A Two-Level Atom in the Field of a de Broglie Gravitational Wave

de Broglie gravitational waves represent a classical realization of a form of dynamics that was proposed by de Broglie at the beginning of the last century. They are oscillations of spacetime with an effective mass, which is responsible for longitudinal effects that are absent in standard gravitational waves. In this article we study the influence of this gravitational field on a two-level atom in a semiclassical way. We will work out a gauge independent expression of the effective potential describing such interaction and we will use it to compute the transition amplitude between two quantum states. For a two-level hydrogen atom we will find an example of gravitational qubit, meaning that the quantum system exhibits periodic transitions between the states (Rabi oscillations) in analogy to the case of electromagnetic interaction. As an application, we will consider a gravity wave associated to a neutrino and we will estimate the transition frequency.