Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps

Abstract: 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.