The general formalism for a three-level atom interacting with a two-mode cavity field

We study the interaction between a three-level atom and a two modes electromagnetic field. The atomic levels are coupled by the multiphotons transitions, the coupling constants between the field and atomic levels are considered to be intensity dependent and the Kerr medium is taken into account. We obtained the constants of motion and the wave function when the atom is given in an arbitrary initial state. We calculate a number of statistical aspects of a theoretically considered model.