Entanglement in an expanding toroidal Bose-Einstein condensate

TL;DR

This paper investigates the entanglement generated in expanding toroidal Bose-Einstein condensates, modeling early universe inflation, and proposes methods for experimental measurement of this entanglement.

Contribution

It introduces a Gaussian state framework to quantify entanglement in expanding BECs, including effects like decoherence and initial squeezing, and proposes an experimental protocol for measurement.

Findings

Expansion induces measurable entanglement between phonons.

Decoherence reduces, while initial squeezing can enhance entanglement.

A feasible experimental protocol for entanglement quantification is described.

Abstract

Recent experiments have employed rapidly expanding toroidal Bose-Einstein condensates (BECs) to mimic the inflationary expansion in the early universe. One expected signature of the expansion in such experiments is spontaneous particle creation (of phonons) which is observable in density-density correlations. We study entanglement of these particles, which are known to result in a two-mode squeezed state. Using techniques for Gaussian states of continuous variable systems, we quantify the entanglement generated in this system, including effects such as decoherence and the use of an initially squeezed state, which can suppress and enhance entanglement, respectively. We also describe a protocol to experimentally measure the correlations entering the covariance matrix, allowing an experimental quantification of the entanglement properties of the inflationary BEC.