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 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. 
K. V. Kheruntsyan, J.-C. Jaskula, P. Deuar, M. Bonneau, G. B.   Partridge, J. Ruaudel, R. Lopes, D. Boiron, C. I. Westbrook
quant-ph cond-mat.quant-gas