Quantumness of gravity in harmonically trapped particles

Abstract: This study investigates the quantumness of gravity under the setup of the atomic interferometry from the viewpoint of mass-energy equivalence. We evaluated interference visibility considering a particle with internal energy levels in a harmonic trapping potential. As per the result, for a spatially superposed gravitational source mass, interference visibility exhibits collapse and revival behavior, which implies that an initial separable internal state evolves to the entangled state with respect to the degrees of freedom of the center of mass, the internal energy levels, and the external source state. In particular, it does not exhibit revival behavior when gravity is treated as a quantum interaction, while it revives with a finite period for a semiclassical treatment of gravity. We also examined the temporal behavior of entanglement negativity and found that the nonrevival behavior of visibility reflects the creation of the entanglement between the internal energy state and the external source state which is uniquely induced by the quantum interaction of gravity in accordance with the weak equivalence principle.