Rate equations between electronic-state manifolds

Abstract

Rate equations are derived to describe the interaction with an ensemble of atoms of a number of optical fields having arbitrary polarizations. The fields drive transitions between two manifolds of levels, each manifold consisting of magnetically degenerate fine and hyperfine levels. The rate equations are written in an irreducible tensor notation using a coupled tensor basis for the fields' polarizations, which significantly simplifies the equations. Validity conditions for the rate equations are discussed, an expression for the friction force of laser cooling is given, and specific values for elements of the coupled-basis polarization tensor are tabulated.