Signatures of the quantum nature of gravity: Principle and practice*

We study the quantum nature of the gravitational interaction between two identical masses in the Newtonian limit. Since gravity only depends on the relative position of the two masses, the differential motion of their centers of mass is a simple and elegant way of exploring its quantum signatures. If the gravitational interaction between the two masses is quantum in the Newtonian limit, the differential mode exhibits quantum squeezing. If the gravitational interaction is semiclassical of the Schrodinger-Newton type, both the differential and common modes exhibit identical quantum squeezing. We thus show the origins of quantum entanglement between two masses in the former case, and their absence in the latter. We close with prospects of experimentally detecting of these signatures.