Theoretical calculation of saturated absorption spectra for multi-level atoms

We have developed a model for calculating saturated absorption spectra for dipole transitions in multi-level atoms. Using a semiclassical density matrix formalism, we derive a set of coupled differential equations for the internal state of the atom in a standing wave light field. The equations are solved using standard integration techniques. The absorption at each laser detuning is found from an average of the absorption for a number of velocities along the laser field, thermally weighted. The method is relatively efficient computationally yet quantitatively predicts important details of saturated absorption spectra including saturation, crossover resonances, merging of absorption lines at high intensity and optical pumping between hyperfine levels. We have measured saturated absorption and fluorescence spectra of 85Rb, and compare to our computational results for a 36-level model.