Entanglement criteria of two two-level atoms interacting with two coupled modes

TL;DR

This paper analyzes how Kerr nonlinearity and detuning influence entanglement dynamics between two two-level atoms and two coupled field modes, using an analytically reduced Jaynes-Cummings model and various entanglement measures.

Contribution

It introduces a model reduction via Bogoliubov-Valatin transformation and evaluates entanglement dynamics under different initial conditions and nonlinear effects.

Findings

Entanglement can be tuned by adjusting system parameters.

Kerr nonlinearity significantly affects entanglement measures.

Detuning influences the degree of atom-atom and atom-field entanglement.

Abstract

In this paper, we study the interaction between two two-level atoms and two coupled modes of a quantized radiation field in the form of parametric frequency converter injecting within an optical cavity enclosed by a medium with Kerr nonlinearity. It is demonstrated that, by applying the Bogoliubov-Valatin canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Then, under particular initial conditions which may be prepared for the atoms (in a coherent superposition of its ground and upper states) and the fields (in a standard coherent state), the time evolution of state vector of the entire system is analytically evaluated. In order to understand the degree of entanglement between subsystems (atom-field and atom-atom), the dynamics of entanglement through different measures, namely, von Neumann reduced entropy, concurrence and negativity is evaluated. In each case, the effects of Kerr nonlinearity and detuning parameter on the above criteria are numerically analyzed, in detail. It is illustrated that the amount of the degree of entanglement can be tuned by choosing the evolved parameters, appropriately.