Topological Defects in Ferromagnetic, Antiferromagnetic and Cyclic Spinor Condensates -- A Homotopy Theory

TL;DR

This paper uses homotopy group theory to classify topological defects in spinor Bose-Einstein condensates, revealing stable defects, clarifying symmetry group controversies, and predicting fractional vortices.

Contribution

It provides a rigorous classification of topological defects in spinor condensates, including non-Abelian line defects and fractional vortices, advancing understanding of their topological properties.

Findings

Identified topologically stable defects for various spin states.

Clarified symmetry groups and order parameter spaces.

Predicted fractional winding number vortices.

Abstract

We apply the homotopy group theory in classifying the topological defects in atomic spin-1 and spin-2 Bose-Einstein condensates. The nature of the defects depends crucially on the spin-spin interaction between the atoms. We find the topologically stable defects both for spin-1 ferromagnetic and anti-ferromagnetic states, and for spin-2 ferromagnetic and cyclic states. With this rigorous approach we clarify the previously controversial identification of symmetry groups and order parameter spaces for the spin-1 anti-ferromagnetic state, and show that the spin-2 cyclic case provides a rare example of a physical system with non-Abelian line defects, like those observed in biaxial nematics. We also show the possibility to produce vortices with fractional winding numbers of 1/2, 1/3 and their multiples in spinor condensates.