Symmetry breaking and singularity structure in Bose-Einstein condensates

TL;DR

This paper analyzes the dynamics of vortex singularities in Bose-Einstein condensates after symmetry-breaking impulses, revealing forces that influence vortex trajectories and conditions for vortex reconstruction.

Contribution

It provides an analytical and numerical study of vortex trajectories post-symmetry breaking, highlighting the effects of effective forces and the impact of interactions.

Findings

Parent vortex is reconstructed in non-interacting case after one trap period.

Weak interactions prevent parent vortex reconstruction.

Analytical trajectories match wavefunction minima with less than 0.5% error.

Abstract

We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity, and a Magnus force that introduces a torque about the axis of symmetry. For the analytical non-interacting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wavefunction, showing less 0.5% error for impulse strength of (v=0.00005). We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry breaking potential does not significantly change the dynamics of the system as long as the strength is below (v=0.0005).