Spontaneous excitation of an accelerated atom coupled with quantum fluctuations of spacetime

A direct consequence of quantization of gravity would be quantum gravitational vacuum fluctuations which induce quadrupole moments in gravitationally polarizable atoms. In this paper, we study the spontaneous excitation of a gravitationally polarizable atom with a uniform acceleration $a$ in interaction with a bath of fluctuating quantum gravitational fields in vacuum, and compare the result with that of a static one in a thermal bath of gravitons at the Unruh temperature. We find that, under the fluctuations of spacetime itself, transitions to higher-lying excited states from the ground state are possible for both the uniformly accelerated atom in vacuum and the static one in a thermal bath. The appearance of terms in the transition rates proportional to $a^4$ and $a^2$ indicates that the equivalence between uniform acceleration and thermal field is lost.