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 limit1-3 set by projections of individual atoms. Large amounts of entanglement4-6 involving the internal degrees of freedom of laser-cooled atomic ensembles4-16 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 sensors17,18, searches for new physics, particles and fields19-23, future advanced gravitational wave detectors24,25 and accessing beyond mean-field quantum many-body physics26-30.

Continuous Real-Time Tracking of a Quantum Phase Below the Standard Quantum Limit.

We propose a scheme for continuously measuring the evolving quantum phase of a collective spin composed of N pseudospins. Quantum nondemolition measurements of a lossy cavity mode interacting with an atomic ensemble are used to directly probe the phase of the collective atomic spin without converting it into a population difference. Unlike traditional Ramsey measurement sequences, our scheme allows for real-time tracking of time-varying signals. As a bonus, spin-squeezed states develop naturally, providing real-time phase estimation significantly more precise than the standard quantum limit of Δϕ_{SQL}=1/sqrt[N] rad.

Deterministic Squeezed States with Collective Measurements and Feedback.

We demonstrate the creation of entangled, spin-squeezed states using a collective, or joint, measurement and real-time feedback. The pseudospin state of an ensemble of N=5×10^{4} laser-cooled ^{87}Rb atoms is deterministically driven to a specified population state with angular resolution that is a factor of 5.5(8) [7.4(6) dB] in variance below the standard quantum limit for unentangled atoms-comparable to the best enhancements using only unitary evolution. Without feedback, conditioning on the outcome of the joint premeasurement, we directly observe up to 59(8) times [17.7(6) dB] improvement in quantum phase variance relative to the standard quantum limit for N=4×10^{5} atoms. This is one of the largest reported entanglement enhancements to date in any system.