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arXiv:2411.04624 · Physical Review A

Transport of vector solitons in spin-dependent nonlinear Thouless pumps

Xuzhen Cao, Chunyu Jia, Hao Lyu, Ying Hu, Zhaoxin Liang

Published Feb 27, 2025• 12 citations
arXivHTMLPDF

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 the 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 reenter 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.

DOI
10.1103/physreva.111.023329

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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 the 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 dr{d}_{r}dr​, leading to a vector soliton state with a relative shift between its components. We demonstrate that dr{d}_{r}dr​, as an independent degree of freedom, offers a novel control parameter for manipulating the nonlinear topological phase transition of vector solitons. Specifically, when dr=0{d}_{r}=0dr​=0, both components are either pumped or arrested, depending on the interaction strength. When fixing the interaction strength and varying dr{d}_{r}dr​, remarkably, we find that an arrested vector soliton can reenter the pumped regime and exhibits a quantized shift. As dr{d}_{r}dr​ continues to increase, the vector soliton transitions into a dynamically arrested state; however, with further increases in dr{d}_{r}dr​, 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.
Thouless pumping of soliton under cyclic and slow modulation of potential opens a window to understand the interplay between topology and interaction. The dynamics of a soliton change from quantized displacement per pumping cycle to its breakdown to self-trap as time-independent nonlinearity increases. Since nonlinearity can be dynamically and flexibly tuned in ultracold atomic systems, time-dependent nonlinearity can be a new degree of freedom to control behaviors of solitons in a Thouless pump. Leveraging time-dependent nonlinearity, we can not only restore quantized displacement of soliton by avoiding self-crossing structures, but also combine topological pumping and self-trap to effectively realize fractional displacement of soliton per cycle. Surprisingly, even when time translation symmetry is broken by linearly changing nonlinearity, we can still achieve the topological transport of a soliton when the initial soliton is symmetrically distributed. Our work provides a new way for dynamical and topological control of solitons.
We study Thouless pumping and arresting of gap solitons in a two-component Bose gas loaded into an optical superlattice. We show that, depending on the atomic interactions and chemical potentials, the two solitons can be simultaneously pumped or trapped, but we also identify regimes where one soliton is pumped and the other arrested. These behaviors can be understood by considering an effective model of the system based on a variational approach, which reveals that the soliton width is a suitable qualifier for the observed behaviors: solitons with a larger width get transported, while solitons with a smaller width get trapped. Since these widths can be controlled by tuning interactions, it should be possible to observe all behaviors experimentally. Published by the American Physical Society 2024
Bose–Einstein Condensation (BEC) of atomic gases has attracted a renewed theoretical and experimental interest in quantum many-body systems at extremely low temperatures (Pethick & Smith; 2002). This excitement stems from two favorable features: (1) by applying magnetic fields and lasers, most of the system parameters, such as the shape, dimensionality, internal states of the condensates, and even the strength of the interatomic interactions, are controllable; (2) due to the diluteness, the mean-field theory explains experiments quite well. In particular, the Gross–Pitaevskii (GP) equation demonstrates its validity as a basic equation for the condensate dynamics. The GP equation is the counterpart of the nonlinear Schrodinger (NLS) equation in nonlinear optics. Thus, a study based on nonlinear analysis is possible and important. In nonlinear physics, a soliton is remarkable object not only for the fact that exact solutions can be obtained but also for its usefulness as a communications tool due to its robustness. In general, solitons are formed under the balance between nonlinearity and dispersion. For atomic condensates, the former is attributed to the interatomic interactions, while the latter comes from the kinetic energy. Either dark or bright solitons are allowable depending on the positive or negative sign of the interatomic coupling constants g, respectively, and indeed have been observed in a quasione-dimensional (q1D) optically constructed waveguide (Strecker et al.; 2002) (Khaykovich et al.; 2002). Such matter-wave solitons are expected in atom optics for applications in atom laser, atom interferometry, and coherent atom transport (Meystre; 2002). In this chapter, we extend the analysis of the matter-wave solitons to a multicomponent case by considering the so-called spinor condensate (Stenger et al.; 1998) whose spin degrees of freedom are liberated under optical traps. Based on theoretical and experimental results, we introduce a new integrable model which describes the dynamical properties of the matter-wave soliton of spinor condensates (Ieda et al.; 2004a). We employ the inverse scattering method to solve this model exactly. As a result, we predict the occurrence of undiscovered physical phenomena such as macroscopic spin precession and spin switching. The chapter is organized as follows. In Sec. 2, the mean field theory of condensate is briefly reviewed. Section 3 introduces an effective interatomic coupling in a q1D condensate. Using these results, we consider a spinor condensate in q1D regime in Sec. 4. Then, in Sec. 5, we
We demonstrate that linear and nonlinear Thouless pumping can be realized in two-component elongated Bose-Einstein condensates using helicoidal spin-orbit coupling that slides with respect to a static optical lattice, identical for both spinor components. Stable quantized transport is found for solitons in semi-infinite and finite gaps, within certain intervals of chemical potentials and numbers of atoms. In the semi-infinite gap, the transport is arrested for solitons with sufficiently large number of atoms. We elucidate the important role of Zeeman splitting in the control of quantized transport, which disappears when the longitudinal component of the Zeeman field is removed.
Thouless pumping provides a paradigmatic platform for studying the effects of interactions on topological transport in periodically driven systems. However, most studies have been constrained by adiabatic conditions, which preclude exploration of interaction-driven novel topological states at high driving frequencies. Here, we experimentally investigate the interplay between interaction and modulation frequency in Thouless pumping realized in a periodically modulated lattice in momentum space of atomic Bose-Einstein condensate. We observe fast Thouless pumping of matterwave solitons at intermediate interactions, with no counterpart in the non- or weakly interacting regimes. Beyond the boundary of topological phase transition induced by interaction, nonadiabatic quantized pumping of solitons emerges at high modulation frequencies over a broad interaction range, in good agreement with theoretical calculations, while the solitons remain trapped in the low-frequency adiabatic pumping regime. Our work opens new avenues for accelerating topological transport in driven quantum systems and engineering fast topological devices.
Abstract Topological pumping provides a robust route to quantized motion under adiabatic modulation, yet its extension to nonlinear matter waves with internal spin degrees of freedom remains an open question. Here we demonstrate quantized soliton transport in a two-component Bose–Einstein condensate with helicoidal spin–orbit coupling, subjected to an adiabatically sliding optical lattice. With each pumping cycle, the helicoidal coupling sustains a periodic inter-component population exchange, while the soliton center-of-mass advances by a quantized displacement set by the Chern number, which is insensitive to both the spin–orbit coupling strength and the Zeeman field. We further identify the Zeeman field as a key control parameter governing both the inter-component dynamics during pumping and the soliton stability after the lattice motion ceases: depending on the Zeeman field strength, the soliton either retains its profile or develops persistent breathing modes. These results demonstrate that the combination of helicoidal spin–orbit coupling and Zeeman field enables topological transport of nonlinear matter waves with independently tunable internal spin dynamics.