Deformation of dark solitons in inhomogeneous Bose-Einstein condensates

TL;DR

This paper investigates how inhomogeneous backgrounds in Bose-Einstein condensates cause dark solitons to deform and emit sound, affecting their stability and profile, with detailed quantitative analysis across various potential landscapes.

Contribution

It provides a detailed quantitative study of sound emission and soliton deformation in inhomogeneous BECs, highlighting the role of background density gradients.

Findings

Sound emission is a significant fraction of soliton energy.

Continuous sound emission causes observable soliton deformation.

Sound power correlates with the square of the soliton's displacement from its density minimum.

Abstract

A dark soliton becomes unstable when it is incident on a background density gradient, and the induced instability results in the emission of sound. Detailed quantitative studies of sound emission are performed for various potentials, such as steps, linear ramps and gaussian traps. The amount of sound emission is found to be a significant fraction of the soliton energy for typical potentials. Continuous emission of sound is found to lead to an apparent deformation of the soliton profile. The power emitted by the soliton is shown to be parametrised by the square of the displacement of the centre of mass of the soliton from its density minimum, thus highlighting the significance of the inhomogeneity-induced soliton deformation.