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

We present a detailed theoretical investigation of the absorption spectrum of a probe beam after transmission through a one-dimensional optical molasses obtained with circularly cross-polarized counterpropagating pump beams (corkscrew molasses). The study is performed for a ${\mathit{J}}_{\mathit{g}}$=1→${\mathit{J}}_{\mathit{e}}$=2 atomic transition and the external degrees of freedom are described by means of a Fokker-Planck equation in the regime where the stationary momentum distribution lies within the range of linearity of the cooling force. We analyze the stimulated Raman transitions occurring between differently populated and light-shifted ground-state Zeeman sublevels. In the case where the probe beam has the same polarization as the copropagating cooling beam, an additional narrow Rayleigh resonance appears for a probe frequency close to the pump frequency. Its width is equal to 2α/M, where α is the friction coefficient of the cooling force and M is the atomic mass. In the case where the probe beam has the same polarization as the counterpropagating cooling beam, a central recoil-induced resonance is expected. Its width is related to the Doppler width of the optical molasses.