Dynamics of dark solitons in quasi-one-dimensional Bose-Einstein condensates
Dynamics of dark solitons in quasi-one-dimensional Bose-Einstein condensates
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DOI：
10.1103/physreva.65.053605
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发表时间：
2002-04
影响因子：
2.9
通讯作者：
Guoxiang Huang;J. Szeftel;Shanhua Zhu
中科院分区：
文献类型：
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作者：
Guoxiang Huang;J. Szeftel;Shanhua Zhu
我们发展了一个系统的分析方法来考虑在被囚禁的准一维玻色-爱因斯坦凝聚体中的线性和非线性激发的动力学与排斥原子-原子相互作用。结果表明，对于两个横向强约束的凝聚体，系统的基态在横向上包含横向约束势的高阶本征模，在轴向上包含有效的高阶Fermas-Fermi波函数.系统的线性激励具有Bogoliubov型谱，激励频率沿轴向沿着缓慢变化。我们发现，在弱非线性近似下，非线性激发的振幅受变系数Korteweg\char21{}de弗里斯方程控制，该方程中附加了凝聚体横向结构和轴向不均匀性的影响，导致暗孤子的振幅、宽度和速度都发生了变化.由于非均匀性的存在，暗孤子在沿轴向沿着传播时发生形变并辐射。最后证明了暗孤子通过阶跃势时将分裂为多个暗孤子和一个剩余的波列。
We develop a systematic analytical approach to consider the dynamics of linear and nonlinear excitations in trapped quasi-one-dimensional Bose-Einstein condensates with repulsive atom-atom interactions. We show that, for a condensate strongly confined in two transverse directions, the ground state of the system involves the high-order eigenmodes of the transverse confining potential in the transverse directions and effective high-order Thomas-Fermi wave functions in the axial direction. The linear excitations of the system have a Bogoliubov-type spectrum with the excitation frequency varying slowly along the axial direction. We find that, in a weak nonlinear approximation, the amplitude of a nonlinear excitation is governed by a variable coefficient Korteweg\char21{}de Vries equation with additional terms contributed from the transverse structure and the inhomogeneity in the axial direction of the condensate, which results in varying amplitude, width, and velocity for dark solitons. Because of the inhomogeneity the dark solitons undergo deformation and emit radiations when traveling along the axial direction. We finally demonstrate that a dark soliton will disintegrate into several ones plus a residual wave train when passing over a steplike potential.