Quantum calculations for one-dimensional laser cooling: Temporal evolution

Temporal integration of density-matrix equations with quantized translational motion gives alternative results for laser cooling of atoms. For polarization gradient cooling, the average kinetic energy in the cold-atom peak after 1000 radiative lifetimes decreases with increasing ${\mathit{F}}_{\mathit{g}}$, and is <1 recoil energy at low laser intensity. With magnetically induced laser cooling (MILC) and low optical pumping rates, atoms cool slowly within the potential wells, giving minima in the velocity distribution at ν=0. MILC is seen as a cyclic process; optical pumping cools and B-field mixing slightly heats.