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Chinese Physics B

Formation of combined solitons in two-component Bose–Einstein condensates

Qiuyan Li, Zai-Dong Li, Yao Shu-Fang, Lu Li, Guangsheng Fu

Published Aug 1, 2010• 12 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/19/8/080501

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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 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.
We demonstrate the formation of bright solitons in coupled defocusing nonlinear Schroedinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type.
We report on the static and dynamical properties of multiple dark-antidark solitons (DADs) in two-component, repulsively interacting Bose-Einstein condensates. Motivated by experimental observations involving multiple DADs, we present a theoretical study which showcases that bound states consisting of dark (antidark) solitons in the first (second) component of the mixture exist for different values of interspecies interactions. It is found that ensembles of few DADs may exist as stable configurations, while for larger DAD arrays, the relevant windows of stability with respect to the interspecies interaction strength become progressively narrower. Moreover, the dynamical formation of states consisting of alternating DADs in the two components of the mixture is monitored. A complex dynamical evolution of these states is observed, leading either to sorted DADs or to beating dark-dark solitons depending on the strength of the interspecies coupling. This study demonstrates clear avenues for future investigations of DAD configurations.
Considering the time-dependent interspecies interactions, we study the dynamic behaviors of bright-bright solitons in two species Bose-Einstein condensates in the harmonic external potentials. In the presence of unchanged attractive interspecies and intraspecies interactions, bright-bright solitons exhibit periodic oscillations. When the attractive intraspecies interactions are fixed but the attractive interspecies interactions are increased exponentially, interestingly, a transition behavior from oscillation to localization is observed. Meanwhile, this transition behavior can be controlled by tuning the transverse trapping frequency of harmonic potential. Furthermore, an experimental protocol is designed to observe the transition behavior in the current experimental conditions.
We investigate numerically the dynamics of paired bright solitons induced by the modulational instability of two-component Bose-Einstein condensates. We derive the analytic gain spectrum by the modulational instability in terms of the interspecies and intraspecies scattering constants and classify the region where the instability occurs. The constraints on the interspecies and intraspecies scattering constants for the existence of the paired bright solitons are found. Using numerical simulations, it is shown that the paired bright solitons induced by the modulational instability exhibit complicated dynamical behaviors depending on the sign and strength of the interspecies and intraspecies scattering constants. - PACS numbers: 03.75.Fi, 05.30.Jp, 32.80Pj, 67.90.+z