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arXiv:1411.0191 · Physical Review A

Proposal for a motional-state Bell inequality test with ultracold atoms

Robert J. Lewis-Swan, Karen V. Kheruntsyan

Published May 20, 2015• 38 citations
arXivHTMLPDF

Abstract

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-$P$ 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 $S\ensuremath{\le}2$.

DOI
10.1103/physreva.91.052114

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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≃2.5S\ensuremath{\simeq}2.5S\ensuremath≃2.5 for experimentally realistic parameter regimes, showing a strong violation of the CSHS-Bell inequality bounded classically by S\ensuremath≤2S\ensuremath{\le}2S\ensuremath≤2.
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.
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.
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.
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.
• We present a free-space interferometer to observe two-particle interference of a pair of atoms with entangled momenta. • The source of atom pairs is a Bose-Einstein condensate subject to a dynamical instability, and the interferometer is realized using Bragg diiraction on optical lattices. • Our observations rule out the possibility of a purely mixed state at the input of the interferometer. • Our current setup can be extended to enable a test of a Bell inequality on momentum observables. Bragg mirror and splitters momentum energy excited state • Mirror: 100 µs pulse (π-pulse) • Splitter: 50 µs pulse (π/2-pulse) • The lasers imprint their phase on the atomic modes (φ A,B) • Spectral broadening induced by the short interaction time: → the same lattice addresses (p,-p') and (-p, p') → addition of a velocity-dependent phase away from the energy resonance • Correlation coefficient: E = V cos(φ A-φ B-2δτ) Interferometer diagram • Input state: • Joint detection probabilities: • Correlation coeecient: • Violation of a Bell inequality if V > 1/√2 Source of atom pairs quasimomentum in the lattice frame energy lowest Bloch band 1st BZ • Dynamical instability driven by moving optical lattice → emission of atom pairs with opposite momenta • Broad resonance → several pairs of modes are coherently populated • Filtering the data reduces the state to the desired form: center-of-mass frame • Analysis of 3 diierent sets of modes → access to 3 diierent phases (φ A-φ B-2δτ)
Witnessing continuous-variable Bell nonlocality is a challenging endeavor, but Bell himself showed how one might demonstrate this nonlocality. Although Bell nearly showed a violation using the Clauser-Horne-Shimony-Holt (CHSH) inequality with sign-binned position-momentum statistics of entangled pairs of particles measured at different times, his demonstration is subject to approximations not realizable in a laboratory setting. Moreover, he does not give a quantitative estimation of the maximum achievable violation for the wave function he considers. In this article, we show how his strategy can be reimagined using the transverse positions and momenta of entangled photon pairs measured at different propagation distances, and we find that the maximum achievable violation for the state he considers is actually very small relative to the upper limit of 222\sqrt{2}22​. Although Bell's wave function does not produce a large violation of the CHSH inequality, other states may yet do so.