# EPR-entangled Bose-Einstein condensates in state-dependent potentials: a dynamical study

## TL;DR

This paper investigates how atomic interactions in bi-modal Bose-Einstein Condensates within state-dependent potentials can generate non-local correlations, enabling EPR steering experiments despite spatial dynamics.

## Contribution

It introduces a combined Fock state and time-dependent Hartree-Fock approach to account for spatial and quantum correlations in BECs, demonstrating feasible entanglement generation.

## Key findings

- Successful generation of non-local entanglement in BECs
- Potential for EPR steering with spatially separated condensates
- Spatial dynamics do not hinder entanglement creation

## Abstract

We study generation of non-local correlations by atomic interactions in a pair of bi-modal Bose-Einstein Condensates in state-dependent potentials including spatial dynamics. The wave-functions of the four components are described by combining a Fock state expansion with a time-dependent Hartree-Fock Ansatz, so that both the spatial dynamics and the local and non-local quantum correlations are accounted for. We find that despite the spatial dynamics, our protocole generates enough non-local entanglement to perform an EPR steering experiment with two spatially separated con-densates of a few thousands of atoms.