M. Gajda et J. Mostowski, 3-DIMENSIONAL THEORY OF THE MAGNETOOPTICAL TRAP - DOPPLER COOLING IN THE LOW-INTENSITY LIMIT, Physical review. A, 49(6), 1994, pp. 4864-4875
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.