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

TL;DR

This paper proposes an experimental scheme to test spatial mode entanglement of massive bosons, challenging the necessity of the particle number superselection rule and advancing understanding of non-locality in quantum fields.

Contribution

It introduces a novel experimental approach to demonstrate mode entanglement in massive particles and questions the fundamental nature of superselection rules.

Findings

Predicted entanglement between spatial modes of massive bosons.

Proposed scheme can demonstrate non-local correlations in such systems.

Challenges the idea that superselection rules are fundamental.

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.