The eigenvalues and eigenstates of the effective Hamiltonian in the interaction of an atom with both classical gravity and quantum radiation

The eigenvalues and eigenstates of the effective Hamiltonian in the interaction of the atom with both classical gravity and quantum radiation within the framework of the Jaynes-Cummings model are obtained. By taking into account both the atomic motion and gravitational field a full quantum treatment of the internal and external dynamics of the atom is presented. By solving exactly the Schrödinger equation in the interaction picture, the evolving state of the system is found by which the the eigenvalues of the atom-field system are obtained. Also, the influence of gravity on atomic dipole squeezing is investigated.