  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.
