# Detection of Bell correlations at finite temperature from matter-wave interference fringes

## TL;DR

This paper demonstrates how matter-wave interference fringes from two overlapping atomic clouds can reveal Bell correlations, even at finite temperatures, linking fundamental quantum non-locality with practical quantum metrology.

## Contribution

It introduces a method to detect Bell correlations via interference fringes in a simple atomic interferometer, accounting for thermal effects and detector resolution.

## Key findings

- Bell correlations can be inferred from interference fringe sensitivity.
- Finite temperature effects still allow Bell correlation detection.
- Detector resolution impacts the measurement of Bell correlations.

## Abstract

We show that matter-wave interference fringes formed by two overlapping atomic clouds can yield information about the non-local Bell correlations. To this end, we consider a simple atomic interferometer, where the clouds are released from the double-well potential and the relative phase is estimated from the density fit to this interference pattern. The Bell correlations can be deduced from the sensitivity of the phase obtained in this way. We examine the relation between these two quantities for a wide range of ground states of the double-well, scanning through the attractive and the repulsive interactions. The presented analysis includes the effects of finite temperature, when excited states are thermally occupied. We also consider the impact of the spatial resolution of the single-atom detectors and the fluctuations of the energy mismatch between the wells. These results establish a link between the fundamental (non-locality) and application-oriented (quantum metrology) aspects of entanglement.