Vortices and Ring Solitons in Bose-Einstein Condensates

TL;DR

This paper investigates the stability of vortices and ring solitons in Bose-Einstein condensates using the nonlinear Schrödinger equation, revealing that vortices can stabilize ring solitons in harmonic traps, a novel finding.

Contribution

It demonstrates the stabilization of ring solitons by vortices in Bose-Einstein condensates, a first in higher-dimensional nonlinear Schrödinger systems.

Findings

Vortices stabilize ring solitons in harmonic traps.

Ring solitons are stable in Bose-Einstein condensates, unlike in optics.

First example of stable dark solitons in higher dimensions.

Abstract

The form and stability properties of axisymmetric and spherically symmetric stationary states in two and three dimensions, respectively, are elucidated for Bose-Einstein condensates. These states include the ground state, central vortices, and radial excitations of both. The latter are called ring solitons in two dimensions and spherical shells in three. The nonlinear Schrodinger equation is taken as the fundamental model; both extended and harmonically trapped condensates are considered. It is found that the presence of a vortex stabilizes ring solitons in a harmonic trap, in contrast to the well known instability of such solutions in the optics context. This is the first known example of a dark soliton in the cubic nonlinear Schrodinger equation which is stable in a number of dimensions greater than one.