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Modern Physics Letters A

BRIGHT SOLITONS MANAGED BY FESHBACH RESONANCE IN BOSE–EINSTEIN CONDENSATES

Zhaoxin Liang, Zhang Zhi-dong, Weijian Liu

Published Feb 20, 2006• 12 citations
Publisher

Abstract

We review the recent experimental and theoretical advances in the generation of matter wave solitons in Bose–Einstein condensates. In particular, the controlled generation and dynamics of stable bright solitons by mean of Feshbach resonance techniques is discussed in details. Several aspects are taking into account, including the variation of the scattering length due to Feshbach resonance, the safe parameters against the collapse and the experimental implications of our scenario.

DOI
10.1142/s0217732306019566

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We review the recent experimental and theoretical advances in the generation of matter wave solitons in Bose–Einstein condensates. In particular, the controlled generation and dynamics of stable bright solitons by mean of Feshbach resonance techniques is discussed in details. Several aspects are taking into account, including the variation of the scattering length due to Feshbach resonance, the safe parameters against the collapse and the experimental implications of our scenario.
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We review our recent theoretical advances in the dynamics of Bose-Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross-Pitaevskii equations are developed to study the nonlinear dynamics of Bose-Einstein condensates. Analytically, we present the integrable conditions for the Gross-Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose-Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose-Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose-Einstein condensates.
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.
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