Nonlinear interactions of multilevel atoms with a near-resonant standing wave

Using a semiclassical density matrix formalism we have calculated the behav ior of multilevel atoms interacting with a standing wave field, and show ho w complex nonlinear phenomena, including multiphoton effects, combine to pr oduce saturation spectra as observed in experiments. We consider both 20-le vel sodium and 24-level rubidium models, contrasting these with a simple 2- level case. The influence of parameters such as atomic trajectory and the t ime the atom remains in the beam are shown to have a critical effect on the line shape of these resonances and the emission/absorption processes. Stab le oscillations in the excited state populations for both the two-level and multilevel cases are shown to be Limit cycles. These limit cycles undergo period doubling as the system evolves into chaos. Finally, using a Monte Ca rlo treatment, these processes average to produce saturated absorption spec tra complete with power and Doppler broadening effects consistent with expe riment. [S1050-2947(99)00406-0].