Scattering State Theory for One-dimensional Floquet Lattices

• URL: http://arxiv.org/abs/2601.19991v2
• Date: Wed, 04 Feb 2026 10:24:37 GMT
• Title: Scattering State Theory for One-dimensional Floquet Lattices
• Abstract summary: We develop a Floquet transfer matrix method to solve scattering in extended 1D Floquet lattices.<n>By engineering a spatial adiabatic boundary, we suppress multi-channel sideband interference.<n>We propose two experimental realizations: cold-atom Bragg scattering to directly verify the transmission shift, and surface-acoustic-wave-induced transport demonstrating the quantized zero-bias current plateau.
• Score: 2.1874189959020423
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a Floquet transfer matrix method to solve scattering in extended 1D Floquet lattices, uncovering an underlying conjugate symplectic structure that enforces current conservation across sidebands. By engineering a spatial adiabatic boundary, we suppress multi-channel sideband interference, allowing us to establish a direct mapping between the bulk winding number $C$ and a rigid shift in the transmission energy windows--quantified as $C\hbarω$. We further propose two experimental realizations: cold-atom Bragg scattering to directly verify the transmission shift, and surface-acoustic-wave-induced transport demonstrating the quantized zero-bias current plateau.

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