The interplay between nonlinear and topological physics has led to intriguing emergent phenomena, such as quantized and fractionally quantized Thouless pumping of solitons dictated by the topological invariants of the underlying band structure. Unlike linear Thouless pumping, which requires excitation of a Wannier function of a uniformly filled band, quantized soliton pumping is observed even with localized excitations that do not represent Wannier functions. Here, we show that similar solitonlike quantized pumping can be observed in the Aubry-André-Harper model by introducing a synthetic nonlinearity in the form of a cutoff on the coupling strengths between lattice sites. More importantly, we reveal that the localized excitations driving quantized soliton pumping are precisely the Wannier functions of the uniformly filled bands of the effectively nonlinear lattice, thus restoring consistency with linear Thouless pumping. We extend this approach to multiband systems and show that the nonlinearity introduces a degeneracy between bands, subsequently leading to the observation of fractionally quantized pumping. Our approach of introducing a synthetic nonlinearity is general and could be extended to reveal soliton dynamics in other nonlinear topological systems.

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• Nonlinear waveguides
• Topological effects in photonic systems
• Solitons