Multipole radiation forces on atoms in laser fields of arbitrary polarization

This paper reports on the techniques of cooling atoms by near resonant laser radiation down to kinetic energies as small as the energy width hγ of the excited state that have enabled the observation of the dynamics of very slow atoms in laser fields. Surprisingly it was found than at these small velocities additional optical damping mechanisms lead to a further decrease of the momentum width, comparable to the range of a few photon recoil momenta. This damping was found to depend on the polarization gradients imposed by the coherent superposition of several cooling beams. For 1-D optical molasses it was shown that the spatial modulation of the polarization leads to a motion-induced retarded modulation of the population of the Zeeman sublevels. The authors extend the analysis of the internal ground state dynamics to 2- and 3-D cooling schemes. To this end it is convenient to eliminate density matrix elements corresponding to the excited states and the optical coherences from the equations of motions