Dynamics of entropy and quantum statistical properties of the field in the interaction of a single two-level atom with a superposition of nonlinear coherent states in the framework of f-deformed Jaynes–Cummings model

Abstract

Based on the f-deformed Jaynes–Cummings model, we investigate the interaction of a single two-level atom with a general superposition of nonlinear coherent states (NCSs) with intensity-dependent coupling in a Kerr-like medium. We propose a solution of this model based on the density operator method. As an especial case the interaction of the atom with an even nonlinear coherent state (ENCS) is studied. By considering the effect of the field intensity and the detuning parameter, we compare such a system with the corresponding linear system which has been already studied in Vidiella-Baranco et al. J. Mod. Opt. 39:1441, (1992) and Gerry and Hach Phys. Lett. A 179:1, (1993). The atomic inversion behaviors of the linear and nonlinear interactions are found to be completely different. However, the most significant features of these interactions is that the field in nonlinear system exhibits sub-Poissonian statistics while the linear one do not show such a nonclassical property. In order to evaluate the degree of entanglement between the atom and the field, we investigate the dynamics of the entanglement by studying the field entropy in both linear and nonlinear cases. Finally studying the field evolutions using the Q-function has shown that the initial fields develop into multiple Schrodinger cat-like states. Especially we found that for the exact resonant case at successive collapses of atomic inversion, the initial field components split into a superposition of the four-component NCSs \({\pi }/{2}\) out of phase which may be potentially considered as the source of the new notion of “four-photon nonlinear coherent states”.