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

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... [ view full 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 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. Our results apply to any multi-mode system where the spin-changing collision drives the scattering into separate regions. The presented inquiry shows that such system is versatile as it can be used for the tests of non-locality, quantum metrology and  quantum information