Semiclassical calculation of the power saturation of the Kerr effect in Rb vapor. II: the effect of incomplete optical pumping

Rubidium vapor cells play a key role in contemporary quantum optics since they have strong nonlinear interactions with a low-power incident laser light. The simplest nonlinear interaction is the Kerr effect. Although most calculations concentrate on the unsaturated Kerr effect, the saturated Kerr effect has been measured in many materials including 85 Rb and 87 Rb vapor. Moreover, entanglement-generating vapor cells often operate in the saturated regime. Here, the calculation of the saturated Kerr effect for rubidium vapor at the D2 line uses a density matrix formulation that includes two hyperfine-split levels and all magnetic sublevels in each of the ground and excited states to account for incomplete optical pumping: the transit time of the atoms through the beam is too short to reach a final population distribution. The calculation shows a rapid qualitative change at low optical power, in semiquantitative agreement with experimental data.