# Skyrmion-string defects with arbitrary topological charges in spinor Bose-Einstein condensates

## TL;DR

This paper demonstrates the existence of Skyrmion-string defects with arbitrary topological charges in spinor Bose-Einstein condensates under cylindrical magnetic fields, using numerical solutions of coupled Gross-Pitaevskii equations.

## Contribution

It introduces a method to realize and analyze topological defects with arbitrary charges in spinor BECs without symmetry assumptions.

## Key findings

- Skyrmion-string defects with arbitrary topological charges are shown to exist.
- The topological charge depends on magnetic boundary conditions.
- Numerical solutions confirm the robustness of these defects.

## Abstract

Under the presence of external magnetic fields with cylindrical symmetry, Skyrmion-string defects with arbitrary topological charges are shown to appear in spinor $F = 1$ Bose-Einstein condensates. We show that, depending on the magnetic field boundary condition, the topological spin texture, at the planes perpendicular to the cylindrical axis, can take zero, half integer, or arbitrary values between $-1/2$ and $1/2$. We argue that these are true topological defects since their charge is independent of the spatial location of the singularity and since the total Skyrmion charge is the sum of the individual charges of the defects present. Our findings are obtained by numerically solving the corresponding fully coupled Gross-Pitaevskii equations without any symmetry assumptions. We analyze, both, polar $^{23}$Na and ferromagnetic $^{87}$Rb condensates.