Localization by entanglement

TL;DR

This paper demonstrates that quantum entanglement enables localization of bosonic atoms in an optical lattice even with very weak interactions, contrasting classical predictions.

Contribution

It reveals that quantum entanglement is essential for localization at weak interactions, challenging classical thresholds and providing explicit solutions for two-particle states.

Findings

Localized states exist for arbitrarily weak interactions.

Entanglement remains finite in the weak interaction limit.

Localization is driven by entanglement, not classical correlations.

Abstract

We study the localization of bosonic atoms in an optical lattice, which interact in a spatially confined region. The classical theory predicts that there is no localization below a threshold value for the strength of interaction that is inversely proportional to the number of participating atoms. In a full quantum treatment, however, we find that localized states exist for arbitrarily weak attractive or repulsive interactions for any number ($>1$) of atoms. We further show, using an explicit solution of the two-particle bound state and an appropriate measure of entanglement, that the entanglement tends to a finite value in the limit of weak interactions. Coupled with the non-existence of localization in an optimized quantum product state, we conclude that the localization exists by virtue of entanglement.