title: Violation of the Cauchy-Schwarz inequality with matter waves.
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.
authors.affiliation: The University of Queensland, School of Mathematics and Physics, Brisbane, Queensland 4072, Australia.
authors.forename: K V
authors.initials: KV
authors.lastname: Kheruntsyan
authors.forename: J-C
authors.initials: JC
authors.lastname: Jaskula
authors.forename: P
authors.initials: P
authors.lastname: Deuar
authors.forename: M
authors.initials: M
authors.lastname: Bonneau
authors.forename: G B
authors.initials: GB
authors.lastname: Partridge
authors.forename: J
authors.initials: J
authors.lastname: Ruaudel
authors.forename: R
authors.initials: R
authors.lastname: Lopes
authors.forename: D
authors.initials: D
authors.lastname: Boiron
authors.forename: C I
authors.initials: CI
authors.lastname: Westbrook