Experiments to Control Atom Number and Phase-Space Density in ...

Figure 2.22: Saturation absorption spectroscopy setup used for locking the laser frequency.
A slow sweep over the atomic transition yields the spectrum as shown. A fast
frequency dither is added to the pump beam. The spectrum and the dithering frequency
are mixed in a lock-in amplifier to generate the Doppler-free error signal. Away from the
transition a change in the pump frequency does not cause changes in the transmitted
power of the pump beam. Close to the transition small changes lead to large changes
in the transmitted signal. The final error signal is thus the Doppler-free derivate of the
spectrum detected by the photodiode. Figure courtesy of Gabriel Price.
2.12.2 Phase Modulation Spectroscopy
Phase-modulation (FM) spectroscopy is a second method frequently used to gen-
erate an error signal usable for locking the laser frequency. It is closely related to the
Pound-Drever-Hall technique usually utilized to lock cavities [45–50].
Consider the setup in figure 2.22 again. Rather than inserting an AOM into the
pump beam, consider adding an electro-optic modulator (EOM) into the path of the
probe beam. This EOM adds sidebands to the laser frequency at a frequency of ωm.
Taking only the two nearest sidebands into account, the electric field of the probe beam
after the EOM is given by
EFM = E0
2
J0(δ)e iωt +J1(δ)e i(ω+ωm)t −J1(δ)e i(ω−ωm)t +c.c., (2.43)
where δ ≪ 1 is the modulation depth, ω the laser frequency and J are Bessel-functions.
All three frequency components will interact differently with the atoms in the spec-
troscopy cell. Combining the absorption (αl) and the optical phase shift (dispersion)
32