Entropy squeezing of time dependent single-mode Jaynes-Cummings model in presence of non-linear effect

A general Hamiltonian for a system which consists of a two-level atom interacting with electromagnetic field is considered. Besides the Stark shift the model includes multi-photon process as well as a non-linear Kerr-like medium effect. Furthermore the field and the atom are assumed to be coupled with modulated coupling parameter which depends explicitly on time. Under an approximation where fast oscillations are ignored, an exact solution for the wave function in Schrödinger picture is given. The atomic inversion as well as the entropy squeezing are considered and it has been shown that existence of the time dependent coupling parameter leads to a time delaying in the interaction which is twice the delay time for the independent case.