High-dimensional non-Abelian holonomy in integrated photonics

Youlve Chen, Yunru Fan, Gulliver Larsonneur, Jinlong Xiang, An He, Guohuai Wang, Xu-Lin Zhang (), Guancong Ma, Qiang Zhou, Guangcan Guo, Yikai Su () and Xuhan Guo ()
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Youlve Chen: Shanghai Jiao Tong University
Yunru Fan: University of Electronic Science and Technology of China
Gulliver Larsonneur: Shanghai Jiao Tong University
Jinlong Xiang: Shanghai Jiao Tong University
An He: Shanghai Jiao Tong University
Guohuai Wang: Jilin University
Xu-Lin Zhang: Jilin University
Guancong Ma: Hong Kong Baptist University
Qiang Zhou: University of Electronic Science and Technology of China
Guangcan Guo: University of Electronic Science and Technology of China
Yikai Su: Shanghai Jiao Tong University
Xuhan Guo: Shanghai Jiao Tong University

Nature Communications, 2025, vol. 16, issue 1, 1-9

Abstract: Abstract Non-Abelian holonomy is known for the robust holonomic unitary behavior exhibited. The associated non-Abelian geometric phase is a promising approach for implementing topologically protected computation. But its realization in application-abundant platforms has been largely elusive. In particular, the observation of universal high-order matrices is difficult due to challenges from increasing the dimensions of degenerate subspace. Here we realize a high-dimensional non-Abelian holonomic device on an integrated multilayer silicon nitride platform, which is compatible with the complementary-metal-oxide-semiconductor process. High dimensional (up to 6), broadband (> 100 nm operating bandwidth), and ultra-compact volume non-Abelian holonomy unitary matrices of arbitrary special orthogonal group are observed, and M × N linear holonomic computation architecture is experimentally realized through singular value decomposition. Our work provides a paradigm for versatile applications of non-Abelian geometric phase for both classical and quantum realms.

Date: 2025
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DOI: 10.1038/s41467-025-58794-3

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