Quantum Statistical Features of the Mth Nonlinear Coherent States within the F-Deformed Jaynes-Cummings Model

Recently, we introduced the mth nonlinear coherent state (mncs), obtained by applying m times the number operator on the nonlinear coherent states (ncss). studying the interaction of such states with an atom is of great importance due to their notable nonclassical features. in this study, relying on the f-deformed jaynes-cummings model, we investigate the interaction between a two-level atom and a single-mode field, which is organized to be a mncs. for this, the time evolution of population inversion and the nonclassical properties of the field, including the mandel q-parameter, normal squeezing, and amplitude-squared squeezing, across various parameters and values of m is studied. it is found that in the presence of the intensity-dependent coupling and kerr medium in the resonance condition, the nonclassical feature of squeezing occurs periodically during the interaction. furthermore, sub-poissonian photon statistics is also evident as a significant nonclassical feature. finally, by measuring the field entropy for all the investigated cases, we examine the entanglement dynamics and determine the degree of atom-field entanglement. additionally, a general comparison between the interaction of a twolevel atom with the mth coherent states (mcss) and the interaction of a two-level atom with the mncss is presented.