Soliton Thouless pumping engineered by inter-site nonlinearities

TL;DR

This paper investigates how inter-site nonlinearities influence soliton Thouless pumping, revealing enhanced transport, the importance of sweeping rates, and the impact of nonlinear interactions on robustness, advancing topological pumping control.

Contribution

It demonstrates that inter-site nonlinearities can significantly alter soliton transport and challenges existing notions about the role of sweeping rates in topological pumping.

Findings

Inter-site nonlinearities enable solitons to achieve anomalously large transport distances.

Lower sweeping rates are required to avoid nonlinear instabilities during pumping.

Multi-soliton pumping lacks robustness due to nonlinear interactions.

Abstract

We study soliton Thouless pumping in an extended diagonal Aubry-Andr\'e-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.