  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 test with ultra-cold atoms
would be challenging, but not implausible with moderate improvements to current
experimental techniques.
