The dynamics of quantum vortices in a toroidal trap

TL;DR

This paper investigates the behavior, stability, and interactions of quantum vortices in a two-dimensional toroidal Bose-Einstein condensate using numerical simulations of the Gross-Pitaevskii equation, revealing complex dynamics and richer solution structures.

Contribution

It provides new insights into vortex dynamics in toroidal geometries, including families of solitary waves, stability analysis, and vortex collision behaviors, expanding understanding beyond previous simpler models.

Findings

Rich dispersion curves in toroidal geometry.

Existence of multiple vortex states at same position and circulation.

Vortex collisions are elastic or inelastic depending on angular velocity.

Abstract

The dynamics of quantum vortices in a two-dimensional annular condensate are considered by numerically simulating the Gross-Pitaevskii equation. Families of solitary wave sequences are reported, both without and with a persistent flow, for various values of interaction strength. It is shown that in the toroidal geometry the dispersion curve of solutions is much richer than in the cases of a semi-infinite channel or uniform condensate studied previously. In particular, the toroidal condensate is found to have states of single vortices at the same position and circulation that move with different velocities. The stability of the solitary wave sequences for the annular condensate without a persistent flow are also investigated by numerically evolving the solutions in time. In addition, the interaction of vortex-vortex pairs and vortex-antivortex pairs is considered and it is demonstrated that the collisions are either elastic or inelastic depending on the magnitude of the angular velocity. The similarities and differences between numerically simulating the Gross-Pitaevskii equation and using a point vortex model for these collisions are elucidated.