Effect of an Impurity on Grey Soliton Dynamics in Cigar-Shaped Bose-Einstein Condensate

TL;DR

This paper investigates how an impurity affects the dynamics of grey solitons in a cigar-shaped Bose-Einstein condensate, revealing modifications in soliton speed, energy, and defect interactions.

Contribution

It provides explicit solutions showing the coexistence of grey solitons and localized defects, highlighting how impurities influence soliton properties and dynamics.

Findings

Impurity lowers the grey soliton speed compared to defect-free cases.

The wave vector of the impurity is controlled by the soliton velocity.

Soliton energy is significantly affected by impurity interactions.

Abstract

In a cigar shaped Bose-Einstein condensate, explicit solutions of the coupled mean-field equations, describing defect-grey soliton dynamics are obtained, demonstrating the coexistence of grey soliton and a localized defect. Unlike the case of dark soliton, where the defect trapping center has vanishing superfluid density, the moving grey soliton necessarily possesses a finite superfluid component at the defect location. The wave vector of the impurity is controlled by the velocity of the grey soliton, which has an upper bound. It is found that the presence of the impurity lowers the speed of the grey soliton, as compared to the defect free case, where it can reach the sound velocity. The grey soliton's energy gets substantially modified through its interaction with the defect, opening up the possibility of its control through defect dynamics.