Spatial entanglement in interacting Bose-Einstein condensates

TL;DR

This paper investigates spatial entanglement in interacting Bose-Einstein condensates using quantum field theory, revealing how entanglement varies with region size relative to the healing length and providing detailed entropy calculations.

Contribution

It introduces a quantum field theoretic approach to analyze spatial entanglement in Bose-Einstein condensates, highlighting the transition from vacuum-like to relativistic-like entanglement regimes.

Findings

Small regions have vanishing entanglement entropy.

Large regions exhibit entanglement similar to a relativistic vacuum with sound velocity.

Calculated von Neumann and Rényi entropies for 1D quasi-condensates.

Abstract

The entanglement between spatial regions in an interacting Bose-Einstein condensate is investigated using a quantum field theoretic formalism. Regions that are small compared to the healing length are governed by a non-relativistic quantum field theory in the vacuum limit, and we show that the latter has vanishing entanglement. In the opposite limit of a region that is large compared to the healing length, the entanglement entropy is like in the vacuum of a relativistic theory where the velocity of light is replaced with the velocity of sound and where the inverse healing length provides a natural ultraviolet regularization scale. Besides the von Neumann entanglement entropy, we also calculate R\'enyi entanglement entropies for a one-dimensional quasi-condensate.