Soft Matter and Complex Systems Seminar

Entanglement between two separate systems is a necessary resource to violate a Bell inequality in a test of local realism. We demonstrate that to overcome the Bell bound, this correlation must be accompanied by the entanglementbetween the constituent particles. This happens whenever a super-selection rule imposes a constraint on feasible local operations. Next, we propose an experiment, where the violation of the Bell inequality occurs between two distant parts of a many-body system of massive particles. The source of correlated atoms is a spinor Bose-Einstein condensate residing in an optical lattice, as in: M. Bonneau, et al., Phys. Rev. A 87, 061603 (2013). We characterize the complete experimental procedure, together with the local operations and the measurements, necessary to run the Bell test. We show how the amplitude of the violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs.