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

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 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 $$3\,.\,{4}_{-0.9}^{+1.1}$$ 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 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.

Spin- and momentum-correlated atom pairs mediated by photon exchange

“…We demonstrate independent control over coherent and dissipative processes, and probe them by measurements of atomic and photonic observables. As the dynamics remains coherent for long times, T coh T int , our results pave the way for fast entanglement generation in spatially separated atomic clouds [42,43]. Combining such a mechanism with mode-selective spin rotations offers a promising route for performing loophole-free Bell tests with massive particles [44,45].…”

Quantum-enhanced differential atom interferometers and clocks with spin-squeezing swapping

“…( 38) one gets In particular, both figures show "jumps" in the minimum-point function that clearly prove the validity of Eqs. ( 47) and (48). In panel (b), we focus on the interval δ ∈ [−7/8π, −3/8π] and show that the results of the numerical minimization of Eq.…”

“…Spin squeezing in momentum modes, suitable for inertial sensing with AIs, can be created through atomatom interaction in Bose-Einstein condensates [44][45][46] or atom-light interaction in an optical cavity [47,48]. Recent experimental achievements include the creation of useful entangled states through the transfer of squeezing generated in internal states into well-defined and separated external momentum modes [49], the demonstration of long-lived spinsqueezed states [50], and the implementation of a full spatial interferometer scheme with a direct observation of sub-SQL sensitivity [48]. Furthermore, entanglement-enhanced atomic clocks using spinsqueezed states have been demonstrated [51][52][53][54].…”

“…x ) 2 is associated to a non-linear evolution due to atom-atom interaction in a Bose-Einstein condensate [44][45][46] or atomlight interaction in a cavity [47,48,59], and generates a two-mode spin-squeezing dynamics, where τ E denotes the effective squeezing time. The term exp{−iν E Ĵ{a,b} z } rotates the state in the Bloch sphere by the angle ν E .…”

Variational waveguide QED simulators

“…The latter allows to discern whether a possible advantage is a consequence of the long-range character of the wQED interaction or its dynamical tunability. Besides, its results can be of interest for cavity QED setups [67][68][69][70][71][72][73], where such infinite range interactions appear naturally.…”