Non-locality of Two Ultracold Trapped Atoms

TL;DR

This paper investigates the non-local quantum entanglement generated between two ultracold trapped atoms due to short-range interactions, analyzing its dependence on trap separation, scattering length, and environmental effects.

Contribution

It provides a detailed analysis of continuous variable entanglement in a two-atom system, including its quantification and violation of Bell inequalities under various conditions.

Findings

Entanglement depends on trap distance and scattering length.

Ground state entanglement can violate Bell inequalities.

Environmental effects can diminish entanglement.

Abstract

We undertake a detailed analysis of the non-local properties of the fundamental problem of two trapped, distinguishable neutral atoms which interact with a short range potential characterised by an s-wave scattering length. We show that this interaction generates continuous variable (CV) entanglement between the external degrees of freedom of the atoms and consider its behaviour as a function of both, the distance between the traps and the magnitude of the inter-particle scattering length. We first quantify the entanglement in the ground state of the system at zero temperature and then, adopting a phase-space approach, test the violation of the Clauser-Horn-Shimony-Holt inequality at zero and non-zero temperature and under the effects of general dissipative local environments.