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Chinese Physics B

Combined periodic wave and solitary wave solutions in two-component Bose-Einstein condensates

Shu-Fang Yao, Qiuyan Li, Zai-Dong Li

Published Nov 1, 2011• 7 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/20/11/110307

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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 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.
We present three families of exact matter-wave soliton solutions for an effective one-dimension two-component Bose—Einstein condensates (BECs) with tunable interactions, harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons, bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential, periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential. Through the Feshbach resonance, these dynamics can be realized in experiments by suitable control of time-dependent trap parameters, atomic interactions, and interaction with thermal cloud.
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.
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.
In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3D) form. Motivated by earlier studies of dark-bright solitons in the 1D case, we explore the stability of these structures in their fully 3D form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal wave forms that are more robust. Finally, using the SO(2) symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.