Searching for signatures of quantum gravity in quantum gases

We explore the possibility of testing the quantum nature of the gravitational field with an ensemble of ultra-cold atoms. The use of many microscopic particles may circumvent some of the experimental obstacles encountered in recent proposals involving a pair of particles with mesoscopic mass. We employ multi-parameter estimation techniques, including the quantum and classical Fisher information to provide a criteria for the observability of the quantum effects, and compare to other recently proposed schemes. Crucially, we find that by preparing the appropriate initial state, interactions mediated via a quantum-valued gravitational field provide a signature that is distinct from classical gravitational interactions. We find that a definitive demonstration of the quantum gravitational interaction is not possible with current experimental capabilities, due to uncertainty in the residual electromagnetic interactions between the atoms. However, it may be possible with significant improvements to current experimental techniques.