Thermal effects in Jaynes-Cummings model derived with low-temperature expansion

TL;DR

This paper analyzes how low-temperature thermal effects influence the dynamics of the Jaynes-Cummings model, particularly the collapse and revival of Rabi oscillations, using a perturbative approach within Thermo Field Dynamics.

Contribution

It introduces a systematic low-temperature expansion method to study thermal effects in the Jaynes-Cummings model, focusing on the atomic population inversion and Rabi oscillations.

Findings

Thermal effects lengthen the revival period of Rabi oscillations.

Numerical results align with the predicted temperature dependence.

Third-order perturbation accurately captures low-temperature dynamics.

Abstract

In this paper, we investigate thermal effects of the Jaynes-Cummings model (JCM) at finite temperature with a perturbative approach. We assume a single two-level atom and a single cavity mode to be initially in the thermal equilibrium state and the thermal coherent state, respectively, at a certain finite low temperature. Describing this system with Thermo Field Dynamics formalism, we obtain a low-temperature expansion of the atomic population inversion in a systematic manner. Letting the system evolve in time with the JCM Hamiltonian, we examine thermal effects of the collapse and the revival of the Rabi oscillations by means of the third-order perturbation theory under the low-temperature limit, that is to say, using the low-temperature expansion up to the third order terms. From an intuitive discussion, we can expect that the period of the revival of the Rabi oscillations becomes longer as the temperature rises. Numerical results obtained with the perturbation theory reproduce well this temperature dependence of the period.