The Dynamics of a Modified Jaynes-Cummings Model

TL;DR

This paper explores a modified Jaynes-Cummings model where the atom interacts with a squeezed coherent photon instead of a single photon, leading to a new Hamiltonian with additional terms and dynamics.

Contribution

It introduces a novel dynamical system replacing photon operators with those of squeezed coherent states, extending the traditional Jaynes-Cummings model.

Findings

Derives a modified Hamiltonian including normally omitted terms.

Shows the model incorporates atom exchange interactions.

Provides a framework for studying non-classical light interactions.

Abstract

We introduce a dynamical system that instead of exchanging a single photon as in the atomic system of the usual Jaynes-Cummings model (JCM), it exchanges instead a squeezed coherent photon. Accordingly, the creation and annihilation photon operators in the JCM are replaced by the creation and annihilation operators of squeezed coherent states, respectively. This transformation generates a photon Hamiltonian that modifies the JCM that includes terms usually omitted in the JCM when making the rotating-wave approximation and, in addition, the transformation introduces atom exchange terms absent in the JCM.