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物理学前沿：英文版

Dynamics of Bose-Einstein condensates near Feshbach resonance in external potential

张晓斐, 胡兴华, 王灯山, 刘循序, 刘伍明

Published Jan 1, 2011• 0 citations

Abstract

我们用 Feshbach 回声和外部潜力与悦耳的相互作用在 Bose 爱因斯坦冷凝物的动力学考察我们的最近的理论进展。为 Gross-Pitaevskii 方程的一套分析、数字的方法被开发学习 Bose 爱因斯坦冷凝物的非线性的动力学。经分解，我们在场为有悦耳的相互作用和外部潜力的 Gross-Pitaevskii 方程的 integrable 条件，并且在一个和二维的盒子获得一个部件和二部件的 Bose 爱因斯坦冷凝物的准确分析解决方案的一个家庭。然后，我们使用这些模型调查在二 solitons 之间的 solitons 和碰撞的动力学。数字地，分析准确答案的稳定性被检查并且现象例如戒指黑暗 soliton 和 vector-soliton 的动力学和调整，经由 Feshbach 回声，使量子化的 soliton 和旋涡在的 soliton 变换伪二维也被调查。两个都，准确、数字的答案证明 Bose 爱因斯坦冷凝物的动力学能被 Feshbach 回声和外部潜力有效地控制，它在 Bose 爱因斯坦冷凝物为原子事波浪和非线性的刺激的操作提供一个好机会。

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我们用 Feshbach 回声和外部潜力与悦耳的相互作用在 Bose 爱因斯坦冷凝物的动力学考察我们的最近的理论进展。为 Gross-Pitaevskii 方程的一套分析、数字的方法被开发学习 Bose 爱因斯坦冷凝物的非线性的动力学。经分解，我们在场为有悦耳的相互作用和外部潜力的 Gross-Pitaevskii 方程的 integrable 条件，并且在一个和二维的盒子获得一个部件和二部件的 Bose 爱因斯坦冷凝物的准确分析解决方案的一个家庭。然后，我们使用这些模型调查在二 solitons 之间的 solitons 和碰撞的动力学。数字地，分析准确答案的稳定性被检查并且现象例如戒指黑暗 soliton 和 vector-soliton 的动力学和调整，经由 Feshbach 回声，使量子化的 soliton 和旋涡在的 soliton 变换伪二维也被调查。两个都，准确、数字的答案证明 Bose 爱因斯坦冷凝物的动力学能被 Feshbach 回声和外部潜力有效地控制，它在 Bose 爱因斯坦冷凝物为原子事波浪和非线性的刺激的操作提供一个好机会。

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.

We consider two coupled Gross—Pitaevskii equations describing a two-component Bose—Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential, and investigate the dynamics of vector solitons. By using a direct method, we construct a novel family of vector soliton solutions, which are the linear combination between dark and bright solitons in each component. Our results show that due to the superposition between dark and bright solitons, such vector solitons possess many novel and interesting properties. The dynamics of vector solitons can be controlled by the Feshbach resonance technique, and the vector solitons can keep the dynamic stability against the variation of the scattering length.

We consider the generalized Gross-Pitaevskii models with varying nonlinearities from the point of view of their exact integrability and obtain the general solutions for these models both for confining and expulsive external potentials. We show that exact soliton solutions exist only under certain conditions and that varying in time nonlinearity and confining harmonic potential cannot be chosen independently; they satisfy the exact integrability conditions. The main features of nonautonomous matter-wave solitons near the Feshbach resonance with continuously tuned scattering length are investigated. We focus on the most physically important situations where the applied magnetic field is varying in time linearly and periodically. It is proved that near a Feshbach resonance the matter wave solitons can be stabilized even without a trapping potential. In the case of periodically varying interaction strength among atoms, variations of the external harmonic potential are found to be sign-reversal. The main difference from the canonical soliton case is that the matter-wave solitons management concept must be consistent with variations of confining potential.

就相互作用和外部潜力的时间依赖而言，我们经分解学习在由使用 Darboux 的 Bose 爱因斯坦冷凝物的二明亮的 solitons 的 collisional 行为转变。为一个关上的外部潜力， soliton-soliton 距离与非线性地增加的相互作用被减少，这被发现，当每 soliton 的振幅增加，它的宽度减少时。为线性地增加的相互作用，但是非线性地减少的外部潜力在二 solitons 之间的，特别原子转移被观察，与在在一个固定外部潜力的 solitons 碰撞的没有原子转移的以前的理论不同。另外， collisional 打字，这被显示出，例如迎头向前，在二 solitons 之间的“追逐”，或碰撞时期，能被调节相互作用和外部潜力控制。预言的现象能在原子运输为未来申请在当前的实验和开的可能性的条件下面被观察。