Abstract
The interaction between a moving two-level atom and squeezed coherent states in the presence of Kerr like medium and an external classical field is studied. We consider the cavity field not to be isolated, so the field suffers from a decay rate. Under the rotating wave approximation, and some certain transformations, the system is transformed to the usual Jaynes-Cummings model with Kerr medium as well as a damping term. The probability amplitude is obtained when the atomic system is prepared in its excited state. The results show that, the evolution of the atomic population inversion, the Pegg-Barnett phase, and the quasi-probability distributions are decaying in the presence of damping. While the detuning parameter delays the decay rate, also enhances a part of the phase space and decrease the rate of another part. The system is very sensitive to the Kerr like medium, where it plays a role in shortening the collapse periods, however it works to cracking and diffusing the phase space.