Jaynes-Cummings model with degenerate atomic levels and two polarization modes of the quantized field

The Jaynes-Cummings model describing the interaction of two polarization modes of the quantized electromagnetic field with an isolated two-level atom with the levels degenerate in the projections of the angular momenta on the quantization axis is studied. The general expression for the evolution operator for such a model is obtained. The examples of low values of the level angular momenta or single photon in the cavity are discussed.