Predictions of laser-cooling temperatures for multilevel atoms in three-dimensional polarization-gradient fields

We analyze the dynamics of atom-laser interactions for atoms having multiple, closely spaced, excited hyperfine manifolds. The system is treated fully quantum mechanically, including the atom's center-of-mass degree of freedom, and motion is described in a polarization gradient field created by a three-dimensional laser configuration. We develop the master equation describing this system, and then specialize to the low-intensity limit by adiabatically eliminating the excited states. We show how this master equation can be simulated using the Monte Carlo wave function technique, and we provide details of how to implement this procedure. Monte Carlo calculations of steady state atomic momentum distributions for two fermionic alkaline earth isotopes, $^{25}$Mg and $^{87}$Sr, interacting with a three-dimensional lin-$\perp$-lin laser configuration are presented, providing estimates of experimentally achievable laser-cooling temperatures