A simple model for a minimal environment: the two-atom Tavis-Cummings model revisited

TL;DR

This paper analyzes a minimal quantum environment model involving two atoms and a cavity field, providing analytical solutions to understand how small environments influence quantum properties like entanglement and squeezing.

Contribution

It offers a full analytical solution to the two-atom Tavis-Cummings model with arbitrary parameters, exploring the environment's impact on quantum dynamics.

Findings

Small environment affects atomic purity and squeezing.

Detuning influences entanglement dynamics.

Degree of environment mixedness impacts quantum properties.

Abstract

Individual quantum systems may be interacting with surrounding environments having a small number of degrees of freedom. It is therefore relevant to understand the extent to which such small (but uncontrollable) environments could affect the quantum properties of the system of interest. Here we discuss a simple system-environment toy model, constituted by a two-level atom (atom 1) interacting with a single mode cavity field. The field is also assumed to be (weakly) coupled to an external noisy subsystem, the small environment, modeled as a second two-level atom (atom 2). We investigate the action of the minimal environment on the dynamics of the linear entropy (state purity) and the atomic dipole squeezing of atom 1, as well as the entanglement between atom 1 and the field. We also obtain the full analytical solution of the two atom Tavis-Cummings model for both arbitrary coupling strengths and frequency detunings, necessary to analyze the influence of the field-environment detuning on the evolution of the above mentioned quantum properties. For complementarity, we discuss the role of the degree of mixedness of the environment by analyzing the time-averaged linear entropy of atom 1.