Abstract 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
3.4−0.9+1.1 3 . 4 − 0.9 + 1.1 dB and
2.5−0.6+0.6 2 . 5 − 0.6 + 0.6 dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach–Zehnder light-pulse interferometer with directly observed sensitivity
1.7−0.5+0.5 1 . 7 − 0.5 + 0.5 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 .
In their paper "Entanglement-enhanced matter-wave interferometry in a high-finesse cavity" Nature (2022), Greve et. al. claim to use entanglement in a matter-wave interferometer to achieve a sensitivity beyond that achievable with the same number of independent particles -- a limit known as the standard quantum limit (SQL). In particular, using squeezed momentum states of 700 atoms, the authors claim to directly observe a sensitivity 3.4 dB (a factor of 1.5) below the SQL. This claim is incorrect. The authors do not measure anything beyond the SQL, nor do they achieve a sensitivity beyond what one could obtain with a single atom. The achieved sensitivity is at least a factor of 39 worse than the claimed value.
Atom interferometers are among the most sensitive instruments for precision measurements and tests of fundamental physics. Their performance, however, is ultimately limited by quantum projection noise when uncorrelated atomic ensembles are employed. Cavity-assisted generation of entangled states has proven to be a promising route toward quantum-enhanced interferometry beyond the standard quantum limit. In this work, we present the realization and characterization of a monolithic bow-tie cavity developed to achieve a strong collective atom-light coupling with strontium atoms. Unlike conventional standing-wave Fabry-Pérot resonators, the traveling-wave geometry of the bow-tie cavity provides homogeneous atom-light coupling over the entire atomic ensemble, making it particularly suitable for entanglement-enhanced atom interferometry with freely falling atoms. The monolithic cavity architecture presents several scientifically relevant features such as high mechanical stability, high finesse, robustness against mirror misalignment, optical and atomic access and the option of generating squeezed states through different strategies. The cavity was realized for operation on the strontium
(5s2)1S0−(5s5p)3P1 transition at 689 nm and achieves a finesse of
F=5.7×104 while keeping the transmission of a single mirror sufficiently large to allow for efficient atomic information extraction. In this geometry, the cavity supports two foci with waists of 164
μm and 31
μm which gives access to different regimes of atom-cavity coupling. For ensembles containing up to
105 atoms, the cavity is expected to enable a Wineland squeezing parameter
ξ2 of 24 dB through cavity-feedback squeezing, and 28 dB through quantum non-demolition measurements, demonstrating its potential as a platform for next-generation quantum-enhanced atom interferometers.
Quantum squeezed states offer metrological enhancement as compared to their classical counterparts. Here, we devise and numerically explore a method for performing SU(1,1) interferometry beyond the standard quantum limit, using quasi-cyclic nonlinear wave mixing dynamics of ultracold atoms in a ring cavity. The method is based on generating quantum correlations between many atoms via photon-mediated optomechanical interaction. Timescales of the interferometer operation are here given by the inverse of photonic recoil frequency, and are orders of magnitude shorter than the timescales of collisional spin mixing--based interferometers. Such shorter timescales should enable not only faster measurement cycles but also lower atomic losses from the trap during measurement, which may lead to significant quantum metrological gain in matter-wave interferometry with state-of-the-art cavity setups.
We propose a quantum-enhanced matter-wave interferometry protocol based on fractional-revival dynamics of a Bose-Einstein condensate in a ring, combined with a controlled interaction quench. Using the Truncated Wigner Approximation, we show that nonlinear evolution to the quarter revival generates modest spin squeezing of
−2.03±0.28dB, which subsequently degrades under further nonlinear evolution. In contrast, starting from a non-interacting condensate, a controlled interaction quench applied after the initial quarter-revival beam-splitter operation generates substantially stronger spin squeezing of
−14.57±0.27dB. We further show that phase control at
t=3Tr/8 rotates the squeezed quadrature onto the phase-sensitive direction
J^y, producing a phase-squeezed state at
t=Tr/2. The subsequent quarter-revival evolution converts this phase-squeezed state into a number-squeezed state, enabling population-difference readout. The resulting sequence provides a route to quantum-enhanced interferometry using the intrinsic fractional-revival dynamics of a ring together with controlled interaction and phase operations.