Entanglement-enhanced matter-wave interferometry in a high-finesse cavity

An ensemble of atoms can operate as a quantum sensor by placing atoms in a superposition of two different states. Upon measurement of the sensor, each atom is individually projected into one of the two states. Creating quantum correlations between the atoms, that is entangling them, could lead to resolutions surpassing the standard quantum limit^1-3 set by projections of individual atoms. Large amounts of entanglement^4-6 involving the internal degrees of freedom of laser-cooled atomic ensembles^4-16 have been generated in collective cavity quantum-electrodynamics systems, in which many atoms simultaneously interact with a single optical cavity mode. Here we report a matter-wave interferometer in a cavity quantum-electrodynamics system of 700 atoms that are entangled in their external degrees of freedom. In our system, each individual atom falls freely under gravity and simultaneously traverses two paths through space while entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed sensitivity [Formula: see text] dB and [Formula: see text] dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach-Zehnder light-pulse interferometer with directly observed sensitivity [Formula: see text] dB below the standard quantum limit. The combination of particle delocalization and entanglement in our approach may influence developments of enhanced inertial sensors^17,18, searches for new physics, particles and fields^19-23, future advanced gravitational wave detectors^24,25 and accessing beyond mean-field quantum many-body physics^26-30.