Non-Markovian Analysis of the Phase Damped Jaynes-Cummings Model in the Presence of a Classical Homogeneous Gravitational Field

In this paper, the non-Markovian dissipative dynamics of the phase damped Jaynes-Cummings model in the presence of a classical homogeneous gravitational field will be analyzed. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a non-Markovian phase damping mechanism. First, the non-Markovian master equation for the reduced density operator of the system in terms of a Hamiltonian describing the atom-field interaction in the presence of a homogeneous gravitational field will be presented. Then, the super-operator technique will be generalized and an exact solution of the non-Markovian master equation will be obtained. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, the non-Markovian effects on the temporal evolution of collapses and revivals of the atomic population inversion and photon counting statistics of the radiation field in the presence of both the phase damping and a homogeneous gravitational field will be investigated.