Many-body gravitating quantum systems with Bose-Einstein condensates and dipolar analogue

Abstract

Quantum probes of gravity in the Newtonian regime, based on mass-energy equivalence in clocks or spatial superpositions in interferometers, share a common description in terms of an effective qubit-qubit coupling. Here we extend this framework to atomic ensembles, regarded as interacting collective qudits. The many-body enhancement boosts the signal-to-noise and increases the effective interaction rate, facilitating the observation of gravitationally-induced entanglement and decoherence, certified by metrological witnesses based on local and collective spin squeezing. We further identify trapped bimodal Bose-Einstein condensates with long-range interactions, including dipolar couplings, as a programmable analogue platform for simulating gravitating quantum dynamics at accessible time and energy scales. Extending the protocol to a sensor network broadens the entanglement-detection window.

22 pages, 5 figures