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Violation of the Cauchy-Schwarz Inequality with Matter Waves

K. V. Kheruntsyan, J.-C. Jaskula, P. Deuar, M. Bonneau, G. B. Partridge, J. Ruaudel, R. Lopes, D. Boiron, and C. I. Westbrook
Phys. Rev. Lett. 108, 260401 – Published 25 June 2012
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Abstract

The Cauchy-Schwarz (CS) inequality—one of the most widely used and important inequalities in mathematics—can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities. Quantum-mechanical correlations can, however, exceed classical bounds. Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo. The correlated atoms have large spatial separations and therefore open new opportunities for extending fundamental quantum-nonlocality tests to ensembles of massive particles.

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  • Received 30 March 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.260401

© 2012 American Physical Society

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Matter Waves and Quantum Correlations

Published 25 June 2012

Colliding matter waves from a Bose-Einstein condensate violate a relation called the Cauchy-Schwarz inequality, proving that such interactions must be considered quantum mechanically.

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Authors & Affiliations

K. V. Kheruntsyan1, J.-C. Jaskula2,*, P. Deuar3, M. Bonneau2, G. B. Partridge2,†, J. Ruaudel2, R. Lopes2, D. Boiron2, and C. I. Westbrook2

  • 1The University of Queensland, School of Mathematics and Physics, Brisbane, Queensland 4072, Australia
  • 2Laboratoire Charles Fabry de l’Institut d’Optique, CNRS, Université Paris-Sud, Campus Polytechnique RD128, 91127 Palaiseau, France
  • 3Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland

  • *Current address: Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA.
  • Current address: Agilent Laboratories, Santa Clara, CA 95051, USA.

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Issue

Vol. 108, Iss. 26 — 29 June 2012

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