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Chinese Physics B

Superposition solitons in two-component Bose—Einstein condensates

Xiaomin Wang, Qiuyan Li, Zai-Dong Li

Published May 1, 2013• 5 citations
Publisher

Abstract

We develop the Hirota bilinear method and obtain the exact one and two superposition soliton solutions for two-component Bose—Einstein condensates. The conversion of three kinds of solitons including the superposition solitons, bright-bright solitons, and dark-bright solitons is discussed. With the energy analysis, we find that the superposition soliton state is an excitation state for this system. Moreover, the collision of two superposition solitons is found to be elastic.

DOI
10.1088/1674-1056/22/5/050311

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We develop the Hirota bilinear method and obtain the exact one and two superposition soliton solutions for two-component Bose—Einstein condensates. The conversion of three kinds of solitons including the superposition solitons, bright-bright solitons, and dark-bright solitons is discussed. With the energy analysis, we find that the superposition soliton state is an excitation state for this system. Moreover, the collision of two superposition solitons is found to be elastic.
We obtain soliton and plane wave solutions for the coupled nonlinear Schrödinger equations, which describe the dynamics of the three-component Bose–Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing (inelastic) collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribution.
This paper develops the Hirota method carefully for applying into the growing model of quasi-one-dimensional Bose–Einstein condensations with attractive and repulsive interaction, respectively. After a tedious calculation it obtains the exact bright and dark soliton solutions analytically. It shows that the growing model has the important effect on the soliton amplitude and the time-dependent potential only contributes to the phase and phase velocity. A detailed analysis for the asymptotic behaviour of two-soliton solutions shows that the collision of two soliton is elastic.
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.
In this paper, the Jacobi elliptic function expansion method provides an effective approach to obtain the exact periodic wave solutions of two-component Bose-Einstein condensates. Exact combined bright-bright and dark-dark soliton wave solutions can be achieved in their limit conditions. We also obtain the different formation regions of combined solitons. Our results show that the intraspecies (interspecies) interaction strengths clearly affect the formation of dark-dark, bright-bright and dark-bright soliton solutions in different regions.
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.
We investigate nondegenerate bound-state solitons systematically in multicomponent Bose-Einstein condensates, through developing the Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound states in effective quantum wells, in sharp contrast to the bright solitons and dark solitons reported before (which usually correspond to ground state and free state, respectively). We further demonstrate that bound-state solitons with nodes are induced by incoherent superposition of solitons in different components. Moreover, we reveal that the interactions between these bound-state solitons are usually inelastic, caused by the incoherent interactions between solitons in different components and the coherent interactions between solitons in the same component. Additionally, the detailed spectral stability analysis demonstrates the stability of nondegenerate bound-state solitons. The bound-state solitons can be used to study many different physical problems, such as beating dynamics, spin-orbit coupling effects, quantum fluctuations, and even quantum entanglement states.