Topological Excitations in Spinor Bose-Einstein Condensates

TL;DR

This paper explores complex topological excitations in spinor Bose-Einstein condensates, focusing on non-Abelian vortices and knots, their unique properties, collision dynamics, and methods of creation in cold atomic systems.

Contribution

It introduces the study of non-Abelian vortices and knots in spinor BECs, highlighting their topological stability and methods for their creation and collision analysis.

Findings

Non-Abelian vortices do not reconnect or pass through each other, but form stable rungs.

Knots characterized by linking number or Hopf invariant can be created using magnetic fields.

Collision dynamics of non-Abelian vortices in the cyclic phase are analyzed.

Abstract

A rich variety of order parameter manifolds of multicomponent Bose-Einstein condensates (BECs) admit various kinds of topological excitations, such as fractional vortices, monopoles, skyrmions, and knots. In this paper, we discuss two topological excitations in spinor BECs: non-Abelian vortices and knots. Unlike conventional vortices, non-Abelian vortices neither reconnect themselves nor pass through each other, but create a rung between them in a topologically stable manner. We discuss the collision dynamics of non-Abelian vortices in the cyclic phase of a spin-2 BEC. In the latter part, we show that a knot, which is a unique topological object characterized by a linking number or a Hopf invariant [$\pi_3 (S^2)=Z$], can be created using a conventional quadrupole magnetic field in a cold atomic system.