Nonlinear topological pumping of edge solitons

TL;DR

This paper investigates how varying nonlinear strength influences topological pumping of edge solitons, revealing complex behaviors including symmetry breaking, selective pumping, hybridization, and eventual suppression of topological transport.

Contribution

It provides a detailed analysis of nonlinear effects on topological pumping, introducing new phenomena like hybridized edge-bulk soliton pumping and the conditions under which topological transport is maintained or destroyed.

Findings

Weak nonlinearity breaks spectral symmetry affecting pumping direction

Moderate nonlinearity enables unidirectional topological pumping

Strong nonlinearity leads to self-trapped edge solitons and halts pumping

Abstract

We study how nonlinear strength affects topological pumping of edge solitons by using nonlinear Gross-Pitaevskii equation. For weak nonlinear strength, the introduction of nonlinearity breaks the symmetry of the energy spectrum, which makes the topological pumping from the left edge to the right edges differ from the inverse process. For moderate nonlinear strength, self-crossing structures appear in the spectrum, the right-to-left adiabatic pumping channel is destroyed, and only left-to-right topological pumping can be achieved under slow modulation. As the nonlinear strength further inreases, although left-to-right topological pumping in one pumping cycle also breaks down, we find that a thin soliton which is located in a single left edge can be mixed with the bulk soliton, and hybridized topological pumping of edge and bulk solitons can be realized after multiple pumping cycles. For stronger nonlinear strength, edge solitons are self-trapped and all topological pumping channels are shut down. Our work could trigger further studies of the interplay between nonlinearity and topology.