General formalism of the interaction of a single-mode cavity field with a four-level atom

In this paper, we study a general model for an atomic system described by a four-level atom and one mode of the radiation field. The model describes multi-photon processes and includes possible forms of nonlinearities of both the field and the intensity-dependent coupling. The general forms for the constants of motion of the considered atomic system are obtained. We used the Schrodinger equation in solving this problem. The wave function is obtained when the atom is prepared initially in a superposition coherent state. Some of the statistical aspects which are related to this atomic system are calculated. Also, the effect of the Kerr medium on the dynamics of a four-level W-type atom one-mode system are examined.