Violation of the Cauchy-Schwarz inequality with matter waves

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 real...

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Bibliographic Details
Published in:Physical review letters 2012-06, Vol.108 (26), p.260401-260401, Article 260401
Main Authors: Kheruntsyan, K V, Jaskula, J-C, Deuar, P, Bonneau, M, Partridge, G B, Ruaudel, J, Lopes, R, Boiron, D, Westbrook, C I
Format: Article
Language:English
Subjects:
Condensed Matter
Physics
Quantum Gases
Quantum Physics
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.108.260401