0.7 or 1.4 kHz per mG? From the solenoid current to the two RF frequencies
Move the solenoid current. The ground sub-levels of Rb-87 (F = 2) spread apart, the Λ gap between the two EIT ground states grows twice as fast as one step, and the double pass of the AOMs halves it again on the RF side. The second slider sets the RF difference by hand, so you can see the EIT peak appear only when the two match.
1. Set the field
Field from the D1 solenoid constant measured in free space ( mG per mA; calibrate in the shield with the fluxgate, then with the atoms).
2. The chain of numbers
The two factors of 2 cancel: × 2 because the Λ spans two steps (Δm = 2), ÷ 2 because each beam passes its AOM twice. So the RF difference per mG is the same 0.7 kHz that the guide quotes for one step, but it is the Λ gap (1.4 kHz per mG) that the light must match.
3. What the atom does
Level shifts are drawn much larger than to scale (the full spread at 100 mG is only 280 kHz on a 377 THz transition). The excited F′ = 1 splits with g = −1/6; it does not enter the two-photon condition, because both beams end on the same m′.
4. Match the RF difference
Illustration: a 7 kHz wide EIT line (in two-photon detuning) on top of the Doppler absorption. In the lab the probe channel is swept slowly around its setting and the peak is found the same way. Which channel must be higher depends on the field direction and on which beam is σ⁺; if no peak shows, swap the sign.
5. One constant, three numbers
| What | per mG | at the present field |
|---|---|---|
| Neighbouring sub-levels, Δm = 1 (the number in Finkelstein et al. 2023) | 0.7 kHz | |
| Our Λ ground states, Δm = 2: the light difference needed | 1.4 kHz | |
| RF difference between the two AOMs (double pass, ÷ 2) | 0.7 kHz |