Probing non-locality of interactions in a Bose-Einstein Condensate using solitons

TL;DR

This paper investigates how non-local interactions in a Bose-Einstein Condensate affect soliton properties, revealing that non-locality enhances soliton stability and modifies their width, with solutions described by a modified Gross-Pitaevskii equation.

Contribution

It provides exact solutions for solitons in a non-local BEC using the modified GP equation and analyzes their stability, highlighting the stabilizing effect of non-local interactions.

Findings

Non-local interactions alter soliton width similarly to the healing length.

Solitons are stable under non-local interactions, confirmed by VK criterion.

Non-locality enhances the stability of soliton solutions.

Abstract

We consider a Bose-Einstein Condensate(BEC) with non-local inter-particle interactions. The local Gross-Pitaevskii(GP) equation is valid for the gas parameter $\nu =: a^{3} n_{0} << 1$, but for $\nu \rightarrow 1$, the BEC is described by modified GP equation(MGPE). We study the exact solutions of the MGPE describing bright and dark solitons. It turns out that the width of these non-local solitons has qualitatively similar behaviour as the modified healing length due to the non-local interactions of the MGPE. We also study the effect of the non-locality and gas parameter({\nu}) on the stability of the solitons using the Vakhitov Kolokolov(VK) stability criterion. We show that these soliton solutions are indeed stable. Further, the stability of these soliton solutions gets enhanced due to the non-locality of interactions.