Year: 2026
Type: preprint
Abstract: We investigate the dynamics of gap solitons found in the Harper-Hofstadter model with an additional cubic nonlinearity, such as that describing weakly-interacting cold atoms or a Kerr nonlinearity in an optical platform. We find that certain solitons with frequencies deep in the band gap travel with a robust, quantized velocity perpendicular to the applied force and maintain their spatial profile over long timescales. Crucially, this velocity is linearly proportional to the applied force, allowing for arbitrary steering of the nonlinear wavepacket, without breakdown, using only a tunable external force. This quantized transport persists despite a highly non-uniform occupation of the linear Bloch states, and contrasts with solitons near the band edge, which deform and delocalize under the same force. These results point to a robust and highly controllable mechanism for steering nonlinear solitons in experimentally accessible platforms.
Source: arXiv (Cornell University)
Language: English
Topic: Nonlinear Photonic Systems
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G3520994907, Quantum Many-Body Physics with Ultracold Polar Molecules, G4583660168, Interacting Topological Matter in Synthetic Dimensions, DTP 2224 Imperial College London, G5280010096, G5343916844, Quantum Advantage in Quantitative Quantum Simulation, Homoclinic bifurcation in mechanical systems: theory and application, G6905147915, G708068764
OpenAlex ID: W7213877793