Abstract

In the limit of asymptotically small photon momentum, a Fokker–Planck equation for the center-of-mass Wigner function suffices to describe laser cooling of an atom. We have devised a procedure to compute the light pressure force and the diffusion tensor for an atom with an arbitrary level structure, traveling with an arbitrary velocity in any given three-dimensional light field. The scheme is based on solving a set of differential equations closely related to the density matrix equations of motion encountered in conventional recoilless laser spectroscopy. Computer programs have been written that automatically construct and solve the required equations from broad specifications of the problem, such as energies and angular momenta of the atomic levels. A Langevin equation stochastic simulation has been implemented to solve the Fokker-Planck equation of laser cooling using the computed force and diffusion. Comparisons of optical-molasses experiments and simulations carried out for a model sodium atom with a J = 2→J = 3 transition show qualitative similarities such as sub-Doppler limit temperatures, but the quantitative agreement of theory and experiment is not satisfactory.

© 1990 Optical Society of America