Dynamic correlation funtions of the generalized Tavis-Cummings model

TL;DR

This paper analyzes a generalized Tavis-Cummings model with Kerr nonlinearity, deriving dynamic correlation functions using quantum inverse methods and Bethe equations, supported by numerical solutions to explore system dynamics.

Contribution

It introduces an analytical approach to compute dynamic correlation functions in a complex atom-field interaction model with Kerr nonlinearity, using Bethe equations.

Findings

Correlation functions depend on Bethe equation solutions

Numerical solutions reveal system dynamics

Photon transition elements are expressed in determinant form

Abstract

The model describing interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution obtained by application of the quantum inverse method (QIM). The dynamic correlation functions are calculated and transition elements of photons are represented in the determinant form. The obtained answers depend on the solutions of Bethe equations. We provide the numerical solutions of these equations for the different parameters of the model and study the behaviour of certain dynamical correlation functions.