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.

References in corpus (9)

• Analogs of quantum Hall effect edge states in photonic crystals
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Adiabatic Theory of Nonlinear Evolution of Quantum States
• Quantized Nonlinear Thouless Pumping
• Adiabatic Condition for Nonlinear Systems

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