The two-photon degenerate Jaynes-Cummings model with and without rotating-wave approximation

We take into account the two-photon process and generalize the Jaynes-Cummi ngs (JC) model to the case of atomic level degenerate in the projections of the angular momenta, and we establish two-photon degenerate JC models with and without the rotating-wave approximation (RWA) quantum theory. Comparin g the atom population inversion of the generalized JC model with that of th e original JC model, we found that the revival period of the degenerate JC model becomes longer and the maximum amplitude of atomic inversion decrease s with RWA. Without RWA, the quantum chaos of the generalized JC model is m uch weaker than that of the original JC model.