The Dynamics of a Five-level (Double Λ)-type Atom Interacting with Two-mode Field in a Cross Kerr-like Medium

In this paper, we propose a new transition scheme (Double I >) for the interaction between a five-level atom and an electromagnetic field and study its dynamics in the presence of a cross Kerr-like medium in the exact-resonance case. The wave function is derived when the atom is initially prepared in its upper most state, and the field is initially prepared in the coherent state. We studied the atomic population inversion, the coherence degree by studying the second-order correlation function, Cauchy-Schwartz inequality (CSI) and the relation with P-function. Finally, we investigate the effect of Kerr-like medium on the evolution of Husimi Q-function of the considered system.