Collision Dynamics and Rung Formation of non-Abelian Vortices

We investigate the collision dynamics of two non-Abelian vortices and find that, unlike Abelian vortices, they neither reconnect themselves nor pass through each other, but create a rung between them in a topologically stable manner. Our predictions are verified using the model of the cyclic phase of a spin-2 spinor Bose-Einstein condensate.

Figure 1

(a) Four closed paths for two colliding vortices, where $A$ and $B$ denote the corresponding topological charges. (b) Path homotopic to path $d$ in (a), and topological charges of vortices. (c) $Y$-shaped junction. (d) Linked vortices. (e)–(g) Collision patterns from two vortices starting from the configuration in (a). (e) Passing through. (f) Rung $AB$ between two vortices. (g) Rung $B{A}^{-1}$ between two vortices. (h) Collision of linked vortices and rung $BA{B}^{-1}{A}^{-1}$.

Figure 2

Collision dynamics of two non-Abelian vortices [27]. (a)–(c) Formation of an $\mathit{F}\ne 0$ rung from two straight vortices. (d)–(f) Formation of an $A_{00}\ne 0$ rung from two straight vortices. (g)–(i) Formation of an $A_{00}\ne 0$ rung from two linked vortices. In all the figures, the isosurfaces of magnetization $|\mathit{F}{|}^2$ and the singlet-pair amplitude $|A_{00}{|}^2$ are shown for vortex cores with $|\mathit{F}{|}^2\ne 0$ and $|A_{00}{|}^2\ne 0$, respectively [see Eq. (2) and the following sentences]. The topological charge of each vortex is also indicated.