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arXiv:0807.1448 · Physical Review Letters

Bell Test for the Free Motion of Material Particles

Clemens Gneiting, Klaus Hornberger

Published Dec 24, 2008• 35 citations
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Abstract

We present a scheme to establish nonclassical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counterpropagating atoms that is capable of violating a Bell inequality by means of correlated single-particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs Bose-Einstein condensation of fermionic lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology.

DOI
10.1103/physrevlett.101.260503

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We present a scheme to establish nonclassical correlations in the motion of two macroscopically separated massive particles without resorting to entanglement in their internal degrees of freedom. It is based on the dissociation of a diatomic molecule with two temporally separated Feshbach pulses generating a motional state of two counterpropagating atoms that is capable of violating a Bell inequality by means of correlated single-particle interferometry. We evaluate the influence of dispersion on the Bell correlation, showing it to be important but manageable in a proposed experimental setup. The latter employs Bose-Einstein condensation of fermionic lithium atoms, uses laser-guided atom interferometry, and seems to be within the reach of present-day technology.
The concept of dissociation-time entanglement provides a means of manifesting non-classical correlations in the motional state of two counter-propagating atoms. In this article, we discuss in detail the requirements for a specific experimental implementation, which is based on the Feshbach dissociation of a molecular Bose-Einstein condensate of fermionic lithium. A sequence of two magnetic field pulses serves to delocalize both of the dissociation products into a superposition of consecutive wave packets, which are separated by a macroscopic distance. This allows to address them separately in a switched Mach-Zehnder configuration, permitting to conduct a Bell experiment with simple position measurements. We analyze the expected form of the two-particle wave function in a concrete experimental setup that uses lasers as atom guides. Assuming viable experimental parameters the setup is shown to be capable of violating a Bell inequality.
This thesis proposes two complementary scenarios to observe Bell correlations in the motion of two macroscopically separated material particles. Both are based on the gradual dissociation of ultracold Feshbach molecules and result in macroscopic delocalizations of the single-atom states. By giving a full account of these scenarios, including the coupled-channel description of the Feshbach dissociation, the optically guided dispersive propagation, interferometric processing and the final position measurements, I demonstrate for both cases their potential to violate a Bell inequality under experimentally viable conditions that correspond to delocalizations and interatomic separations on the order of centimeters.
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.
The concept of dissociation-time entanglement provides a means of manifesting non-classical correlations in the motional state of two counter-propagating atoms. In this article, we discuss in detail the requirements for a specific experimental implementation, which is based on the Feshbach dissociation of a molecular Bose-Einstein condensate of fermionic lithium. A sequence of two magnetic field pulses serves to delocalize both of the dissociation products into a superposition of consecutive wave packets, which are separated by a macroscopic distance. This allows to address them separately in a switched Mach-Zehnder configuration, permitting to conduct a Bell experiment with simple position measurements. We analyze the expected form of the two-particle wave function in a concrete experimental setup that uses lasers as atom guides. Assuming viable experimental parameters the setup is shown to be capable of violating a Bell inequality.
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 $S\ensuremath{\le}2$.
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.