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

Using a semiclassical density matrix formalism we have calculated the behavior of multilevel atoms interacting with a standing wave field, and show how complex nonlinear phenomena, including multiphoton effects, combine to produce saturation spectra as observed in experiments. We consider both 20-level sodium and 24-level rubidium models, contrasting these with a simple 2-level case. The influence of parameters such as atomic trajectory and the time 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. Stable 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 Carlo treatment, these processes average to produce saturated absorption spectra complete with power and Doppler broadening effects consistent with experiment.