Thermal Effects in Jaynes–cummings Model Derived With Low-Temperature Expansion

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.

Relation between the usual and the entanglement temperature, in a simple quantum system

“…Ref. [13] obtains an explicit expression for the atomic state population as a function of temperature, namely P e = e β ω/2 e β ω/2 + e −β ω/2 ,…”

“…Also in the 80's, the Thermo Field Dynamics (TFD) formalism [12,13] was applied to the JCM. The TFD is a method, developed in the 70's by Takahashi and Umezawa [14], for describing Quantum Mechanical systems at finite temperature.…”

“…The relative simplicity of the JCM and its extensions has drawn much attention in the physics community and, more recently, in the field of the quantum computing [15,16]. Also in the 80's, the Thermo Field Dynamics (TFD) formalism [12,13] was applied to the JCM. The TFD is a method, developed in the 70's by Takahashi and Umezawa [14], for describing Quantum Mechanical systems at finite temperature.…”

A thermal coherent state defined with the Lie-Trotter product formula

“…Time evolution of the Jaynes-Cummings model with the thermal coherent state at initial time is examined in Ref. [7].…”