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arXiv:2502.12392 · Nature Communications

Bell correlations between momentum-entangled pairs of 4He* atoms

Y. S. Athreya, Suresh Kannan, X. T. Yan, Robert J. Lewis-Swan, Karen V. Kheruntsyan, Andrew G. Truscott, Sean S. Hodgman

Published Feb 4, 2026• 2 citations
arXivHTMLPDF

Abstract

Nonlocal entanglement between pair-correlated particles is a highly counter-intuitive aspect of quantum mechanics, where measurement on one particle can instantly affect the other, regardless of distance. While the rigorous Bell’s inequality framework has enabled the demonstration of such entanglement in photons and atomic internal states, no experiment has yet involved motional states of massive particles. Here we report the experimental observation of Bell correlations in motional states of momentum-entangled ultracold helium atoms. Momentum-entangled pairs are first generated via s-wave collisions. Using a Rarity-Tapster interferometer and a Bell-test framework, we observe atom-atom correlations required for violation of a Bell inequality. This result shows the potential of ultracold atoms for fundamental tests of quantum mechanics and opens new avenues to studying gravitational effects in quantum states. Momentum-entangled atom pairs are used to demonstrate quantum non-locality, where changing one atom in an entangled pair instantly alters the state of the other atom. This result paves the way to study interactions between quantum states and gravity.

DOI
10.1038/s41467-026-69070-3

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Nonlocal entanglement between pair-correlated particles is a highly counter-intuitive aspect of quantum mechanics, where measurement on one particle can instantly affect the other, regardless of distance. While the rigorous Bell’s inequality framework has enabled the demonstration of such entanglement in photons and atomic internal states, no experiment has yet involved motional states of massive particles. Here we report the experimental observation of Bell correlations in motional states of momentum-entangled ultracold helium atoms. Momentum-entangled pairs are first generated via s-wave collisions. Using a Rarity-Tapster interferometer and a Bell-test framework, we observe atom-atom correlations required for violation of a Bell inequality. This result shows the potential of ultracold atoms for fundamental tests of quantum mechanics and opens new avenues to studying gravitational effects in quantum states. Momentum-entangled atom pairs are used to demonstrate quantum non-locality, where changing one atom in an entangled pair instantly alters the state of the other atom. This result paves the way to study interactions between quantum states and gravity.
Bell's theorem revealed the fundamental incompatibility between the predictions of quantum mechanics and local realism. Bell inequality violations have since demonstrated quantum nonlocality using photons and internal states of massive particles, but never using their motional states. Here we report the first Bell inequality violation in the motional states of massive particles. Using momentum-entangled pairs of metastable helium atoms manipulated by matter-wave interferometry, we measure a Clauser-Horne-Shimony-Holt (CHSH) Bell parameter of S=2.52±0.17S = 2.52 \pm 0.17S=2.52±0.17, violating the CHSH-Bell inequality (S≤2S \le 2S≤2). Our work completes a long-standing objective in quantum atom optics by extending Bell tests from internal quantum variables to the external degrees of freedom of massive particles, opening a new regime for exploring quantum nonlocality in matter waves and for investigating the interplay between quantum mechanics and gravity.
Bell correlations are a foundational demonstration of how quantum entanglement contradicts the classical notion of local realism. Rigorous validation of quantum nonlocality have only been achieved between solid-state electron spins, internal states of trapped atoms, and photon polarisations, all weakly coupling to gravity. Bell tests with freely propagating massive particles, which could provide insights into the link between gravity and quantum mechanics, have proven to be much more challenging to realise. Here we use a collision between two Bose-Einstein condensates to generate spin entangled pairs of ultracold helium atoms, and measure their spin correlations along uniformly rotated bases. We show that correlations in the pairs agree with the theoretical prediction of a Bell triplet state, and observe a quantum mechanical witness of Bell correlations with [Formula: see text] significance. Extensions to this scheme could find promising applications in quantum metrology, as well as for investigating the interplay between quantum mechanics and gravity.
This manuscript describes quantum atom optics experiments using metastable helium atoms with a single-atom momentum resolved detector. In the first part of this manuscript, the second order correlation measurement of the superradiance from a metastable helium Bose-Einstein condensate is presented. The superradiance effect is the collective radiation of dense ensemble where a strong gain of the radiation is expected. We have shown the thermal like statistics of the emission even in the presence of the strong gain. The next part of the manuscript is devoted to the quantum nonlocality test using a pair of atoms entangled in momentum. The protocol we came up with is inspired from the one of Rarity and Tapster with pairs of photons entangled in momentum. The essential ingredients of this protocol are the atomic pair produced by dynamical instability of the Bose-Einstein condensate in a moving optical lattice, the coherent control of the atomic pair by Bragg diffraction and the correlation measurement of the atoms in different output modes of the interferometric protocol. The experimental characterization and preparation of coherent control by Bragg diffraction are presented showing the proof of principle of such a protocol. The last part of the manuscript discusses the realization of the atomic Hong-Ou-Mandel experiment using the same atomic pair with an atomic beamsplitter. The non-classical interference result of this experiment has opened an opportunity for us to realize Bell’s inequality test with massive particles correlated in external degrees of freedom.
Abstract We present an experimentally viable approach to demonstrate quantum non-locality in a matter-wave system via a Rarity–Tapster interferometer using two sss s -wave scattering halos generated by colliding helium Bose–Einstein condensates. The theoretical basis for this method is discussed, and its suitability is experimentally quantified. As a proof of concept, we demonstrate an interferometric visibility of V=0.42(9)V=0.42(9)V=0.42(9) V = 0.42 ( 9 ) , corresponding to a maximum CSHS-Bell parameter of S=1.1(1)S=1.1(1)S=1.1(1) S = 1.1 ( 1 ) , for the Clauser–Horne–Shimony–Holt (CHSH) version of the Bell inequality, between atoms separated by ∼4\sim 4∼4 ∼ 4 correlation lengths. This constitutes a significant step toward a demonstration of a Bell inequality violation for motional degrees of freedom of massive particles and possible measurements of quantum effects in a gravitationally sensitive system.
We propose and theoretically simulate an experiment for demonstrating a motional-state Bell inequality violation for pairs of momentum-entangled atoms produced in Bose-Einstein condensate collisions. The proposal is based on realizing an atom-optics analog of the Rarity-Tapster optical scheme: it uses laser-induced Bragg pulses to implement two-particle interferometry on the underlying Bell state for two pairs of atomic scattering modes with equal but opposite momenta. The collision dynamics and the sequence of Bragg pulses are simulated using the stochastic Bogoliubov approach in the positive-PPP representation. We predict values of the Clauser-Horne-Shimony-Holt (CHSH) parameter up to $S\ensuremath{\simeq}2.5$ for experimentally realistic parameter regimes, showing a strong violation of the CSHS-Bell inequality bounded classically by $S\ensuremath{\le}2$.
We propose a Bell test experiment using momentum-entangled atom pairs of different masses, specifically metastable helium isotopes 3 H e ∗ and 4 H e ∗ , though the method extends to other atom species. Entanglement is generated via collisions, after which the quantum states are manipulated using two independent atom interferometers, enabling precise phase control over each species. Numerical simulations predict a significant violation of Bell's inequality under realistic conditions. This proposal opens a new paradigm to study the intersection of quantum mechanics and gravity.