Bell correlations in a split two-mode-squeezed Bose-Einstein condensate

TL;DR

This paper proposes a protocol to observe Bell inequality violations using split two-mode-squeezed Bose-Einstein condensates, demonstrating robustness to noise and measurement imperfections.

Contribution

It introduces a novel method for creating and measuring Bell correlations in BECs, including three approaches for evaluating Bell inequality violations.

Findings

Bell inequality violations are achievable with split BECs.

The proposed methods are robust against noise and detection inefficiencies.

Sign-binning improves the detection of Bell violations without auxiliary assumptions.

Abstract

We propose and analyze a protocol for observing a violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality using two spatially separated Bose-Einstein condensates (BECs). To prepare the Bell-correlated state, spin-changing collisions are used to first prepare a two-mode squeezed BEC. This is then split into two BECs by controlling the spatial wavefunction, e.g., by modifying the trapping potential. Finally, spin-changing collisions are also exploited locally, to compensate local squeezing terms. The correlators appearing in the inequality are evaluated using three different approaches. In the first approach, correlators are estimated using normalized expectation values of number operators, in a similar way to evaluating continuous-variable Bell inequalities. An improvement to this approach is developed using the sign-binning of total spin measurements, which allows for the construction of two-outcome measurements and violations of the CHSH inequality without auxiliary assumptions. Finally, we show a third approach where maximal violations of the CH inequality can be obtained by assigning zero values to local vacua outcomes under a no-enhancement assumption. The effect of loss and imperfect detection efficiency is investigated and the observed violations are found to be robust to noise.