标题： 矢量孤子在自旋依赖非线性托勒斯泵中的传输 显示英文标题

标题： Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps

摘要： 在非线性拓扑物理中，非线性激发的Thouless泵浦是一个核心课题，通常由标量孤子来说明。具有额外自旋自由度的矢量孤子，由于非线性与拓扑之间更丰富的相互作用，表现出标量孤子所没有的现象。在这里，我们通过数值求解Gross-Pitaevskii方程和拉格朗日变分方法，理论研究了在自旋依赖的光学超晶格中受限的两组分玻色-爱因斯坦凝聚体中的矢量孤子的Thouless泵浦。自旋向上的成分和自旋向下的成分经历的超晶格势场被位移了一个可调距离$d_r$，导致其成分之间存在相对位移的矢量孤子态。我们证明了$d_r$作为一个独立的自由度，为操控矢量孤子的非线性拓扑相变提供了新的控制参数。具体来说，当$d_r=0$时，两个成分要么都被泵浦，要么被阻止，这取决于相互作用强度。当固定相互作用强度并改变$d_r$时，我们发现一个被阻止的矢量孤子可以重新进入泵浦区域，并表现出量化位移。随着$d_r$的持续增加，矢量孤子转变为动态阻止状态；然而，随着$d_r$的进一步增加，量化位移会再次出现。我们的工作通过利用不同自旋成分之间的相对运动自由度，为在自旋系统中工程化孤子的非线性拓扑泵浦开辟了新途径。 显示英文摘要

摘要： In nonlinear topological physics, Thouless pumping of nonlinear excitations is a central topic, often illustrated by scalar solitons. Vector solitons, with the additional spin degree of freedom, exhibit phenomena absent in scalar solitons due to enriched interplay between nonlinearity and topology. Here, we theoretically investigate Thouless pumping of vector solitons in a two-component Bose-Einstein condensate confined in spin-dependent optical superlattices, using both numerical solutions of the Gross-Pitaevskii equation and the Lagrangian variational approach. The spin-up and spin-down components experience superlattice potentials that are displaced by a tunable distance $d_r$, leading to a vector soliton state with a relative shift between its components. We demonstrate that $d_r$, as an independent degree of freedom, offers a novel control parameter for manipulating the nonlinear topological phase transition of vector solitons. Specifically, when $d_r=0$, both components are either pumped or arrested, depending on the interaction strength. When fixing the interaction strength and varying $d_r$, remarkably, we find that an arrested vector soliton can re-enter the pumped regime and exhibits a quantized shift. As $d_r$ continues to increase, the vector soliton transitions into a dynamically arrested state; however, with further increases in $d_r$, the quantized shift revives. Our work paves new routes for engineering nonlinear topological pumping of solitons in spinor systems by utilizing the relative motion degrees of freedom between different spin components.