Atom-field interactions: Density-matrix equations including quantization of the center-of-mass motion

Master equations are derived for the time evolution of density-matrix elements characterizing atoms interacting with classical radiation fields that drive transitions between electronic-state manifolds of levels. The atomic center-of-mass motion is quantized and recoil accompanying absorption, stimulated emission, and spontaneous emission is included. An adiabatic elimination of the optical coherences is used to obtain quantum rate equations for ground- and excited-state density-matrix elements. Subsequent adiabatic elimination of excited-state density-matrix elements results in rate equations for the slow evolution of ground-state density-matrix elements. It is shown that recoil during spontaneous emission mixes spatial and internal atomic degrees of freedom.