Fractional windings of the spinor condensates on a ring

TL;DR

This paper investigates fractional winding states in one-dimensional spinor Bose-Einstein condensates on a ring, revealing their connection to super-current, spin rotation, and gauge-spin symmetry, with implications for fractional vortices.

Contribution

It introduces a method to analyze fractional windings in spinor condensates on a ring, linking super-current, spin rotation, and gauge-spin symmetry.

Findings

Identification of fractional winding numbers in spinor condensates.

Connection between fractional windings and gauge-spin symmetry.

Potential application to fractional vortices in 2D condensates.

Abstract

We study the uniform solutions to the one-dimensional spinor Bose-Einstein condensates on a ring. These states explicitly display the associated motion of the super-current and the spin rotation, which give rise to fractional winding numbers according to the various compositions of the hyperfine states. It simultaneously yields a fractional factor to the global phase due to the gauge-spin symmetry. Our method can be applied to explore the fractional vortices by identifying the ring as the boundary of two-dimensional spinor condensates.