Probe transmission in one-dimensional optical molasses: Theory for linearly cross-polarized cooling beams

We present a detailed theoretical investigation of the transmission spectrum of a probe beam interacting with atoms in a one-dimensional optical molasses obtained with linearly cross-polarized counterpropagating pump beams. The study is performed for a J₆=1/2J₄=3/2 atomic transition in the limit where the Hamiltonian part of the atom-field coupling is predominant over the relaxation part. We analyze the stimulated Raman transitions occurring between different vibrational levels of the atoms in the periodic potential created by the light shifts, and we show a dramatic lengthening of the damping time of coherences between such levels due to the Lamb-Dicke effect. Very narrow Rayleigh resonances with a shape sensitive to the probe polarization appear for a probe frequency close to the pump frequency. We interpret these resonances in terms of scattering of the pump waves on density and magnetization gratings, and show that they provide important information about the dynamics and localization of atoms at the bottom of the potential wells. Such information should also be accessed by phase-conjugation experiments. Finally, indications on the treatment of other atomic transitions are given.