# Quantum non-local effects with Bose-Einstein condensates

## TL;DR

This paper theoretically investigates how measurements on two Bose-Einstein condensates in different spin states can lead to the emergence of a definite relative phase, and how quantum effects like Bell inequality violations reappear with many measurements.

## Contribution

It demonstrates the emergence and re-emergence of quantum non-local effects in Bose-Einstein condensates through sequential measurements, highlighting the transition between quantum and classical regimes.

## Key findings

- A fixed relative phase rapidly emerges from initial undefined states.
- Bell inequalities are violated even with a large number of particles.
- Quantum effects reappear at maximum measurements, indicating non-local correlations.

## Abstract

We study theoretically the properties of two Bose-Einstein condensates in different spin states, represented by a double Fock state. Individual measurements of the spins of the particles are performed in transverse directions, giving access to the relative phase of the condensates. Initially, this phase is completely undefined, and the first measurements provide random results. But a fixed value of this phase rapidly emerges under the effect of the successive quantum measurements, giving rise to a quasi-classical situation where all spins have parallel transverse orientations. If the number of measurements reaches its maximum (the number of particles), quantum effects show up again, giving rise to violations of Bell type inequalities. The violation of BCHSH inequalities with an arbitrarily large number of spins may be comparable (or even equal) to that obtained with two spins.