Dark-Solitons-in-F-=-1-Spinor-Bose–Einstein-Condensate.pdfVIP

Typeset with jpsj2.cls ver.1.2 Full Paper Dark Solitons in F = 1 Spinor Bose–Einstein Condensate Masaru Uchiyama1 ∗ , Jun’ichi Ieda2 † and Miki Wadati1 1Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033 2 Institute for Materials Research, Tohoku University, Sendai, 980-8577 We study dark soliton solutions of a multi-component Gross–Pitaevskii equation for hy- perfine 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 Schr¨odinger equation with non- vanishing 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 bound- ary 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. KEYWORDS: Bose–Einstein condensate, integrable, nonlinear Schr¨odinger equation, multi- component, dark soliton, magnetic property ∗E-mail address: uchiyama@monet.phys.s.u-tokyo.ac.jp †E-mail address: ieda@imr.tohoku.ac.jp 1/19 J. Phys. Soc. Jpn. Full Paper 1. Introductio