Half-knot in the spinor condensates

TL;DR

This paper presents an exact solitonic solution describing a twisted half-skyrmion in spinor Bose-Einstein condensates, revealing a linked half-unknot structure with fractional Hopf charge.

Contribution

It provides the first exact analytical solution for a half-knot in spinor condensates, linking topological structures with fractional Hopf charge.

Findings

Identifies a twisted half-skyrmion as a solitonic solution.

Demonstrates the linked half-unknot topology in 3D.

Connects the solution to fractional Hopf charge.

Abstract

We present an exact solution to the stationary coupled nonlinear Gross-Pitaevskii equations which govern the motion of the spinor Bose-Einstein condensates. The solitonic solution is a twisted half-skyrmion in the three-dimension (3D) space. By making a map from and the Cartesian coordinates to the toroidal coordinates, we demonstrate it is a linked half-unknot with a fractional Hopf charge.