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Chinese Physics Letters

Vector Solitons and Soliton Collisions in Two-Component Bose–Einstein Condensates

Xunxu Liu, Zhang Xiao-Fei, Peng Zhang

Published Jul 1, 2010• 15 citations
Publisher

Abstract

With realistic parameters, both analytical and computational studies demonstrate the feasibility of forming bright-bright vector solitons in a self-repulsive two-component Bose-Einstein condensate with attractive inter-component interaction. Moreover, the stability of such solitons is confirmed by direct numerical simulations, by a Bogoliubov spectrum analysis, and by examining the collisions between two vector solitons. Our results are of considerable experimental interest.

DOI
10.1088/0256-307x/27/7/070306

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With realistic parameters, both analytical and computational studies demonstrate the feasibility of forming bright-bright vector solitons in a self-repulsive two-component Bose-Einstein condensate with attractive inter-component interaction. Moreover, the stability of such solitons is confirmed by direct numerical simulations, by a Bogoliubov spectrum analysis, and by examining the collisions between two vector solitons. Our results are of considerable experimental interest.
We analyze the dynamics of two-component vector solitons, namely, dark-bright solitons, via the variational approximation in Bose-Einstein condensates. The system is described by a vector nonlinear Schr\"odinger equation appropriate to multicomponent Bose-Einstein condensates. The variational approximation is based on a hyperbolic tangent (hyperbolic secant) for the dark (bright) component, which leads to a system of coupled ordinary differential equations for the evolution of the ansatz parameters. We obtain the oscillation dynamics of two-component dark-bright solitons. Analytical calculations are performed for same-width components in the vector soliton, and numerical calculations extend the results to arbitrary widths. We calculate the binding energy of the system and find it to be proportional to the intercomponent coupling interaction and numerically demonstrate the breakup or unbinding of a dark-bright soliton. Our calculations explore observable eigenmodes, namely, the internal oscillation eigenmode and the Goldstone eigenmode. We find analytically that the number of atoms in the bright component is required to be less than the number of atoms displaced by the dark soliton in the other component in order to find the internal oscillation eigenmode of the vector soliton and support the existence of the dark-bright soliton. This outcome is confirmed by numerical results. Numerically, we find that the oscillation frequency is amplitude independent. For dark-bright solitons in 87Rb^{87}\mathrm{Rb}87Rb we find that the oscillation frequency range is 90 to 405 Hz and therefore observable in multicomponent Bose-Einstein condensate experiments.
Two-dimensional (2D) vector matter waves in the form of soliton-vortex and vortex-vortex pairs are investigated for the case of attractive intracomponent interaction in two-component Bose-Einstein condensates. Both attractive and repulsive intercomponent interactions are considered. By means of a linear stability analysis we show that soliton-vortex pairs can be stable in some regions of parameters while vortex-vortex pairs turn out to be always unstable. The results are confirmed by direct numerical simulations of the 2D coupled Gross-Pitaevskii equations.
We have numerically studied the head-on collisions of the bright-bright solitons and bright-dark solitons with different relative phases, based on Gross-Pitaevskii(GP) equation of the quasi-one-dimensional heteronuclear two-component Bose-Einstein condensates. If there is no external potential well, the relative phase zc leads to elastic collision of the bright-bright solitons, but they collide with each other accompanied by some energy transfer for the relative phase π /2. If there is external potential well, they collide periodically with the relative phase π, but with the relative phase π /2, the two solitons combine to one soliton after collision with energy escape. For the bright-dark solitons, their bright-bright solitons in the first component collide periodically with the relative phase 0 or π. The difference of them is that the former has one collision point, the latter two collision points. Furthermore, we have found that the bright-bright solitons are always stable and the bright-dark solitons are unstable by solving its co~esponding Bogoliubov-de Gennes equations.
We investigate the interactions between components of various vector solitons in Bose—Einstein condensates by means of the least action principle, and derive the effective potentials for different vector solitons, which indicate that the interactions are of short range, and may be repulsive or attractive decided by the different intra- and inter-species interactions in such a system. In the case of attraction, the two solitons will oscillate about and pass through each other around the equilibrium state. The comparison of analytical results with mumertical simulation is presented.