Violation of the Cauchy-Schwarz inequality with matter waves

TL;DR

This paper demonstrates the violation of the classical Cauchy-Schwarz inequality using matter waves from colliding Bose-Einstein condensates, highlighting quantum correlations in massive particles and expanding quantum nonlocality tests.

Contribution

It reports the first experimental violation of a multimode Cauchy-Schwarz inequality with atomic matter waves from Bose-Einstein condensates.

Findings

Quantum correlations exceed classical bounds.

Violation observed in atom number correlations.

Potential for new quantum nonlocality experiments with massive particles.

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.