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.
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, leading to a vector soliton state with a relative shift between its components. We demonstrate that
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, both components are either pumped or arrested, depending on the interaction strength. When fixing the interaction strength and varying
dr, remarkably, we find that an arrested vector soliton can reenter the pumped regime and exhibits a quantized shift. As
dr continues to increase, the vector soliton transitions into a dynamically arrested state; however, with further increases in
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.
Nonlinear Thouless pumping has been established in periodic lattices; its counterpart in quasiperiodic lattices remains unexplored. Here, we show a nonlinear topological pumping of gap solitons in quasiperiodic lattices where the local nonlinear self-consistent potentials lead to a lattice potential reconstruction; as a result, an emergent topological structure induced by this local reconstruction governs the dynamics of the gap solitons. This enables solitons to adiabatically occupy a single topological band, realizing quasi-quantized Thouless pumping. In addition, the intrinsic lattice perturbations disrupt this band occupation, which drives solitons into a non-quantized drifting regime. However, even in this regime, we also find that the soliton transport is constrained by the topological properties of a critical rational approximant. Tuning nonlinearity or lattice scaling reveals a controllable switching among topological pumping, drifting, and localization. Our work uncovers a mechanism for nonlinearity-induced topological behavior in complex lattice potentials.
We study soliton Thouless pumping in an extended diagonal Aubry-André-Harper model with on-site nonlinearities and inter-site nonlinearities. We show that the inter-site nonlinearities can make solitons acquire anomalous transport distances far beyond the ones predicted by the linear bands, and the quantized displacements can be engineered well. We uncover that nonlinear instabilities require lower limits on sweeping rates for soliton pumping, challenging the common notion that slower modulation enables a more favorable realization of topological transport. The nonlinear interactions between solitons make multi-soliton pumping generally lack the robustness characteristic of Thouless pumping as linear systems. Our results provide many possibilities to engineer topological pumping by nonlinearities, and further make a step for applications of soliton pumping.
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.
We consider theoretically the nonlinear quantized Thouless pumping of a Bose-Einstein condensate loaded in two-dimensional dynamical optical lattices. We encountered three different scenarios of the pumping: a quasilinear one occurring for gradually dispersing wave packets, transport carried by a single two-dimensional soliton, and a multisoliton regime when the initial wave packet splits into several solitons. The scenario to be realized depends on the number of atoms in the initial wave packet and on the strength of the two-body interactions. The magnitude and direction of the displacement of a wave packet are determined by Chern numbers of the populated energy bands and by the interband transitions induced by two-body interactions. As a case example we explore a separable potential created by optical lattices whose constitutive sublattices undergo relative motion in the orthogonal directions. For such potentials, obeying parity-time symmetry, fractional Chern numbers, computed over half period of the evolution, acquire relevance. We focus mainly on solitonic scenarios, showing that one-soliton pumping occurs at relatively small as well as at sufficiently large amplitudes of the initial wave packet, while at intermediate amplitudes the transport is multisolitonic. We also describe peculiarities of the pumping characterized by two different commensurate periods of the modulations of the lattices in the orthogonal directions.
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