles) | holds the cell on its axis 20 mm above the base; M4 hole for a ½-inch post or two M6 slots 75 mm apart; M3 nut traps |
| Two straps | close over the saddles with nylon M3 screws; 1 mm felt pads take the load, never the bare plastic |
| Cover | keeps room light and draughts off the cell and the SAS photodiode; Ø10 mm beam holes in both ends, closed top over a stem up to 13 mm |
Before printing: confirm the cell's length over the windows, the window diameter and the stem (the holder takes a stem at mid-length, pointing up, up to 13 mm high, and windows up to Ø23 mm; see the next question). Matte black PETG cuts stray light. Do not use it for the EIT cell: that one is heated to 65 °C inside the shield and has its own stack (D2).
Q24 Real cells have a torch-sealed stem (tip-off). Do our printed holders and the solenoid take it into account?
Not fully until now: the SAS holder did, the EIT cell stack and the solenoid did not. Both are now designed for a real cell. A vapour cell is filled through a glass tube on its side, which is then sealed with a torch. What is left is the stem (tip-off), a small glass nub on the side of the tube, usually at mid-length. It is also the coldest point of the cell, where the rubidium metal collects.
What real cells look like
| Source | What it shows |
|---|---|
| Thorlabs drawing of the Ø19 × 75 mm rubidium cell (GC19075-RB) | stem Ø6 mm (typical) at mid-length, at most 10 mm high; windows Ø21 mm on the Ø19 mm tube, 3 mm thick, wedged 2° and tilted 11° |
| Precision Glassblowing stock cell photo (AB-RB-Q-UV-19X75, our SAS cell S01) | a short nub at mid-length on the side; window plates slightly larger than the tube (no dimensions given) |
SAS reference cell (DIY D11): fits. The saddles hold the tube 20–30 mm from the centre, so a stem at mid-length points up between them, and the windows sit outside the saddles. The cover was changed to a closed top: it clears a stem up to 13 mm and windows up to Ø23 mm, and it no longer lets light in through the old stem slot. The reference model in the STL folder now has the real shape (Ø21 windows, Ø6 stem 10 mm high).
EIT cell in the solenoid (DIY D1 and D2): the bore limits the stem. The wrapped cell slides into the former *after* the winding is done, so everything, stem included, must pass the Ø34 mm bore:
- bore radius 17 = cell radius 12.5 + stem + 0.5 mm clearance, so the stem must be at most 4 mm high;
- the order specification for the EIT cell (BOM C01) and both quotation requests now ask for a tip-off at mid-length, at most 4 mm above the glass and Ø8 at its base. Earlier text allowed "up to 15 mm" with a slot in the former, which could not work: the cell could not slide past the winding, and the stem would reach the shield.
- Heater: the film is now 68 mm instead of 80 mm on the 78.5 mm circumference, so a 10.5 mm strip stays free under the stem (15 runs at 4.4 mm pitch, the same 12 Ω). The stem stays inside the foam, a little colder than the barrel: it is the cold spot where the rubidium collects, never a window.
- Foam sleeve: a Ø10 mm hole for the stem; wrapped on, not slid.
- A second NTC at the stem base reads the cold spot. The rubidium vapour density follows the temperature of the coldest point, so this is the temperature that sets the optical depth.
- Printed former (STL changed): a channel 10 mm wide and 0.6 mm deep runs along the top of the bore, over the lead mark, from the cable end to 86 mm (just past the mid-plane). The stem slides along it with 1.1 mm to spare instead of 0.5 mm, which also allows for a printed bore that comes out a little undersize. The wall under the wire seats is still 1.0 mm. Both ends of the bore have a 1 mm entry chamfer. The winding groove is unchanged, so the field is unchanged.
- Test-fit: the 50 mm test coupon has the same channel along its whole length. Push the wrapped cell, stem up, through it before the cell goes into the wound former.
- Fit check in the files: a new view-only model, d1-cell-stack-reference.stl, shows the cell, stem, foam and Delrin tubes inside the former. The build script stops if any part touches the former, also along the stem's whole path from the cable end to the middle (all overlaps 0).
The winding: unchanged, and the stem must not pass through it. A stem through a hole in the winding was calculated (Biot–Savart on the true 42-turn helix, the wire bent round a hole of radius 3.5 to 5.5 mm). In the beam (within 3 mm of the axis) the field spread stays about 0.2 %, as without the hole; only near the glass under the stem does it reach 1 to 4 %. So the field is not the problem. The problems are that the cell could no longer be slid in after the winding, and that a stem sticking out of the heater becomes the coldest point and lowers the rubidium density.
If the vendor can only make a taller stem
| Stem height | Former bore / outside | Field spread over the cell | Innermost shield bore |
|---|---|---|---|
| up to 4 mm (our design) | Ø34 / Ø38 | 0.20 % with 3 end turns (0.15 % with 4) | Ø46 |
| up to 6 mm | Ø38 / Ø42 | 0.24 % → 0.18 % with 4 end turns | Ø50 |
| up to 10 mm | Ø46 / Ø50 | 0.33 % → 0.17 % with 5 end turns | Ø58 |
A larger bore means a larger winding radius, a slightly less uniform field (a few more end turns fix it) and a larger shield, because the winding keeps its clearance to the innermost layer. The shield size is still to be confirmed with its maker, so a taller stem is possible but costs a bigger shield.
Printed files changed: d1-former-petg.stl, d1-former-test-coupon.stl and their 0.65 mm seat variants (stem channel, entry chamfers), the new d1-cell-stack-reference.stl, sas-cell-cover.stl (closed top) and sas-cell-assembly-reference.stl (real cell shape). The SAS cradle and straps, the spacer rings and the shield cradle did not need a change.
All numbers come from the DIY build scripts and are re-checked by the DIY audit (80 checks, 0 failed, including sections of the printed former's STL). The D2 drawings, the heater pattern and the 3D build simulator of D1 (stem, rubidium droplet at its base, heater gap) are updated.
Sources: Thorlabs GC19075-RB drawing (24094-E0W) · Precision Glassblowing, rubidium vapor cell quartz (photo)
Q25 Our shield is bigger than the Spain-style module: what beam height should the whole bench use?
One beam height for every part: 100 mm (decided and applied everywhere on 11 Oct 2026). The 40 mm that was written in the equipment list (M03), in DIY D9 and D10 and in the 3D bench came from the illustrative bench and does not work with our shield.
| Check | Number |
|---|---|
| Shield outer radius (outer layer and caps, assumed sizes) | about 35 mm |
| Degaussing coil groups outside the shield (D4) | out to about 41 mm from the axis |
| Beam height needed for the shield, its cradle and the coil | at least about 60 mm |
| At 40 mm | the shield bottom would be 5 mm above the table and the coil groups below it: impossible |
| At 100 mm | the shield bottom is 65 mm above the table, room for a cradle and the coil |
The other parts at 100 mm
- The ½-inch posts in the list (TR75/M in PH75/M holders) reach about this height with the usual mounts. Check each mount's centre height and cut or choose posts to suit.
- SAS cell holder (D11): post height = 100 − 20 = 80 mm.
- AOMs on the D9 platform: set the aperture to 100 mm with the post, then shim.
- Fibre collimator, cubes, wave plates, Glan-Taylor, photodiodes: all on posts, so any common height works.
- Shield: the printed cradle of DIY D1 (d1-shield-cradle.stl, BOM M06), axis at 100 mm, touching the shield only between the three outside degaussing groups.
A second point the height check turned up: the end-cap holes. The beam goes along the axis, so the Ø20 mm hole in the middle of each end cap is the beam's hole. The coil leads, the cell cables and the degaussing bundle cannot share it without crossing the beam. The caps now get a Ø14 mm beam hole on the axis and a Ø12 mm cable hole 16 mm off the axis, lined up in all three caps at both ends (cable end: coil leads, cell cables, fluxgate cable and degaussing bundle; far end: degaussing bundle).
Why the Spain-style bench can be lower: their cell module is a small enclosure, so its axis can sit close to the breadboard.
Does 100 mm cost more? No. The posts already in the list (TR75/M in PH75/M holders, 60 sets) are the ones for this height; a 40 mm bench would have needed shorter posts and holders instead. The shield cradle is printed or cut from Delrin. ½-inch posts at 100 mm are stiff enough for mirrors, cubes and the AOM platform; the heavy shield sits on its own wide cradle bolted to the breadboard.
Does the EIT cell need its own enclosure at 100 mm? No. The shield with its end caps already is the cell's enclosure: it keeps room light out (light enters only through the Ø14 mm beam holes), it holds the heat together with the foam and the former, and it stops air currents at the cell. What is needed:
- Short black beam tubes (SM1 type) from the last optic to the end cap, and from the far cap to the Glan-Taylor and the detector, so no stray light reaches the detector along the beam.
- Taller covers over the AOM arms (D10): they were drawn 80 mm high for a 40 mm beam. At 100 mm the inner height must be about 160 to 200 mm.
- An optional draught cover over the shield, if the room has strong air flow: black hardboard, inner size about 350 × 120 × 170 mm (the shield is 282 mm long plus the caps and the degaussing loops, and its top is about 140 mm above the table). It must contain no steel: no steel screws, brackets or hinges.
Q26 How do we make sure every optical part stands at 90° (vertical and square to the beam)? Is it practically doable?
Yes, and it is routine. Nobody measures 90° with a protractor or a bubble level. The beam itself is the ruler. The standard practice in optics labs has two stages. First, one beam is made parallel to the table at a fixed height (100 mm on our bench) with two mirrors and two irises ("beam walking"). Then every optic is squared to that beam by looking at where its own reflection goes. Both checks are far more sensitive than any angle you could set by eye.
Stage 1: one straight, level beam (panels A and B) 1. Screw two irises (BOM O11, ID12/M) into one row of table holes, both set to the same 100 mm centre height with one height gauge: the same post and holder type, a calliper and slip-on post collars. Put I1 near the steering mirrors and I2 as far away as the table allows. 2. Mirror M1 puts the spot on I1, mirror M2 puts it on I2. Repeat until the beam passes both closed-down irises. The first mirror mostly sets the position, the second mostly the angle, so alternating converges. 3. The beam is now on the hole row and level. The error is simply angle × distance: 1 mrad (0.057°) gives 1 mm per metre, which you see at once on the far iris. 4. The irises stay in place as the permanent reference of that axis. Each 90° turn (a mirror or the PBS) gets its own pair of irises on the next hole row.
Stage 2: square each part to the beam
| Part | How it is set | How it is checked |
|---|---|---|
| Posts and holders | same post, holder and collar type for every part, height set with the calliper | the beam passes the reference irises after the part is put in |
| Steering mirrors | beam walking (stage 1) | no extra check: the two irises fix their angle |
| Wave plates, Glan-Taylor, cube faces, cell windows | turn the mount until the weak reflection from the face goes back through the iris hole (panel C) | a tilt θ moves the return spot by 2θL: at L = 0.5 m, 1 mrad gives 1 mm |
| PBS cubes (roll about the beam) | turn the cube in its holder until the reflected beam stays at 100 mm (panel D) | a roll of 1° lifts the reflected beam 17 mm per metre: easy to see |
| Lenses | centred so the far spot does not move when the lens is put in or taken out | back reflection from the lens surfaces centred on the iris |
| AOMs | aperture at 100 mm with the post, beam through the 2 mm aperture | Bragg angle by the most first-order power (D9 micrometer), not by a protractor |
| Detector | spot centred on the diode with the IR card or the camera | signal maximum |
How exact does it have to be? Much less exact than the checks can show. Tilting a plate by 1° changes its path length through the glass only by 1 − cos 1° = 0.015 %. The things that matter are that the beam stays centred on the small apertures (2 mm AOM aperture, the irises, the 14 mm beam holes in the shield caps), that the control and probe overlap in the cell, and that no reflection goes straight back to the laser. The back-reflection check reaches about 1 mrad. Wave plate and polarizer axes are set by rotating them for a power minimum or maximum, not mechanically.
A deliberate exception. After squaring, the cell windows and some plates are often tilted by a small angle on purpose, so that their reflections miss the beam path and do not form etalons or reach the laser. Our free-space isolator (L06) protects the laser in any case.
Practical points
- 795 nm is only faintly visible. Use the IR viewing card or the camera the lab already owns, wear the laser goggles, and turn the laser current down to a few mW while aligning. Block stray reflections, keep the beam at 100 mm (well below eye level), and take off watches and rings.
- Start at the laser and work outward, one part at a time. After each part, check that the beam still passes the reference irises.
- Printed holders (D11, D12) are made square by their datum walls; their acceptance test is the reflected spot drift (less than 0.5 mm at 2 m after a day).
Sources: Edmund Optics, Laser alignment activity 1 (beam walking with two mirrors and two irises) · Stony Brook Laser Teaching Center, Understanding "walking the beam" · UW Clean Energy Institute, alignment guide (two irises at the same height) · KAUST laser alignment guidelines (safety)
Q27 How do we calculate the distances between the optical parts?
Most distances on our bench are free. Only a few are fixed by optics, and those can be calculated. After the collimator the beam is collimated with a Rayleigh range of about 4 m (z_R = π w₀² / λ), so over a 2 m bench its diameter grows by less than 10 %. The distances between mirrors, wave plates, cubes and the isolator therefore do not change the physics. They are set by the size of the mounts, the 25 mm hole grid, and the rule that the beam must fit every aperture.
Try it: the distance calculator does all of the steps below with our parts, shows every formula, and lets you change the numbers. Its maths is checked by a test script (32 checks against Thorlabs' worked examples, the G&H rise times, ray traces and a numerical integration).
| Distance | Fixed by | Our value | How exact |
|---|---|---|---|
| AOM → cat's-eye lens | lens focal length f | 100 mm | loose: 10 mm off moves the return beam by under 1 µm for our ±200 kHz scan |
| cat's-eye lens → retro mirror | f (mirror at the focus) | 100 mm | the critical one: 1 mm off makes the return beam converge like a 5 m lens |
| telescope lens → lens (control expander) | f₁ + f₂ | 50 + 100 = 150 mm | set so the output beam has the same size near and far |
| collection lens → photodiode | the spot must fit the chip | about 40–50 mm | loose: the 3.6 × 3.6 mm chip takes a spot of a millimetre |
| control path − probe path (split → cell) | laser linewidth | within about 0.5 m | 1 MHz linewidth: 0.48 m keeps 99 % of the two-photon drive narrow |
| between flat optics | mounts, holes, apertures | free | the beam must fit each aperture; mounts must not touch |
| the two alignment irises | accuracy wanted | as far apart as possible | angle error about 2e/L (e = centring error) |
The calculation, step by step 1. Beam from the fibre collimator: D = 4 λ f / (π MFD) (Thorlabs). With the planned 11 mm collimator and a PM780 fibre (MFD 5.3 µm): D = 2.1 mm. 2. Beam along the path: w(z) = w₀ √(1 + (z/z_R)²); a lens changes the beam through its ABCD matrix. A round aperture of radius a passes 1 − exp(−2a²/w²) of a beam of radius w: an aperture 1.5 × the beam diameter passes 98.9 %. 3. Double-pass cat's eye: AOM → lens = f and lens → mirror = f. The two orders are f × λ f_RF / v = 1.51 mm apart at the mirror, and a 1 mm beam focuses to about 0.10 mm there, so a razor blade between them blocks the 0th order cleanly. The ABCD matrix of the arm shows why the mirror distance is the critical one. A mirror δ beyond the focus returns a converging beam (like a lens of f²/2δ: 5 m for 1 mm). An AOM-to-lens error only moves the return beam by 2 (f − d) λ Δf / v (0.76 µm for 10 mm and ±200 kHz). 4. The two arms: both beams come from one laser, so its phase noise cancels only if they arrive together. The share of the two-photon drive that stays narrow is exp(−2π Δν ΔL / c) (Lorentzian laser, as in delayed self-heterodyne theory). At 1 MHz that is 99 % for ΔL = 0.48 m. 5. Rise time of the AOM pulses: about 0.64 D / v, that is 150 ns per mm of beam in TeO₂ (G&H drawing: 65 ns at 0.4 mm).
What the calculator found for our plan: the beam is bigger than the equipment list assumes. The planned collimator (BOM L05, CFC11A-B) gives about 2.1 mm (Thorlabs' own table also gives 2.1 mm), not 1.5 mm. With the fibre's MFD tolerance (5.3 ± 1.0 µm) it can be anywhere from 1.8 to 2.6 mm. In the AOM's 2.5 × 2.0 mm aperture about 93 % of a 2.1 mm beam passes on each pass (a first-order estimate). The rise time is about 0.32 µs, still fine for microsecond pulses. Options, not yet decided:
- a collimator with f ≈ 7.5–8 mm (about 1.5 mm beam);
- a 2:1 telescope in front of the AOM arms;
- first measure the real beam with the lab camera, then decide.
Setting the fixed distances on the bench
- A focal length is measured from the lens's principal plane, not from the mount face. For an achromatic doublet, use the back focal length from its data sheet (the distance from the last glass surface) for the first placement.
- Then fine-tune optically:
- Cat's-eye mirror: move it until the returned beam has the same size far away (2–3 m) as the incoming beam. - Telescope: change the lens gap until the output beam has the same size at 0.5 m and at 3 m (IR card or camera).
- Path lengths: measure with a tape along the beam. A double-pass arm counts twice.
Sources: H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966) (Gaussian beams, ABCD) · S. A. Self, Appl. Opt. 22, 658 (1983) (focusing) · Thorlabs CFC-11X-B sheet (collimator formula and table) · Thorlabs PM fibre table (PM780-HP MFD 5.3 ± 1.0 µm at 850 nm) · G&H 3080-125 outline drawing 97-01598-01 rev D · Donley et al., Rev. Sci. Instrum. 76, 063112 (2005) · T. Okoshi et al., Electron. Lett. 16, 630 (1980) and L. E. Richter et al., IEEE J. Quantum Electron. 22, 2070 (1986) (delayed self-heterodyne)
Q28 How is the magnetic shield of the Spain-style EIT cell probably made? It looks like a small enclosure.
Most likely a compact cell module: a short, small-diameter shield (one or two layers, closed ends) inside the white 3D-printed housing, with the coil and the heater wound round the cell inside it. This is a reading of one photograph, not a confirmed design: the shield itself is not visible.
What the photo does show:
- A white 3D-printed housing with red leads for the heater and the coil, and nothing larger round it. A long three-layer tube like ours (Ø70 × 250 mm) would be obvious.
- A HEATER supply at about 2.40 V and 0.50 A (about 1.2 W, plain DC, no temperature loop visible).
- A COILS supply at about 1.00 V and 80 mA, so the coil is about 12.5 Ω: many turns of thin wire, a short solenoid.
Why a small shield works:
- The shielding factor of a closed cylinder grows as μ·t / D (wall thickness over diameter), so a narrow tube shields better for the same metal.
- Closed mu-metal ends act like mirrors for the coil inside, so a short solenoid in a short closed shield still gives a fairly uniform field. That is how compact vapour-cell modules are built.
- It is cheap: little mu-metal, and a printed housing that also holds the cell and the windows.
Plain DC heater current: a constant heater current makes a constant field, which only adds to the bias. It becomes a problem when a temperature loop changes the current; that is why our heater is bifilar (D2) and runs in a loop.
What this means for our design: we built for 0.1 mG stability and a cell field error of 0.2 %, which needs the long three-layer shield, the 42-turn solenoid with end turns, and degaussing. A compact module like theirs is simpler and cheaper and gives clear EIT, but with a broader, less reproducible line, and its temperature drifts without a loop. A compact version of ours (for example two layers, inner bore about Ø40 mm, about 120 mm long with caps) is possible, but the field uniformity would have to be recalculated with the end caps included before choosing it.
Q29 Can we make the mu-metal shield ourselves: roll a sheet into a cylinder and close it with (3D-printed) end caps?
Rolling works only if the shield is annealed afterwards, and a printed end cap is not a magnetic end cap. Mu-metal gets its permeability from a hydrogen anneal (about 1100 to 1150 °C). Bending, cutting, punching or welding after the anneal lowers the permeability many times over in the worked metal. A plastic cap only holds things in place: magnetically the end stays open, and the axial field (the field our 50 mG bias adds to) is the one an open end lets in most.
Rough estimate for one closed cylinder, Ø46 mm, against a field across it: S ≈ 1 + μ·t / D (shielding factor S, wall thickness t, diameter D, permeability μ).
| One layer | μ (assumed) | S |
|---|---|---|
| 1 mm sheet, formed, then hydrogen-annealed | about 20 000 | about 400 |
| 1 mm sheet, rolled by hand, not annealed | about 2 000 | about 40 |
| 0.1 mm annealed foil, wrapped gently, not re-annealed | about 5 000 | about 10 |
Three layers multiply these roughly, if the gaps between them are a few millimetres. The values of μ are typical figures, not data for a particular alloy, so measure the result.
What works
- Best: buy the shield annealed and finished (BOM C05), with caps, a Ø14 mm beam hole on the axis and a Ø12 mm cable hole 16 mm off it. Give the maker the inner bore (at least Ø46), the inner length (at least 250) and the hole positions.
- Workshop route: a sheet-metal shop rolls the layers and caps from mu-metal sheet, overlaps the seam, spot-welds it, and then a heat-treatment service anneals them in hydrogen. After that, do no more cutting or bending, and do not drop the layers.
- DIY without annealing: wrap annealed foil gently (large radius, no creases), overlap the seam by 20 to 25 mm, and hold it with Kapton tape or brass or nylon screws, never steel. It works, but it is much weaker; measure it with the fluxgate (D7) before you trust it.
Seam and caps
- The seam is an overlap, not an end cap: at least 20 × the thickness, pressed flat, magnetically continuous along the whole length.
- The caps must be mu-metal too: a disc with a collar that overlaps the tube by 10 to 15 mm, with the Ø14 mm beam hole in the middle and the Ø12 mm cable hole beside it.
- 3D-printed parts are fine as holders: printed rings that keep the three layers concentric with about 4 mm gaps, and printed cap frames that press a mu-metal disc against the tube end. They hold the metal; they do not shield.
Check: after assembly and degaussing (D4), measure the residual field at the cell with the fluxgate plate. Then turn the whole shield in the room and read it again: the reading should change by less than about 0.1 mG.
Q30 Which DC source should drive the solenoid, and how do I wire the second ITC502 laser output for it? (Is the Rigol DP832A needed?)
Not needed: use the free laser half of the second ITC502, wired like a laser diode with its cathode grounded. A battery with a resistor is the cheap back-up.
Requirement. The EIT line is about 7 kHz wide, and the field shifts it by 1.4 kHz per mG, so the line is about 5 mG wide. Keeping the field stable to about 0.1 mG (10 nT) shifts the line by only 140 Hz, which is 0.2 % of the 50 mG bias. The solenoid current is small (B = µ0·n·I: about 2 mA for one layer of 0.5 mm wire, tens of mA for several layers), so the allowed noise and drift are only a few to a few tens of microamps.
| Option | Noise and drift | Verdict |
|---|---|---|
| ITC502 laser half (unit 2) | 1.5 µA rms noise, 10 µA drift per 24 h, 0–200 mA, compliance above 6 V, low-noise by design | first choice, no cost: the TEC half of the same unit runs the cell heater; check the solenoid resistance (under about 300 Ω at 20 mA) and set the current limit low |
| Battery + low-TC resistor (+ trimmer) | microvolt-level noise, no mains pick-up; drift from the battery voltage and the resistor | cheapest back-up; measure the current with a multimeter, and let it settle |
| Home-built current source (op-amp and MOSFET, DIY Section part D5, or for example an LT3092) | very low noise if built carefully | cheap, needs a little electronics |
| Rigol DP832A (3 channels) | linear supply with mV-level ripple; the current-mode noise and the 1 mA setting steps were not checked | works, but expensive and coarse (1 mA steps are 5–50 % of a 2–20 mA current) |
| Multicomp 72-2710 and similar | 3 mArms ripple | no: larger than the current itself |
Wiring the ITC502 laser output. From the ITC500 manual, the laser output is a 9-pin D-sub: pin 8 = laser anode, pin 7 = laser cathode, pin 3 = ground of the laser output, pins 9 and 6 = laser voltage sense (anode, cathode), pins 2 and 4 = monitor diode, pins 1 and 5 = interlock.
| Step | What to do |
|---|---|
| Solenoid | one end to pin 8, the other end to pin 3; set the polarity button LD POL to CG (cathode grounded). The 4-wire voltage readout is optional (pin 9 to the + end, pin 6 to the − end of the coil) |
| Interlock | link pin 1 to pin 5 (a short is allowed, under 100 Ω); without the link the output cannot be switched on |
| Monitor diode | leave pins 2 and 4 open, keep the bias voltage off (PD POL, SW4 up) |
| Mode | constant current (SW1 up) |
| Current limit | set the hardware limit ILD LIM with the 25-turn ADJ pot, a little above the working current; connect the coil with the output off |
| Cable | twisted pair in a shield, shield grounded |
Numbers that matter. Range 0 to ±200 mA, compliance above 6 V (so the coil must be under about 300 Ω at 20 mA), set-point resolution 10 µA from the front panel (3 µA remote), accuracy ±100 µA, noise and 50/60 Hz ripple under 1.5 µA rms each, drift under 10 µA per 24 h, transients under 0.2 mA.
Design the coil for 10–20 mA, not 2 mA. B = µ0·n·I, so 50 mG needs n·I of about 4 A·turns per metre. One close-wound layer of 0.5 mm wire (2000 turns per metre) needs only 2 mA, where the 10 µA step and the 10 µA drift are 0.5 % of the current (0.25 mG). At 10–20 mA (200–400 turns per metre, so a winding with gaps between the turns, or thinner wire with fewer turns) the same 10 µA is 0.05–0.1 %, well inside the 0.1 mG target. The displayed current is only accurate to ±100 µA, so calibrate the field against the current with the fluxgate (and best of all with the atoms: 1.4 kHz per mG). The home-made coil of the DIY Section (part D1) has 42 turns on a 160 mm former, 3.4 mG per mA, so 50 mG needs 14.7 mA.
Switching. Switch the output on and off slowly and not while measuring: the output transients are up to 0.2 mA. Heater (TEC) and solenoid (laser output) are independent sections of the same box.
Effect on the BOM. If the ITC502 route works, BOM C08 (Rigol DP832A) and, with the heater on the TEC half, C04 (TC300B) can be dropped. This has not been applied; test the solenoid and the heater on the bench first, with the fluxgate inside the shield.
Q31 Can a home-wound solenoid really give 3.39 mG per mA, and how and where do we measure it?
Yes, close to it, and the exact value does not have to be reached: it has to be measured. 3.39 mG/mA is the calculated field per milliampere of our 42-turn coil (DIY D1) in free space. It depends only on the number of turns and the coil geometry, so a careful winding gets within a few percent. Inside the µ-metal shield the value changes (the shield carries part of the return flux), which is why D1 says "calibrate in the shield". The experiment never needs exactly 3.39: it needs to know the field, so that the RF difference can be matched to it (or the current to the RF difference).
What can make it differ, and by how much
- Number of turns: counted while winding, so exact.
- Coil radius and length: the printed former holds them to a fraction of a millimetre, a change of well under 1 %.
- The shield: can raise the field inside by a larger amount than the winding errors; only a measurement in the shield gives the real value.
- Uniformity matters more than the absolute value: 0.2 % over the cell, that is about 0.1 mG at 50 mG, which broadens the EIT line by about 0.14 kHz, small against its 10–30 kHz width.
How and where to measure (three steps, from rough to exact) 1. On the bench, before the shield (D1): put the fluxgate (FLC100, DIY D7) on the coil axis where the cell will sit. Step the current (for example 0, ±5, ±10, ±15 mA, both directions) and plot the field against the current. The slope is the coil constant in free space; reversing the current cancels the Earth's field and the sensor offset. 2. Inside the shield, after degaussing (D1 step 10, D4): replace the cell by the fluxgate plate (D7) at the cell position and repeat ±5, ±10, ±15 mA. This slope is the working value. The fluxgate reads differences well (noise about 0.03 mG) but its absolute accuracy is only about ±2 % and ±3 mG offset, so it gives the slope, not the absolute zero. 3. With the atoms, the final and absolute calibration: with the cell back in place and EIT running, sweep the probe RF channel and note where the EIT peak sits for several solenoid currents. The two-photon resonance moves by exactly 1.4 kHz of light frequency (0.7 kHz of RF difference) per mG, an atomic constant, so the peak positions give the field directly, and the current at which the peak sits at zero RF difference shows the residual field left by the shield.
In short: wind it carefully, measure the slope with the fluxgate in free space and in the shield, and let the atoms give the final number. Whatever value comes out, the current (about 15 mA for 50 mG) or the RF difference is adjusted to it.
Why the fluxgate goes in first and then comes out. The order on the bench (and in the D1 build simulator) is: shield closed, degauss, fluxgate plate at the cell position, calibrate mG per mA, then swap the plate for the cell stack, degauss again, heat the cell, and do the final calibration with the atoms. This is the usual practice for a magnetometer and a vapour cell that need the same spot:
- They need the same place. The sensor must sit where the atoms will be (centre of the solenoid, on the axis), and our bore holds either the cell stack or the sensor plate, not both.
- The sensor would disturb the measurement. A fluxgate drives its permalloy core with a kHz excitation current: a small AC field and a piece of magnetic metal next to the cell. It is fine for a calibration, not next to the atoms during EIT.
- What survives the swap and what does not. The coil constant (mG per mA) depends only on the winding, so it stays valid. The residual field does not: opening the caps to swap lets the Earth's field magnetise the layers again, which is why the stack goes in and the shield is degaussed a second time.
- The atoms are the final judge. The fluxgate offset is about ±3 mG, so the absolute zero and the final constant come from the EIT peak itself (1.4 kHz per mG, an atomic constant); the fluxgate gives the quick, independent first numbers and checks each later degauss when the cell is out.
Could it stay inside during the whole experiment? Not at the cell position: that place belongs to the cell. It could stay as a drift monitor a little away from the cell, with four conditions:
- Where: in the far-end Delrin tube, about 60 mm from the cell centre, off the axis so it stays clear of the beam (the 14 mm wide board fits beside the beam inside the Ø26.5 mm bore of the tube). It then reads the field there, not at the atoms: good for changes (drift), not for the absolute value.
- Test with the atoms first: a fluxgate drives its core into saturation at kHz, so it makes a small AC field of its own. Record the EIT line with the sensor powered and unpowered; if the position or the width changes, power it only between measurements.
- The cable: it adds about 7 mm² to the cable hole of the end caps, which is already close to full (see the DIY audit); with the thinner degaussing wire there is room.
- Temperature: the tube near the heated cell runs warm, and the sensor zero drifts with temperature (data sheet: below 2 nT per kelvin, 0.02 mG/K), so read it as a relative monitor.
During EIT the best field monitor is the atoms themselves: the EIT peak moves 1.4 kHz per mG, far more sensitively than the fluxgate.
Q32 Can the Stefan Mayer FLC100 be the fluxgate magnetometer with milligauss resolution?
Yes for the resolution; use it for differences, and check the supplier. The FLC100 is a small single-axis fluxgate sensor board (44.5 × 14 × 5.5 mm, 5 V ± 5 %, about 2 mA, differential analog output). Figures below are from the Stefan Mayer data sheet: range ±100 µT, ±1 V per 50 µT, noise below 0.5 nT rms or 3 nT peak-to-peak (0.1 to 10 Hz), DC to 1 kHz at −3 dB, zero drift below 2 nT per kelvin, accuracy ±2 % ± 0.3 µT at 20 °C. The Alibaba page itself could not be read. Ask Stefan Mayer for the calibration sheet.
| Need | FLC100 | Verdict |
|---|---|---|
| Resolution: 1 mG = 100 nT; the working field is about 50 mG = 5 µT | noise 3 nT peak-to-peak (0.1–10 Hz) = 0.03 mG: about 30 times finer than 1 mG | more than enough |
| Range | ±100 µT (±1 G): covers the shield interior and the 50 mG solenoid field, and even the Earth's field outside | fine |
| Bandwidth | DC to 1 kHz | fine |
| Absolute zero | accuracy ±0.3 µT (±3 mG) at 20 °C | not enough for the absolute residual field: use differences (coil current reversed, heater on and off, one degauss against the next), the end-for-end flip, and the atoms (1.4 kHz per mG) |
| Axes | one, along the long axis of the board | the 44.5 mm board fits the former only axially; a transverse field changes the total field only at second order (1 mG across 50 mG is 0.01 mG) |
Wiring (yes, you wire it yourself). The data sheet shows five solder pads on a 0.1 inch grid at the end of the board away from the detection coil; from top to bottom in the drawing: 0V, +5V, SYNC, OUT−, OUT+. The output is differential: OUT+ is read against OUT−, which is a 2.5 V reference, so use a floating multimeter across the two pads, never OUT+ against ground. The scale is 20 mV per µT, 2 mV per mG. Supply it from a quiet linear 5 V regulator. The pads, the supply, the cable and the holder are drawn in the DIY Section (part D7).
Cautions. (1) The zero offset and its drift decide how well you can null the field; flip the sensor end for end and average the two readings to cancel the offset. (2) The sensor and its leads must be kept clear of the shield and the solenoid while the shield is open; it fits through a port of about 16 mm or more. (3) It is a bare sensor: you need a 5 V supply, a stable readout (the oscilloscope or a 6½-digit multimeter) and a calibration against a known coil field. (4) A "new stock" listing on Alibaba is a counterfeit and old-stock risk (the manufacturer's page warns about replicas): order from Stefan Mayer Instruments or an authorised distributor and ask for the calibration sheet. (5) The data sheet does not say how the sensor tolerates the strong field of a degaussing coil: keep it unpowered during a degauss and check its offset afterwards.
Sources: Stefan Mayer FLC 100 data sheet · Stefan Mayer Instruments
The Quantum Spain-style bench
Q33 Is the Spain-style arrangement correct, in theory and in practice?
It is a correct Zeeman EIT chain, with three drawing faults (fixed) and several practical cautions. Everything rests on one photograph, so the real bench may differ.
What checks out (simulator run): control and probe orthogonal and co-propagating (opposite circular after the quarter-wave plates); 160.000 and 159.930 MHz after the double pass, so a 70 kHz difference equal to the ground-state splitting at 50 mG; the SAS lock closes; no light returns to the laser; control 0.75 mW (7.3 mW/cm², the paper used 1.3–5.5), probe about 2 µW; predicted optical depth 10 at 60 °C, linewidth about 34 kHz, contrast 0.96; no parts closer than 30 mm.
Three faults, now fixed
- The control beam expander had two lenses 40 mm apart: not a telescope. It is now f = 30 mm plus f = 100 mm, 130 mm apart (×3.3).
- The cat's-eye lenses in the AOM arms need f of about 75 mm (80 mm after the AOM, 70 mm to the mirror); the guide's parts list has only 100 and 50 mm lenses.
- The simulator hides a lock offset: the double-pass AOMs add +160 MHz and the SAS arm has no AOM. A real bench needs the lock moved by about 160 MHz (for example an AOM in the SAS arm); the photo does not show how.
Practical cautions
- Heater: 2.4 V at 0.5 A is about 1.2 W through a 3D-printed housing; reaching 60 °C is doubtful (PLA softens near 60 °C), and a plain DC heater wire makes a magnetic field that shifts the Zeeman line (use bifilar, or switch it off while measuring). No temperature sensor or controller is visible.
- AOM drive: Rigol generators give about +10 to +20 dBm, typical AOMs need about +27 to +33 dBm: amplifiers must exist off-camera.
- No lock box is visible; without a real lock the laser drifts and EIT disappears.
- A white plastic box is not a magnetic shield; Zeeman EIT is first-order field sensitive, so a µ-metal shield is probably inside.
- The blue PM fibres suggest fibre between the boards (about half the power lost, axis alignment needed); the simulator draws free space.
- No beam dumps or tubes are visible (laser safety).
- The AOM tilt is exaggerated to 8° in the drawing, hence the 160 mm from separator cube to AOM; a real build can be tighter but needs an iris or block for the zeroth order. Do not use the drawing as a build recipe.
Q34 What is the cell label TRT-Rb/Ne-10T-20x75 on the Spain-style EIT cell, and would it suit our bench?
It reads as a Triad Technology rubidium cell (natural Rb by Triad's naming) with 10 Torr of neon, 20 mm × 75 mm, most likely a custom order. The label was read from the YouTube videos of that bench and the maker (Triad Technology Inc.) was given by the owner of this guide; I cannot watch videos. “TRT-…” is not in Triad's public catalogue, which lists cells as TT-RB-75-V-x (natural Rb), TT-RB85-… and TT-RB87-…, in two sizes only (Ø25 × 75 mm Pyrex, Ø19 × 75 mm quartz), with neon and other buffer gases and custom cells available on request (Triad, Sacher brochure of Triad cells). Neither page defines “TRT”, so the reading of that prefix, and of the size, is an interpretation.
| Part | Reading | Confidence |
|---|---|---|
| TRT | a Triad series or order code for a custom cell | unknown |
| Rb | plain “RB” is natural rubidium in Triad's naming (72 % ⁸⁵Rb, 28 % ⁸⁷Rb); isotope cells are RB85 or RB87 | likely natural |
| Ne | neon buffer gas | clear |
| 10T | 10 Torr: the same fill as our EIT cell (C01) | likely |
| 20x75 | Ø20 × 75 mm (diameter × length; maybe outside length); Ø20 is not a Triad standard size | likely, probably custom |
What a cell like this does
- Neon at 10 Torr: broadens the D1 line by about 100 MHz (10 ± 1 MHz per Torr) and shifts it by about −11 MHz (−1.1 MHz per Torr) (Optics and Spectroscopy 2021). The shift is small against the 500 MHz Doppler width, but it is one more reason the lock reference (the cell without buffer gas) and the EIT cell differ by about 11 MHz.
- Diffusion: for Rb in Ne, D = 0.214 cm²/s at 1 atm and 24 °C (Pouliot et al., Phys. Rev. A 111, 033108). At 10 Torr and 45–60 °C this is about 17 cm²/s, which gives a lowest-mode decay of about 15 Hz for the whole cell and about 240 Hz for atoms leaving a 2.55 mm beam (about 3 kHz for a 0.75 mm beam). All are far below the EIT line (about 7 kHz), so 10 Torr is more than enough, for both cells.
- Natural rubidium is fine for this line. I summed all the D1 hyperfine lines of both isotopes (Voigt profiles, thermal populations). The ⁸⁷Rb F = 2 → F′ = 1 working line is about 1.7 GHz from the nearest ⁸⁵Rb line, so ⁸⁵Rb takes only about 5 to 20 % of the probe (optical depth 0.05 to 0.2) at 45 to 62 °C. The price of natural Rb is the low ⁸⁷Rb density (28 %).
- The length: the optical depth on the ⁸⁷Rb line scales with the path. Taking OD ≈ 10 at 60 °C for our 25 mm enriched cell, a 75 mm path needs about 62 °C for a natural cell (about 47 °C if it were enriched).
- The heater on the shelf: the HEATER supply reads about 2.4 V and 0.5 A (1.2 W). Scaling our loss estimate (about 2× the surface of our cell, loss proportional to the temperature excess) gives about 1.1 W at 47 °C and about 1.8 W at 62 °C. So the cell probably runs near 45 to 50 °C, where a natural cell has an optical depth of only about 2 to 4 on the ⁸⁷Rb line: clear EIT, but less contrast than the OD ≈ 10 of the published set-up. This is a guess: the insulation of their housing is unknown.
What it means for the magnetic field. A 75 mm cell needs a uniform field over 75 mm. Our 42-turn solenoid (0.2 % over 25 mm) would give 2.4 % over ±37.5 mm, 1.2 mG at 50 mG, which broadens the line by about 1.7 kHz (1.4 kHz per mG) against 7 kHz. To get 0.2 % over 75 mm one needs about 72 main turns (a groove of about 270 mm, a former of about 290 mm and a shield of about 400 mm). A compact Spain-style module probably accepts a broader line.
| Our cell (C01) | A 20 × 75 cell (natural Rb) | |
|---|---|---|
| Path | 25 mm (Ø25) | 75 mm (Ø20) |
| ⁸⁷Rb OD ≈ 10 at | 60 °C (enriched) | 62 °C |
| ⁸⁷Rb OD at 45–50 °C | about 3 (at 45 °C) | about 2 to 4 |
| Solenoid | 140 mm winding, shield 282 mm | about 270 mm winding, shield about 400 mm |
| Heater loss | about 0.9 W in the stack | about 2× the surface |
| Buffer gas | 10 Torr Ne | the same |
Verdict for our bench: keep C01 (the published Ø25 × 25 mm geometry, enriched ⁸⁷Rb, 10 Torr Ne). The buffer gas and pressure match, so nothing about their label argues against ours; a 75 mm cell would force a longer coil and shield and add little for continuous-wave EIT. A long cell would only be worth it for light storage with a stronger delay, or if a cheap natural-Rb cell is the only one available.
Is their cell specification theoretically correct for Zeeman EIT? As far as a label allows me to judge: yes, it is a sound choice, with three caveats. It is not a proof: the beam sizes, powers, coil and shield of that bench are not known.
| Point | Their cell | Theory | Verdict |
|---|---|---|---|
| Buffer gas | Ne, 10 Torr | the ground-state coherence must outlive the time atoms cross the beam; neon is gentle on it, and 10 Torr is the fill of the published cell. Diffusion limit about 15 to 240 Hz against a line of about 7 kHz | correct |
| Optical line | broadened by about 100 MHz | the Doppler width is 530 MHz and the excited-state splitting of ⁸⁷Rb D1 is 817 MHz, so the F′ levels stay resolved | correct |
| Isotope | natural Rb (by Triad's naming) | ⁸⁵Rb takes only 5 to 20 % of the probe at the working line, 1.7 GHz away; spin exchange between the isotopes is small against 7 kHz | works; ⁸⁷Rb density is 28 % |
| Optical depth | 2 to 4 at 45 to 50 °C (guess) | on resonance T = exp(−OD·(1 − contrast)); for OD 3 and contrast 0.8 about 55 % passes, against about 14 % for OD 10: a brighter, clearer window but a smaller delay | correct for demonstration, weak for storage |
| Length 75 mm | long | more atoms at lower temperature; but the field must be uniform over 75 mm | the weak point |
The three caveats
- Field uniformity over 75 mm is the real limit: a few per cent spread of the 50 mG field broadens the line by kilohertz (1.4 kHz per mG), as large as the line itself. A compact coil would give that.
- Natural Rb needs a higher temperature or a longer path for the same ⁸⁷Rb optical depth; at their heater power the optical depth is low.
- Contrast against power: with a pressure-broadened line a stronger control field is needed for the same transparency, which is why the published cell uses about 1 mW of control light.
To pin it down: ask Triad what “TRT” means (they can read it from their order records), and whether the cell is natural or enriched. A screenshot of the label from the video, with its time stamp, would also help.
About this guide
Q35 How does the lab inventory enter the costed BOM and the Spain-style cost?
A main switch, "Count what the lab already owns", on both cost views (equipment tab and the Spain-style bench). It is on by default and is kept in the browser. When it is on:
- every Lab Inventory item with status use and a "covers" BOM id is matched to the BOM rows by quantity (an item of 10 covers 10 units);
- fully covered rows are green, partly covered rows are light green with "n of N in the lab", and the covered units are taken off the totals (a separate line shows what the lab inventory covers);
- the Spain-style box counts the inventory against its own parts, and our bill of materials against the same inventory, so the comparison stays fair.
Rules and limits. Items marked "check" or "no" are not counted. An item that covers a row only in part is counted only for the units it can supply (for example 6 post holders against 60 post sets). The Credix SG-1710 is not counted against the dual-channel RF synthesizer, which needs two phase-locked channels. Mounts whose aperture is not measured yet (the Melles Griot set) are counted as 10 of the 11 mirror mounts; measure them. The prices stay behind the group password; the switch only changes how the totals are computed.
Q36 Can the Thorlabs PM100USB CAD file be used for the 3D pictures?
Used as a visual reference, not loaded directly. The SolidWorks part file (.sldprt) is a closed format and cannot be opened here. The Thorlabs web drawing (an eDrawings page) does open in a browser and shows the real shape: a ribbed aluminium extrusion with black end caps, the Thorlabs label on top, the sensor connector at one end and USB at the other. The guide's three.js model of the PM100USB now follows that look, with the S140C head on its cable beside it; the dimensions are estimated from the drawing, not measured.
It appears in the Lab Inventory (item I12), the equipment pictures and the power meter in both 3D benches. To use the exact CAD mesh, export it from SolidWorks as STL or glTF.