含时Gross-Pitaevskii方程模拟的准一维玻色-爱因斯坦凝聚体中的亮孤子和暗孤子
Bright and dark solitons in a quasi 1D Bose-Einstein condensates modelled by 1D Gross-Pitaevskii equation with time-dependent parameters
摘要：
在相互作用能远小于横向动能的假设下，研究了一维玻色-爱因斯坦凝聚体（BEC）的精确亮、暗孤波解.特别地，在文献Pérez-García等人[Physica D 221（2006）31]、Serkin等人[Phys. Rev. Lett. 98（2007）074102]，Gürses [arXiv：0704.2435]和Kundu [Phys. Rev. E 79（2009）015601]的基础上，指出通过改变坐标和波函数的变量，可以将Gross-Pitaevskii（GP）方程导出的有效一维方程转化为具有完全可积的标准孤子（亮/暗）的一维非线性薛定谔（NLS）方程.我们分别考虑了束缚势和排斥势，并将原子散射长度、增益/损耗项和陷阱频率作为实验控制参数，将它们作为时间的函数进行调制。在陷阱频率不变的情况下，当原子的散射长度和增益/损耗项改变时，我们得到了不同类型的孤子解，如周期振荡孤子、凝聚体的崩塌和恢复、蛇形孤子、稳定孤子、孤子的增长和衰减以及双孤子束缚态的形成.然而，当陷阱频率也被调制时，我们显示的崩溃和复苏的双孤子的束缚态形成的双调制周期势和明亮和黑暗的孤子的阶梯调制势的凝聚体的现象。
英文摘要：
We investigate the exact bright and dark solitary wave solutions of an effective one dimensional (1D) Bose-Einstein condensate (BEC) by assuming that the interaction energy is much less than the kinetic energy in the transverse direction. In particular, following the earlier works in the literature Pérez-García et al. [Physica D 221 (2006) 31], Serkin et al. [Phys. Rev. Lett. 98 (2007) 074102], Gürses [arXiv:0704.2435] and Kundu [Phys. Rev. E 79 (2009) 015601], we point out that the effective 1D equation res ulting from the Gross-Pitaevskii (GP) equation can be transformed into the stand ard soliton (bright/dark) possessing, completely integrable 1D nonlinear Schrö dinger (NLS) equation by effecting a change of variables of the coordinates and the wave function. We consider both confining and expulsive harmonic trap potentials separately and treat the atomic scattering length, gain/loss term and trap frequency as the experimental control parameters by modulating them as a function of time. In the case when the trap frequency is kept constant, we show the existence of different kinds of soliton solutions, such as the periodic oscillating solitons, collapse and revival of condensate, snake-like solitons, stable solitons, soliton growth and decay and formation of two-soliton like bound state, as the atomic scattering length and gain/loss term are varied. However when the trap frequency is also modulated, we show the phenomena of collapse and revival of two-soliton like bound state formation of the condensate for double modulated periodic potential and bright and dark solitons for step-wise modulated potentials.
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