Wigner-function approach to laser cooling in the recoil limit

Abstract

We derive an equation of motion for the center-of-mass Wigner function (WF) of a two-level atom interacting with a linearly polarized, monochromatic standing plane wave of light. The derivation is based on a truncation of the spatial Fourier expansion of the WF and is consequently valid only at low intensities of the driving light, but no assumption regarding the size of the recoil velocity need be made. The stationary state of laser cooling is studied analytically and numerically. The asymptotic velocity distribution at large velocities is found to obey a power law, with a power independent of the linewidth of the optical transition.