Bipolar harmonics method in the semiclassical theory of sub-doppler cooling

Abstract

The bipolar harmonics method is extended to the case of complex elliptic polarization vectors. The method is used to study, on the basis of the semiclassical theory, the multipole moments of the ground state of atoms under conditions of sub-Doppler cooling with a monochromatic light field possessing spatial gradients of the polarization. It is shown that for stationary atoms with an initial isotropic distribution over sublevels the multipole moments of rank κ decompose, in accordance with the parity κ of the rank, according to one of two minimal sets of bipolar harmonics with different symmetry under inversion. An expansion of the corrections, which are linear in the velocity, to the multipole moments with respect to the indicated minimal sets of bipolar harmonics is studied for a stationary state, and the expansion coefficients are analyzed. The orientation vector J of the atomic ensemble is studied on the basis of the proposed method for the dipole transition 1/2 → 1/2, and the light-induced forces for a specific 2D configuration of the light field, including radiation friction forces and Lorentz-type forces, are analyzed.