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Journal of the Physical Society of Japan

Wave Propagations in theF=1 Spinor Bose–Einstein Condensates

Miki Wadati, Naoshi Tsuchida

Published Jan 15, 2006• 36 citations
Publisher

Abstract

Propagations of nonlinear waves in the quasi-one dimensional F =1 spinor Bose–Einstein condensates are studied. The three-component macroscopic wavefunction obeys a generalized Gross–Pitaevskii equation (nonlinear Schrödinger equation). Plane wave and solitary wave solutions are obtained explicitly. It is shown that the analysis of the plane waves leads to a classification of solitary waves, which are known as polar solitons and ferromagnetic solitons.

DOI
10.1143/jpsj.75.014301

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Propagations of nonlinear waves in the quasi-one dimensional F =1 spinor Bose–Einstein condensates are studied. The three-component macroscopic wavefunction obeys a generalized Gross–Pitaevskii equation (nonlinear Schrödinger equation). Plane wave and solitary wave solutions are obtained explicitly. It is shown that the analysis of the plane waves leads to a classification of solitary waves, which are known as polar solitons and ferromagnetic solitons.
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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 2×22\times 22×2 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.
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In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an F=2 spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain the explicit bright one- and two-soliton solutions for the equation via symbolic computation. With the choice of polarization parameter and spin density, the one-soliton solutions are divided into four types: one-peak solitons in the ferromagnetic and cyclic states and one- and two-peak solitons in the polar states. For the former two, solitons share the similar shape of one peak in all components. Solitons in the polar states have the one- or two-peak profiles, and the separated distance between two peaks is inversely proportional to the value of polarization parameter. Based on the asymptotic analysis, we analyze the collisions between two solitons in the same and different states.
Abstract Nonlinearity is one of the most remarkable characteristics of Bose–Einstein condensates (BECs). Much work has been done on one- and two-component BECs with time- or space-modulated nonlinearities, while there is little work on spinor BECs with space–time-modulated nonlinearities. In the present paper we investigate localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with nonlinearities dependent on time and space. We solve the three coupled Gross–Pitaevskii equations by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and the Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasi-breathing solitons and resonant solitons. The results show that one-order vector breathing solitons, quasi-breathing solitons, resonant solitons and the moving breathing solitons ψ ±1 are all stable, but the moving breathing soliton ψ 0 is unstable. We also present the experimental parameters to realize these phenomena in future experiments.