Cavity-Mediated Programmable Interactions for Quantum Metrology and Simulation*

Quantum sensing and simulation benefit from fine control over long-range interactions. We leverage such control in an array of atomic ensembles coupled to an optical cavity for applications in entanglement-enhanced multiparameter sensing and in simulating topological physics. We demonstrate quantum-enhanced sensing of spatially patterned fields using a scheme that employs cavity-mediated interactions both to generate squeezing and to subsequently amplify the signal in a spatial mode of interest, facilitating detection of the entangled state. We further demonstrate simultaneous sensing of conjugate observables with precision beyond the standard quantum limit, by entangling an array of sensor ensembles with an array of ancilla ensembles. Crucial to our protocol is the use of interaction-based readout to access nonlocal observables forming a "quantum-mechanics free" subsystem. The capability of accessing nonlocal observables via coupling to a delocalized cavity mode additionally offers a powerful tool for probing topological physics. As a proof of principle, we employ the cavity as a nonlocal interferometer for probing topological edge states in a bosonic Su-Schrieffer-Heeger (SSH) model, composed of magnons that hop between sites of the array of spin ensembles. We benchmark the realization of the SSH model by probing its topological invariant, the Zak phase, and by observing edge-state oscillations. We further demonstrate tunability of the on-site interactions and apply cavity-based nonlocal interferometry to probe the influence of interactions on the edge-mode dynamics. Finally, we present an outlook towards applying cavity-mediated entanglement towards simulations of quantum gravity, introducing a measurement-based scheme for producing models of holographic duality in the lab.