Entropy squeezing and atomic inversion in the $k$-photon Jaynes-Cummings model in the presence of Stark shift and Kerr medium: full nonlinear approach

TL;DR

This paper investigates the nonlinear dynamics of a $k$-photon Jaynes-Cummings model incorporating Stark shift and Kerr medium effects, analyzing how different initial field states influence atomic inversion and entropy squeezing.

Contribution

It introduces a full nonlinear $f$-deformed Hamiltonian model including Stark and Kerr effects, and studies the impact of various initial field states on system dynamics.

Findings

Initial field states significantly affect atomic inversion and entropy squeezing.

Kerr medium and Stark shift modify the dynamical behavior of the atom-field system.

Different initial states lead to distinct squeezing and inversion patterns.

Abstract

In this paper the interaction between a two-level atom and a single-mode field in the $k$-photon Jaynes-Cummings model (JCM) in the presence of Stark shift and Kerr medium is studied. All terms in the respected Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be $f$-deformed. In particular, the effect of the initial state of radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states. To achieve this purpose, coherent, squeezed and thermal states as initial field states are considered.