Dark solitons in F=1 spinor Bose--Einstein condensate

TL;DR

This paper analyzes dark soliton solutions in a spinor Bose--Einstein condensate with F=1, revealing distinct ferromagnetic and polar states, their interactions, and spin-mixing phenomena during collisions.

Contribution

It provides explicit solutions for one- and two-soliton states in a multi-component condensate, highlighting the role of boundary conditions and spin states.

Findings

Ferromagnetic solitons have domain-wall wavefunctions with nonzero total spin.

Polar solitons are hole-like with zero total spin.

Spin-mixing occurs during two-soliton collisions, with ferromagnetic solitons actively transferring spin.

Abstract

We study dark soliton solutions of a multi-component Gross--Pitaevskii equation for hyperfine spin F=1 spinor Bose--Einstein condensate. The interactions are supposed to be inter-atomic repulsive and anti-ferromagnetic ones of equal magnitude. The solutions are obtained from those of an integrable $2\times 2$ matrix nonlinear Schr\"{o}dinger equation with nonvanishing boundary conditions. We investigate the one-soliton and two-soliton solutions in detail. One-soliton is classified into two kinds. The ferromagnetic state has wavefunctions of domain-wall shape and its total spin is nonzero. The polar state provides a hole soliton and its total spin is zero. These two states are selected by choosing the type of the boundary conditions. In two-soliton collisions, we observe the spin-mixing or spin-transfer. It is found that, as "magnetic" carriers, solitons in the ferromagnetic state are operative for the spin-mixing while those in the polar are passive.