Bell inequality, Einstein-Podolsky-Rosen steering and quantum metrology with spinor Bose-Einstein condensates

TL;DR

This paper proposes an experiment using spinor Bose-Einstein condensates to violate Bell inequalities, demonstrate EPR paradox, and enhance quantum metrology, advancing the understanding of quantum correlations in many-body systems.

Contribution

It introduces a detailed experimental scheme for Bell tests in massive particles and analyzes how correlations influence Bell violation and quantum metrology applications.

Findings

Bell inequality violation depends on correlation strength and pair number

System can demonstrate the EPR paradox in a many-body setting

Scattered pairs serve as resources for quantum-enhanced metrology

Abstract

We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor $F=1$ Bose-Einstein condensate residing in an optical lattice. We characterize the complete experimental procedure--- the local operations, the measurements and the inequality---necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. Also, the scattered pairs are an excellent many-body resource for the quantum-enhanced metrology. With the possibility to generalize our analysis to other configurations in a straightforward way, the presented inquiry can be important in the planning of the forthcoming Bell tests in correlated atomic systems.