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Acta Physica Sinica

Evolvement between bright and dark soliton of condensates

He Zhang-Ming, Denglong Wang, (1)湘潭大学物理系和低维材料及其应用技术教育部重点实验室，湘潭 411105; (2)湘潭大学物理系和低维材料及其应用技术教育部重点实验室，湘潭 411105; 南京航空航天大学理学院，南京 210016

Published Jan 1, 2007• 10 citations
Publisher

Abstract

By using Darboux transformation method, we study analytically the nonlinear dynamics properties of Bose-Einstein condensates trapped in an stable external poten tial. It is shown that the strength of inter-atomic interaction condensate has an important effect on its nonlinear dynamics properties. When atom-atom repulsive interaction of condensate is strong enough, there only exhibits bright soliton. While the inter-atomic repulsive interaction is less than a critical value, the alternative evolvement phenomenon between bright and dark soliton appears.

DOI
10.7498/aps.56.3088

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By using Darboux transformation method, we study analytically the nonlinear dynamics properties of Bose-Einstein condensates trapped in an stable external poten tial. It is shown that the strength of inter-atomic interaction condensate has an important effect on its nonlinear dynamics properties. When atom-atom repulsive interaction of condensate is strong enough, there only exhibits bright soliton. While the inter-atomic repulsive interaction is less than a critical value, the alternative evolvement phenomenon between bright and dark soliton appears.
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.
We investigate the combined soliton solutions of two-component Bose–Einstein condensates with external potential. The "phase diagram" is obtained for the formation regions of different combined solitons. Our results show that the intraspecies (interspecies) interaction strengths and the external trapped potential clearly affect the formation of dark-dark, bright-bright, and dark–bright soliton solutions in different regions. Especially, we find that the bright–bright (dark–dark) soliton can exist in the case of both repulsive (attractive) intraspecies interaction strengths in the presence of external potential. This novel phenomenon is completely different from the formation of soliton solution of one-component Bose–Einstein condensates without external potential, and it will be useful for the study of two-component Bose–Einstein condensates.
In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions,motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. Inparticular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interactionbetween two dark-bright solitons in a homogeneous environment beyond the integrable regime, by consideringgeneral inter/intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case wherethe bright solitons are out of phase. As the inter-component interaction is increased, we also identify an exponentialinstability of the two-soliton state, associated with a subcritical pitchfork bifurcation. The latter givesrise to an asymmetric partition of the bright soliton mass and dynamically leads to spontaneous splitting of thebound pair. In the case of the in-phase bright solitons, we explain via parsing the analytical approximations andmonitoring the direct dynamics why no such pair is identified, despite its prediction by the variational analysis.
By using Darboux transformation, this paper studies analytically the nonlinear dynamics of a one-dimensional growing Bose–Einstein condensate (BEC). It is shown that the growing model has an important effect on the amplitude of the soliton in the condensates. In the absence of the growing model, there exhibits the stable alternate bright solitons in the condensates. In the presence of the growing model, the obtained results show that the amplitude of the bright soliton decreases (increases) for the BEC growing coefficient Ω < 0 (Ω > 0). Furthermore, we propose experimental protocols to manipulate the amplitude of the bright soliton by varying the scattering length via the Feshbach resonance in the future experiment.
In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions, motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. In particular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interaction between two dark-bright solitons in a homogeneous environment beyond the integrable regime, by considering general inter- and intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case where the bright solitons are out of phase. As the intercomponent interaction is increased, we also identify an exponential instability of the two-soliton state, associated with a subcritical pitchfork bifurcation. The latter gives rise to an asymmetric partition of the bright soliton mass and dynamically leads to spontaneous splitting of the bound pair. In the case of the in-phase bright solitons, we explain via parsing the analytical approximations and monitoring the direct dynamics why no such pair is identified, despite its prediction by the variational analysis.