Bell-inequality test of spatial mode entanglement of a single massive particle

Abstract

Experiments showing the violation of Bell inequalities have formed our belief that the world at its smallest is genuinely non-local. While many non-locality experiments use the first quantised picture, the physics of fields of indistinguishable particles, such as bosonic gases, is captured most conveniently by second quantisation. This implies the possibility of non-local correlations, such as entanglement, between modes of the field. In this paper we propose an experimental scheme that tests the theoretically predicted entanglement between modes in space occupied by massive bosons. Moreover, the implementation of the proposed scheme is capable of proving that the particle number superselection rule is not a fundamental necessity of quantum theory but a consequence of not possessing a distinguished reference frame.

5 pages, 2 figures. Version two has been accepted for publication in Physical Review A

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• Entanglement consumption of instantaneous nonlocal quantum measurements
• Bell's experiment with intra- and inter-pair entanglement: Single-particle mode entanglement as a case study
• Deterministic teleportation using single-photon entanglement as a resource
• Bell inequality for pairs of particle-number-superselection-rule restricted states
• Reference frames for Bell inequality violation in the presence of superselection rules
• NRG for the bosonic single-impurity Anderson model: Dynamics
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles
• Proposal for a Bell Test with Entangled Atoms of Different Mass
• Quantifying entanglement when measurements are imperfect or restricted
• Teleportation of a quantum state of a spatial mode with a single massive particle
• Introduction to Measurement Space and Application to Operationally Useful Entanglement and Mode Entanglement