旋量玻色-爱因斯坦凝聚体中的暗孤子复合体
Bright-Dark Soliton Complexes in Spinor Bose-Einstein Condensates
摘要：
本文研究了准一维旋量（F=1）玻色-爱因斯坦凝聚体中的亮暗矢量孤子。利用多尺度展开技术，我们将相应的三个耦合Gross-Pitaevskii方程（GPE）的不可积系统约化为完全可积的Yajima-Oikawa系统。用这种方法，我们分别得到了暗-暗-亮和亮-亮-暗两类小振幅矢量孤子的$m_{F}=+1,-1,0$旋量近似解。通过对完整GPE系统的数值模拟，我们证明了这些态确实具有孤子特性，即，它们无畸变地传播并经历准弹性碰撞。研究还表明，当存在强度为$ω$的抛物型陷阱时，亮分量由暗分量引导，结果小振幅矢量孤子在浅孤子极限下整体上作频率为$ω/ \sqrt{2}$的谐振.我们调查的数值偏差从这个预测，作为孤子的深度增加，以及当自旋相关的相互作用的强度被修改。
英文摘要：
We present bright-dark vector solitons in quasi-one-dimensional spinor (F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations (GPEs) to a completely integrable Yajima-Oikawa system. In this way, we obtain approximate solutions for small-amplitude vector solitons of dark-dark-bright and bright-bright-dark types, in terms of the $m_{F}=+1,-1,0$ spinor components, respectively. By means of numerical simulations of the full GPE system, we demonstrate that these states indeed feature soliton properties, i.e., they propagate undistorted and undergo quasi-elastic collisions. It is also shown that, in the presence of a parabolic trap of strength $ω$, the bright component(s) is (are) guided by the dark one(s), and, as a result, the small-amplitude vector soliton as a whole performs harmonic oscillations of frequency $ω/ \sqrt{2}$ in the shallow soliton limit. We investigate numerically deviations from this prediction, as the depth of the solitons is increased, as well as when the strength of the spin-dependent interaction is modified.
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