Entanglement in the Bogoliubov vacuum

TL;DR

This paper investigates how entanglement varies in the Bogoliubov vacuum of an interacting Bose-Einstein condensate on lattices, revealing that entanglement depends on interaction strength and geometry, with notable finite size effects.

Contribution

It provides a detailed analysis of entanglement properties in the Bogoliubov vacuum, including the effects of geometry, interaction strength, and finite size, using logarithmic negativity as a measure.

Findings

Short-range entanglement grows linearly with group size and is enhanced by strong interactions.

Long-range entanglement is more prominent under weaker interactions.

No bound entanglement was observed in the studied configurations.

Abstract

We analyze the entanglement properties of the Bogoliubov vacuum, which is obtained as a second order approximation to the ground state of an interacting Bose--Einstein condensate. We work on one and two dimensional lattices and study the entanglement between two groups of lattice sites as a function of the geometry of the configuration and the strength of the interactions. As our measure of entanglement we use the logarithmic negativity, supplemented by an algorithmic check for bound entanglement where appropriate. The short-range entanglement is found to grow approximately linearly with the group sizes and to be favored by strong interactions. Conversely, long range entanglement is favored by relatively weak interactions. Working with periodic boundary conditions we find some surprising finite size effects for the very long range entanglement. No examples of bound entanglement is found.