3-DIMENSIONAL THEORY OF THE MAGNETOOPTICAL TRAP - DOPPLER COOLING IN THE LOW-INTENSITY LIMIT

We derive a Fokker-Planck equation for the center-of-mass Wigner funct ion of an atom moving in a Zeeman neutral-atom trap. The Zeeman struct ure of atomic sublevels is taken into account. Our analysis is limited to optical transitions between two sets of sublevels corresponding to angular momenta j(b) = 0 and j(a) = 1. Expressions for the light pres sure, friction, and diffusion forces in the case of low intensity of t he laser light are presented. An analytical solution for the stationar y center-of-mass Wigner function as well as the size and geometry of t he trap are found and discussed.