Homotopy Theory of Topological Defects in Spinor Condensates

TL;DR

This paper applies homotopy group theory to classify topological defects in spinor Bose-Einstein condensates, revealing new non-Abelian line defects and fractional winding numbers, thus advancing understanding of quantum topological phenomena.

Contribution

It provides a rigorous homotopy-theoretic classification of defects in spinor condensates, resolving previous ambiguities and identifying novel non-Abelian and fractional defects in these systems.

Findings

Clarifies symmetry groups and order parameter spaces for spin-1 condensates.

Identifies non-Abelian line defects in spin-2 condensates.

Predicts the existence of fractional winding numbers such as 1/3.

Abstract

We investigate the topological defects in atomic spin-1 and spin-2 Bose-Einstein condensates by applying the homotopy group theory. With this rigorous approach we clarify the previously controversial identification of symmetry groups and order parameter spaces for the spin-1 case, and show that the spin-2 case provides a rare example of a physical system with non-Abelian line defects, and the possibility to have winding numbers of 1/3 and its multiples.