Bell tests have confirmed the nonlocality of the quantum world for half a century, but until now experiments with massive particles have only used their internal states, such as spin. A particle's motion is fundamentally different: it determines how matter propagates through space and responds to gravity. This work joins a series of recent achievements in controlling the momentum states of ultracold atoms, where Bell correlations have been observed, but independent choice of local measurement bases for spatially separated modes remained an open challenge.
The experiment begins with a Bose-Einstein condensate of about $10^5$ atoms of metastable helium-4. A short Bragg pulse splits the condensate into three momentum components, and collisions between them produce pairs of atoms with opposite momenta, forming two spherical scattering halos. To independently control the phases in the two halves of the halo, a double-resonance Bragg grating is created by amplitude modulation of the laser field. This allows the implementation of the local measurement bases required for the Bell test. A Rarity-Tapster interferometer with mirror and beam-splitter pulses recombines the paths of the pairs, and a microchannel plate detector reconstructs the three-dimensional momenta of the atoms.
The measured Bell correlation function shows a cosine dependence on the sum of phases with a visibility of V = 0.93(2), consistent with a model that accounts for the contribution of higher Fock states and averaging over finite detector windows. For four chosen phase settings, the CHSH parameter was S = 2.52 ± 0.17, violating the local realism bound S ≤ 2 by about three standard deviations. This is the first direct proof of nonlocal correlations in the momentum states of massive particles.
Unlike neighboring works that were limited to observing Bell correlations or theoretical proposals, here a full Bell test is realized for the first time, with independent choice of local phases for spatially separated momentum modes. This completes a long-standing goal of quantum atom optics and opens a new regime for studying nonlocality in matter waves, as well as providing a platform for tests of the interplay between quantum mechanics and gravity.
The double-resonance Bragg grating enables measurements in arbitrary interferometric bases, which will allow full quantum state tomography and characterization of multiparticle entanglement. In the future, the platform could be extended to mixtures of helium-3 and helium-4 isotopes to study the influence of mass on quantum nonlocality and gravity.
The results will impact precision atom interferometry, quantum information with continuous variables, and fundamental tests of quantum gravity.
Immediate next steps include increasing the statistics to strengthen the significance of the violation, as well as adapting the scheme to work with entangled pairs of atoms of different masses.
This work is directly related to the open problem of reconciling quantum mechanics and general relativity: testing nonlocality in the motion of massive particles brings experiments closer to the regime where gravitational effects could influence quantum correlations.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors implemented a Bell test on momentum states of massive particles using pairs of helium atoms entangled in momentum from a Bose-Einstein condensate. Using a double-resonance Bragg grating, they independently controlled phases in spatially separated modes and measured the CHSH parameter S = 2.52 ± 0.17, violating the classical bound by three standard deviations. This is the first direct evidence of nonlocal correlations in the external degrees of freedom of massive particles.
Where its strength is
This work completes a long-standing goal in quantum atom optics: a full Bell test with independent choice of local bases for momentum modes. The platform combines high visibility of correlations with three-dimensional momentum resolution, opening the way to probing the interplay between quantum mechanics and gravity.
Where it could go next
Worth trying
Why this may matter
Extending Bell tests to external degrees of freedom of massive particles opens an experimental path to addressing fundamental questions about the quantum nature of gravity and the limits of quantum mechanics in curved spacetime.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.55, against a usual 0.64. It looks like few have drilled nearby.
The detector was located 848 mm below the trap, and the atoms fell onto it for about 0.416 seconds, reaching a speed of roughly 65 mm/s at the moment of detection.