Topological Wigner Crystal of Half-Solitons in a Spinor BEC

TL;DR

This paper studies a one-dimensional spinor Bose-Einstein condensate with half-solitons, revealing that their interactions lead to a spontaneous formation of a topological Wigner crystal, modeled via kinetic equations.

Contribution

It introduces a topological interaction potential for half-solitons and demonstrates their collective crystallization in a gaseous phase using a kinetic model.

Findings

Half-solitons interact via a topological potential.

The system spontaneously forms a Wigner crystal.

The gaseous phase is marginally stable.

Abstract

We consider a one-dimensional gas of half-solitons in a spinor Bose-Einstein condensate. We calculate the topological interaction potential between the half-solitons. Using a kinetic equation of the Vlasov-Boltzmann type, we model the coupled dynamics of the interacting solitons. We show that the dynamics of the system in the gaseous phase is marginally stable and spontaneously evolves towards a Wigner crystal.