Internal oscillations of a dark-bright soliton in a harmonic potential
Internal oscillations of a dark-bright soliton in a harmonic potential
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DOI：
10.1088/1361-6455/aadfb2
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发表时间：
2018-10-28
影响因子：
1.6
通讯作者：
Carr, Lincoln D.
中科院分区：
文献类型：
--
作者：
Alotaibi, Majed O. D.;Carr, Lincoln D.
利用平均场方法，通过耦合非线性薛定谔方程，研究了多组分玻色-爱因斯坦凝聚体中暗-亮孤子的动力学行为。我们使用修改的扰动动力学变分拉格朗日近似，其中扰动是由于陷阱引起的，取为托马斯-费米剖面。在标量情形下，分别对孤子的暗分量和亮分量取正确的双曲正切解和正割解。我们还解决了问题的数值与伪谱龙格库塔方法。通过解析和数值计算，我们发现，对于弱囚禁，暗-亮孤子的内模几乎与质心运动无关。相比之下，在更紧密的陷阱的内部模式强烈耦合到质心运动，表明暗亮孤子在谐波势的质心和相对自由度是不独立的。该结果在初始条件下对噪声是鲁棒的，因此应该是实验上可观察的。
We investigate the dynamics of a dark-bright soliton in a harmonic potential using a mean-field approach via coupled nonlinear Schrodinger equations appropriate to multi-component Bose-Einstein condensates. We use a modified perturbed dynamical variational Lagrangian approximation, where the perturbation is due to the trap, taken as a Thomas-Fermi profile. The wave function ansatz is taken as the correct hyperbolic tangent and secant solutions in the scalar case for the dark and bright components of the soliton, respectively. We also solve the problem numerically with pseudo-spectral Runge-Kutta methods. We find, analytically and numerically, for weak trapping the internal modes are nearly independent of center of mass motion of the dark-bright soliton. In contrast, in tighter traps the internal modes couple strongly to the center of mass motion, showing that for dark-bright solitons in a harmonic potential the center of mass and relative degrees of freedom are not independent. This result is robust against noise in the initial condition and should, therefore, be experimentally observable.