Existence, stability and nonlinear dynamics of vortices and vortex clusters in anisotropic Bose-Einstein condensates

TL;DR

This paper investigates how anisotropic confinement affects the existence, stability, and dynamics of vortices and vortex clusters in Bose-Einstein condensates, combining bifurcation analysis and particle interaction models.

Contribution

It introduces a combined bifurcation and particle interaction framework to analyze vortex behavior in anisotropic Bose-Einstein condensates, extending understanding beyond isotropic cases.

Findings

Anisotropy breaks rotational symmetry, affecting vortex configurations.

Bifurcation analysis reveals symmetry-breaking pathways for vortex states.

Numerical simulations confirm the particle-like behavior of vortices.

Abstract

We study vortex excitations in one-component Bose-Einstein condensates, with a special emphasis on the role of anisotropic confinement for the existence, stability and dynamical properties of vortices and particularly few-vortex clusters. Symmetry breaking features are pervasive within this system even in its isotropic installment, where cascades of symmetry breaking bifurcations give rise to the multi-vortex clusters, but also within the anisotropic realm which naturally breaks the rotational symmetry of the multi-vortex states. Our first main tool for analyzing the system consists of a weakly nonlinear (bifurcation) approach which starts from the linear states of the problem and examines their continuation and bifurcation into novel symmetry-broken configurations in the nonlinear case. This is first done in the isotropic limit and the modifications introduced by the anisotropy are subsequently presented. The second main tool concerns the highly nonlinear regime where the vortices can be considered as individual topologically charged "particles" which precess within the parabolic trap and interact with each other, similarly to fluid vortices. The conclusions stemming from both the bifurcation and the interacting particle picture are corroborated by numerical computations which are also used to bridge the gap between these two opposite-end regimes.