Abstract
General formalisms of a four-level atom in different configurations interacting with a single mode quantized electromagnetic field under multi-photon process with additional forms of nonlinearities of both the field and the intensity-dependent atom-field coupling are investigated. Analytical expressions for the time unitary evolution operator and density operator are obtained. The atom is prepared in its upper most and the field is prepared in a binomial state. The effects of the mean photon number, photon multiplicity, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are considered. General conclusions reached are illustrated by numerical results.