Nonlinearity-induced Fractional Thouless Pumping of Solitons

TL;DR

This paper demonstrates that nonlinearity can induce fractional Thouless pumping of solitons in a nonlinear Aubry-Andre9-Harper model, even when the underlying linear bands are topologically trivial, by modifying the system's topology.

Contribution

It reveals that nonlinearity can generate fractional topological pumping in systems with trivial linear bands, expanding the understanding of topological phenomena in nonlinear systems.

Findings

Solitons can be pumped across multiple unit cells over different periods.

Fractional displacements of 1/2, 1/3, 1/4 unit cells per cycle are observed.

Nonlinearity induces nontrivial topology in the modified Hamiltonian.

Abstract

Recent studies have shown that a soliton can be {\it fractionally} transported by slowly varying a system parameter over one period in a nonlinear system. This phenomenon is attributed to the nontrivial topology of the corresponding energy bands of a linear Hamiltonian. Here we find the occurrence of fractional Thouless pumping of solitons in a nonlinear off-diagonal Aubry-Andr\'{e}-Harper model. Surprisingly, this happens despite the fact that all the energy bands of the linear Hamiltonian are topologically trivial, indicating that nonlinearity can induce fractional Thouless pumping of solitons. Specifically, our results show that a soliton can be pumped across one unit cell over one, two, three or four pump periods, implying an average displacement of $1$, $1/2$, $1/3$ or $1/4$ unit cells per cycle, respectively. We attribute these behaviors to changes in on-site potentials induced by a soliton solution, leading to the nontrivial topology for the modified linear Hamiltonian. Given that our model relies solely on varying nearest-neighbor hoppings, it is readily implementable on existing state-of-the-art photonic platforms.