Analogue many-body gravitating quantum systems with a network of dipolar Bose-Einstein condensates

Operational probes of the interface between quantum mechanics and general relativity in the Newtonian regime - via mass-energy equivalence in clocks or spatial superpositions in interferometers - share a common description in terms of an effective qubit-qubit Ising coupling. Here we generalize both paradigms to interacting (N+1)-level effective qudits made of atomic ensembles with particle number, N. 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 measurements. Furthermore, we show that quantum effects induced by gravitational interaction can be simulated by trapped bimodal Bose-Einstein condensates with long-range (e.g. dipolar) coupling, providing a programmable analogue platform to explore gravitating quantum dynamics at accessible time and energy scales. Finally, extending the protocol to a sensor network broadens the entanglement-detection window.