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Relaxation mechanisms affecting magneto-optical resonances in an extremely thin cell: experiment and theory for the cesium D$_1$ line

We have measured magneto-optical signals obtained by exciting the $D_1$ line of cesium atoms confined to an extremely thin cell (ETC), whose walls are separated by less than one micrometer, and developed an improved theoretical model to describe these signals with experimental precision. The theoretical model was based on the optical Bloch equations and included all neighboring hyperfine transitions, the mixing of the magnetic sublevels in an external magnetic field, and the Doppler effect, as in previous studies. However, in order to model the extreme conditions in the ETC more realistically, the model was extended to include a unified treatment of transit relaxation and wall collisions with relaxation rates that were obtained directly from the thermal velocities of the atoms and the length scales involved. Furthermore, the interaction of the atoms with different regions of the laser beam were modeled separately to account for the varying laser beam intensity over the beam profile as well as saturation effects that become important near the center of the beam at the relatively high laser intensities used during the experiments in order to obtain measurable signals. The model described the experimentally measured signals for laser intensities for magnetic fields up to 55~G and laser intensities up to 1~W/cm$^2$ with excellent agreement.