Statics and dynamics of atomic dark-bright solitons in the presence of delta-like impurities

TL;DR

This paper investigates how delta-like impurities affect the static and dynamic behavior of dark-bright solitons in a two-component Bose-Einstein condensate, revealing counter-intuitive impurity effects on soliton motion.

Contribution

It introduces an analytical framework for understanding impurity effects on dark-bright solitons, validated by numerical simulations and Bogoliubov-de Gennes analysis.

Findings

Attractive impurities create effective barriers for solitons.

Repulsive impurities act as effective wells for solitons.

Analytical predictions agree with numerical and BdG results.

Abstract

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the stat- ics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counter-intuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscil- lations of solitons are found to be in good agreement with results obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.