Nonlocal interactions in a BEC: an Analogue Gravity perspective

TL;DR

This paper investigates how minimal non-local interactions in a Bose-Einstein Condensate affect the healing length and sound velocity, with implications for analogue gravity models and vortex dynamics.

Contribution

It introduces a correction to the Gross-Pitaevskii equation to model non-locality and analyzes its effects on BEC properties relevant to analogue gravity and condensed matter physics.

Findings

Non-locality decreases healing length more rapidly with increasing scattering length.

Sound velocity remains unaffected by the non-local correction.

Vortex size can be tuned by adjusting the healing length at finite scattering lengths.

Abstract

We add a minimal correction term to the local Gross-Pitaevskii equation to represent non-locality in the interactions. We show that the effective minimal non-locality can make the healing length decrease more rapidly with the increase of $s$-wave scattering length leaving the expression of the velocity of sound unaltered. We discuss the implication of this result for a Bose-Einstein Condensate (BEC) being used as an analogue gravity system. The presented result is important in the context of condensed matter physics as well because one can considerably change the size of a quantized vortex at finite $s$-wave scattering length by tuning the healing length.