# Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates: Existence, Stability and Dynamics

## TL;DR

This paper investigates the existence, stability, and dynamics of single and multiple vortex rings in three-dimensional Bose-Einstein condensates, extending previous bifurcation studies to the Thomas-Fermi regime and analyzing their stability and interactions.

## Contribution

It extends the analysis of vortex ring states to the large chemical potential regime and explores their stability, dynamics, and interactions using a particle picture approach.

## Key findings

- Vortex rings exist and are stable in the Thomas-Fermi limit.
- Multi-ring states exhibit specific equilibrium radii and inter-ring distances.
- Instability scenarios include breakup, reconnections, and vortex line formation.

## Abstract

In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of the linear limit, for isotropic or anisotropic three-dimensional harmonic traps. Here, we extend these states to the regime of large chemical potentials, the so-called Thomas-Fermi limit, and explore their properties such as equilibrium radii and inter-ring distance, for multi-ring states, as well as their vibrational spectra and possible instabilities. In this limit, both the existence and stability characteristics can be partially traced to a particle picture that considers the rings as individual particles oscillating within the trap and interacting pairwise with one another. Finally, we examine some representative instability scenarios of the multi-ring dynamics including breakup and reconnections, as well as the transient formation of vortex lines.