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Acta Physica Sinica

Controlling interactions between bright solitons in Bose-Einstein condensate

He Zhang-Ming, Zhiqiang Zhang

Published Jan 1, 2016• 1 citation
Publisher

Abstract

Considering the periodically driving linear potential, we study the interactions between two solitons in Bose-Einstein condensate (BEC). By using Darboux transformation, the double bright soliton solution of Gross-Pitaevskii equation is obtained. Then we numerically calculate the properties of interaction between the two bright solitons in BEC, and obtain a critical value of the S-wave scattering length (SL). It is shown that, when the SL is more than the critical value, the attractive interaction and the atom transfer between two bright solitons can be observed. While the SL is less than the critical value, two bright solitons can keep stable and localized. Furthermore, the stable periodic oscillations of two solitons can be observed by slowly changing the potential. These results will be conducive to the BEC soliton experiments.

DOI
10.7498/aps.65.110502

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Considering the periodically driving linear potential, we study the interactions between two solitons in Bose-Einstein condensate (BEC). By using Darboux transformation, the double bright soliton solution of Gross-Pitaevskii equation is obtained. Then we numerically calculate the properties of interaction between the two bright solitons in BEC, and obtain a critical value of the S-wave scattering length (SL). It is shown that, when the SL is more than the critical value, the attractive interaction and the atom transfer between two bright solitons can be observed. While the SL is less than the critical value, two bright solitons can keep stable and localized. Furthermore, the stable periodic oscillations of two solitons can be observed by slowly changing the potential. These results will be conducive to the BEC soliton experiments.
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By using the split-step fast Fourier transform (SSFFT) method, we numerically study the collision properties between two bright solitons in the growth Bose–Einstein condensates (BECs) with different interaction strengths under a harmonic potential. It is shown that the soliton’s collision property of the condensates can be controlled by adjusting the gain term, the initial position and the interaction strength between atoms. The number of collisions of the two bright solitons decreases first, then increases, with increasing the values of the gain term. As the initial distance between solitons increases, the number of collisions between the two bright solitons is reduced, and the first collision time is also postponed. The increase in interaction strength between atoms delays the collision time of the two bright solitons. Meanwhile, a critical interaction strength between atoms is found, the amplitude of the soliton’s first collision peak increases slowly when the interaction strength is less than the critical value, but the amplitude increases sharply when the interaction strength is more than the critical value.
We present an analytical study on the dynamics of bright and dark solitons in Bose–Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross–Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton's parameters (amplitude, width, and period) can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.
We study the interaction of dark–bright solitons in two-component Bose–Einstein condensates by suitably tailoring the trap potential, atomic scattering length and atom gain or loss. We show that the coupled Gross–Pitaevskii equation can be mapped onto the Manakov model. An interesting class of matter wave solitons and their interaction are identified with time-independent and periodically modulated trap potentials, which can be experimentally realized in two-component condensates. These include periodic collapse and revival of solitons, and snake-like matter wave solitons as well as different kinds of two-soliton interactions.
We study the interaction of dark-bright solitons in two component Bose-Einstein condensates by suitably tailoring the trap potential, atomic scattering length and atom gain or loss. We show that the coupled Gross-Pitaevskii (GP) equation can be mapped onto the Manakov model. An interesting class of matter wave solitons and their interaction are identified with time independent and periodically modulated trap potentials, which can be experimentally realized in two component condensates. These include periodic collapse and revival of solitons, and snake-like matter wave solitons as well as different kinds of two soliton interactions.
Considering time-dependence of both interactions and external potential, we analytically study the collisional behaviors of two bright solitons in Bose-Einstein condensates by using Darboux transformation. It is found that for a closed external potential, the soliton-soliton distance is decreased with nonlinearly increased interactions, while the amplitude of each soliton increases and its width decreases. For linearly increased interactions but nonlinearly decreased external potential, especially, the atom transfer between two solitons is observed, different from previous theory of no atom transfer in solitons collision in a fixed external potential. In addition, it is shown that the collisional type, such as head-on, “chase", or collision period between two solitons, can be controlled by tuning both interactions and external potential. The predicted phenomena can be observed under the condition of the current experiments and open possibilities for future application in atoms transport.