Approach to a Parity Deformed Jaynes-Cummings Model and the Maximally Entangled States

A parity deformed Jaynes-Cummings model (JCM) is introduced, which describes an interaction of a two-level atom with a $\lambda$-deformed quantized field. In the rotating wave approximation (RWA), all eigen-values and eigen-functions of this model are obtained exactly. Assuming that initially the field is prepared in the Wigner cat state (WCS) and the two-level atom is in the excited state, it has been shown that the atomic Rabi oscillations exhibit a quasi-periodic behavior in the collapse and revival patterns. The influence of the deformation parameter on the time evolution of non-classical features of the radiation field such as the sub-Poissonian statistics and squeezing effect are also analyzed. Interestingly, the main finding here is that we can realize maximally entangled atom-field states. In this note it is shown that the high fidelity is possible in the weak coupling regime, while the deformation parameter becomes large values.