Polarization Selection Rules for Two-Photon Processes

Abstract

We consider two-photon absorption by a sodium atom from two lasers of frequencies υ1 and υ2, where υ1 and υ2add to give the frequency of the two photon transition υfg. It is well-known that the selection rules governing a 2S1/2 − 2S1/2 two-photon absorption when both υ1 and υ2 are far from resonance with any intermediate states, {|i>}, are ΔF = ΔmF= 0, [l]. This is true when |υ1 − υgi| is much larger than the fine and hyperfine structure splittings of {| i>} which are ~ 6 A and ~ 100 MHz respectively for the 3p intermediate states in the sodium 3s-5s transition. Consideration of the angular momenta of the levels involved leads us to expect selection rules ΔF= 0,± 1, ΔmF = 0, + 1 when |υ1 − υgi| is comparable with the fine structure splitting of the intermediate states and ΔF= 0,± 1, ± 2, ΔmF = 0, ± 1, ± 2, when |υ1 − υgi| is comparable with the hyperfine splitting, [2,3,4, 5]. We have experimentally examined the absorption of two photons circularly polarized in the same sense [5]. In the absence of a magnetic field or collisions this corresponds to ΔmF=±2. The previous discussion indicates that we would expect this absorption to drop close to zero when the detuning from the 32P3/2,1/2 intermediate states is greater than the hyperfine splitting of the state involve’d. However, this is not what we find in our experiment.