We present a simple Fokker-Planck model for the evolution of the number of atoms and the spatial distribution in a ${\mathrm{CO}}_2$ laser trap which is loaded from a magneto-optical trap (MOT). Deep ${\mathrm{CO}}_2$ laser traps can achieve very high densities, but reach equilibrium slowly compared to shallow traps. Equilibrium times range from milliseconds for shallow traps to seconds in traps which are deep compared to the thermal energy. A universal function for the maximum number of trapped atoms is given, assuming that the optical dipole trap reaches thermal equilibrium with the MOT.

• Received 20 July 2000

DOI:https://doi.org/10.1103/PhysRevA.63.043403