Core structure of static ferrodark solitons in a spin-1 Bose-Einstein condensate

TL;DR

This paper analytically describes static ferrodark solitons in spin-1 Bose-Einstein condensates, revealing their structure, properties, and relation to topological defects, with results validated by numerical simulations.

Contribution

It introduces analytical ansatzes for ferrodark solitons, characterizes their types and length scales, and links them to topological defects in the condensate.

Findings

Type-I ferrodark soliton has a single width

Type-II ferrodark soliton exhibits two length scales

Ferrodark solitons agree well with numerical results

Abstract

We develop an analytical description of static ferrodark solitons, the $\mathbb{Z}_2$ topological defects in the magnetic order, in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed ansatzes show excellent agreement with numerical results. Spin-singlet amplitudes, nematic tensor densities and nematic currents of ferrodark solitons are also discussed. The $\mathbb{Z}_2$ topological defects in the mass superfluid order, dark-dark-dark vector solitons, are obtained exactly in the parameter regime where exact ferrodark solitons exist. The dark-dark-dark vector soliton has higher excitation energy than ferrodark solitons.