Dark Solitons in F = 1 Spinor Bose – Einstein Condensate

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× 2 matrix nonlinear Schrödinger 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.