General formalism of interaction of a two-level atom with cavity field in arbitrary forms of nonlinearities

We propose a general formalism of a nonlinear Jaynes–Cummings-model by including possible forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. We obtain an exactly analytic solution of the model, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Under the condition of an initial coherent field, the atomic inversion shows the collapse-revival phenomenon, which have different features in different forms of the nonlinearities. It is shown that features of the degree of entanglement is influenced significantly by the kinds of the nonlinearities of the single-mode field. The influences of the nonlinearities on the photon number distribution and phase properties are examined.