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arXiv:2411.08356 · Quantum

Proposal for a Bell Test with Entangled Atoms of Different Mass

X. T. Yan, S. Kannan, Y. S. Athreya, Andrew G. Truscott, Sean S. Hodgman

Published Dec 11, 2025• 1 citation
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Abstract

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.

DOI
10.22331/q-2025-12-11-1939

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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.
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We propose an experiment to test the weak equivalence principle (WEP) with a test mass consisting of two entangled atoms of different species. In the proposed experiment, a coherent measurement of the differential gravity acceleration between the two atomic species is considered, by entangling two atom interferometers operating on the two species. The entanglement between the two atoms is heralded at the initial beam splitter of the interferometers through the detection of a single photon emitted by either of the atoms, together with the impossibility of distinguishing which atom emitted the photon. In contrast to current and proposed tests of the WEP, our proposal explores the validity of the WEP in a regime where the two particles involved in the differential gravity acceleration measurement are not classically independent, but entangled. We propose an experimental implementation using ^{85}Rb and ^{87}Rb atoms entangled by a vacuum stimulated rapid adiabatic passage protocol implemented in a high-finesse optical cavity. We show that an accuracy below 10^{-7} on the Eötvös parameter can be achieved.
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.
We propose an experiment to test Bell nonlocality, a genuine nonclassicality, for the gravitational field. Two masses with embedded entangled spins (e.g., two diamonds with their NV-centre spins entangled) are placed well outside each other's light cones, ensuring a locality-loophole-free scenario. The spins are then coupled to the motion of their respective masses to generate spatial superpositions. Finally, local measurements are performed only on the gravitational fields of the two masses. If gravity is quantum, then the two entangled masses would entangle their gravitational fields, leading to correlations certifying Bell nonlocality of gravity. Trapped and ground-state cooled nano-objects with micron-sized spatial superposition are sufficient for this test. This goes beyond the recent proposals to test nonclassicality of gravity by providing, for the first time in the literature, a minimal tool to (i) create Einstein-Podolsky-Rosen (EPR) state of gravitational curvatures, (ii) witness entangled gravitational curvatures, (iii) rule out any local-realist description of gravity, and (iv) achieve a loophole-free test of gravity's nonclassicality in a fully device-independent way.
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.
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 $S\ensuremath{\le}2$.