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arXiv · 2607.11000

Non-Abelian holonomic transformations in digitally coupled acoustic waveguides guided by the global adiabatic criterion

Jin-Kang Guo·Jia Li·Jin-Lei Wu·Chuan-Cun Shu
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Abstract

An acoustic platform is validated for implementing compact non-Abelian holonomic transformations (NHTs) guided by a global adiabatic criterion (GAC). A tripod model is mapped onto a digitally coupled four-waveguide structure, where designed coupling envelopes and an acoustically-induced-transparency phase-control module implement a two-stage phase-stitched holonomic evolution. Compared with a reference Gaussian envelope, the GAC-guided power-law profile flattens the spatial distribution of the global nonadiabatic burden, thereby providing a quantitative basis for compact acoustic implementation. Full-wave simulations show Pauli-$X$ and Hadamard-type target transformations, with excellent agreement between the extracted normalized intensities and analytical coupled-mode predictions. These target responses are obtained with half the coupling length required by the reference Gaussian implementations. More uniquely, the same phase-stitched structure also supports unidirectional acoustic mode conversion, which is closely related to a reduced two-mode non-Hermitian picture associated with an encircled exceptional point (EP). These results validate acoustic NHTs as a robust geometric route for compact wave control, establish the GAC as a powerful guideline for fast adiabatic transport in digitally coupled systems, and further demonstrate that the same phase-stitched architecture supports unidirectional mode conversion through EP-assisted branch selection.

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Jin-Kang Guo, Jia Li, Jin-Lei Wu, Chuan-Cun Shu. 2026-07-13. Non-Abelian holonomic transformations in digitally coupled acoustic waveguides guided by the global adiabatic criterion. https://arxiv.org/abs/2607.11000

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