Stabilization of ring dark solitons in Bose-Einstein condensates

TL;DR

This paper demonstrates that applying a radial Gaussian external potential can stabilize ring dark solitons in two-dimensional Bose-Einstein condensates, which are typically unstable, by analyzing stability across various parameters.

Contribution

It introduces a method to stabilize ring dark solitons using a radial Gaussian potential and explores their stability and particle-like behavior.

Findings

Ring dark solitons can be stabilized within specific potential and chemical potential ranges.

Numerical results confirm the effectiveness of the stabilization method.

Particle picture models agree well with numerical simulations.

Abstract

Earlier work has shown that ring dark solitons in two-dimensional Bose-Einstein condensate are generically unstable. In this work, we propose a way of stabilizing the ring dark soliton via a radial Gaussian external potential. We investigate the existence and stability of the ring dark soliton upon variations of the chemical potential and also of the strength of the radial potential. Numerical results show that the ring dark soliton can be stabilized in a suitable interval of external potential strengths and chemical potentials. We also explore different proposed particle pictures considering the ring as a moving particle and find, where appropriate, results in very good qualitative and also reasonable quantitative agreement with the numerical findings.