Stability and dynamics of vortex clusters in nonrotated Bose-Einstein condensates

TL;DR

This paper systematically analyzes the stability and dynamics of vortex clusters in nonrotated Bose-Einstein condensates, revealing conditions for stability and the complex evolution of unstable vortex configurations.

Contribution

It provides a comprehensive stability analysis of vortex clusters in BECs, clarifying previous contradictions and exploring their dynamical behaviors under various parameters.

Findings

Stability depends on interaction strength and trap anisotropy.

Certain parameter ranges allow stable vortex clusters.

Unstable clusters can undergo vortex annihilation and regeneration.

Abstract

We study stationary clusters of vortices and antivortices in dilute pancake-shaped Bose-Einstein condensates confined in nonrotating harmonic traps. Previous theoretical results on the stability properties of these topologically nontrivial excited states are seemingly contradicting. We clarify this situation by a systematic stability analysis. The energetic and dynamic stability of the clusters is determined from the corresponding elementary excitation spectra obtained by solving the Bogoliubov equations. Furthermore, we study the temporal evolution of the dynamically unstable clusters. The stability of the clusters and the characteristics of their destabilizing modes only depend on the effective strength of the interactions between particles and the trap anisotropy. For certain values of these parameters, there exist several dynamical instabilities, but we show that there are also regions in which some of the clusters are dynamically stable. Moreover, we observe that the dynamical instability of the clusters does not always imply their structural instability, and that for some dynamically unstable states annihilation of the vortices is followed by their regeneration, and revival of the cluster.