The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps

Abstract

Nonlinear Thouless pumps for bosons exhibit quantized pumping via soliton motion, despite the lack of a meaningful notion of filled bands. However, the theoretical underpinning of this quantization, as well as its relationship to the Chern number, has thus far been lacking. Here we show that for low power solitons, transport is dictated by the Chern number of the band from which the soliton bifurcates. We do this by expanding the discrete nonlinear Schrödinger equation (equivalently, the Gross-Pitaevskii equation) in the basis of Wannier states, showing that the soliton's position is dictated by that of the Wannier state throughout the pump cycle. Furthermore, we describe soliton pumping in two dimensions.

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• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Quantized Topological Anderson-Thouless Pump
• Vortex solitons in topological disclination lattices
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Probing topology in nonlinear topological materials using numerical $K$-theory
• Breakdown of quantization in nonlinear Thouless pumping
• Thouless pumping in a driven-dissipative Kerr resonator array
• Thouless pumping and trapping of two-component gap solitons
• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Bulk soliton dynamics in bosonic topological insulators
• Nonlinearity-induced Fractional Thouless Pumping of Solitons
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Standing and Traveling Waves in a Model of Periodically Modulated One-dimensional Waveguide Arrays
• Nonlinear breathers with crystalline symmetries
• Nonadiabatic nonlinear non-Hermitian quantized pumping
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Quantum theory of fractional topological pumping of lattice solitons
• Dark solitons in nonlinear Su-Schrieffer-Heeger lattices
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Quantized transport of two-dimensional multifrequency solitons
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• Soliton Pumping in the Rice-Mele Model with On-Cell Kerr Nonlinearity