Emergence and Stability of Vortex Clusters in Bose-Einstein Condensates: a Bifurcation Approach near the Linear Limit

TL;DR

This paper analyzes how vortex clusters form and remain stable in Bose-Einstein condensates using bifurcation theory, revealing the emergence of various vortex configurations near the system's linear limit.

Contribution

It introduces an analytical bifurcation approach to track the emergence and stability of vortex clusters in Bose-Einstein condensates near the linear limit.

Findings

Vortex clusters emerge from symmetry-breaking bifurcations.

Different vortex configurations, including polygonal and diagonal clusters, are identified.

Mixed states combining dark solitons and vortex clusters are also found.

Abstract

We study the existence and stability properties of clusters of alternating charge vortices in Bose-Einstein condensates. It is illustrated that such states emerge from cascades of symmetry-breaking bifurcations that can be analytically tracked near the linear limit of the system via weakly nonlinear few-mode expansions. We present the resulting states that emerge near the first few eigenvalues of the linear limit, and illustrate how the nature of the bifurcations can be used to understand their stability. Rectilinear, polygonal and diagonal vortex clusters are only some of the obtained states while mixed states, consisting of dark solitons and vortex clusters, are identified as well.