Cavity QED with degenerate atomic levels and polarization-degenerate field mode

The Jaynes-Cummings model with degenerate atomic levels and polarization-degenerate field mode is considered. The general expression for the system evolution operator is derived. The analytical expressions for such operators in the case of low values ($J \leq 3/2$) of atomic angular momentum are obtained. The polarization properties of the photon emitted into the cavity by an excited atom are studied with an account of relaxation processes for arbitrary angular momenta of atomic levels.