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<p>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 (&gt; 100 nm operating bandwidth), and ultra-compact volume non-Abelian holonomy unitary matrices of arbitrary special orthogonal group are observed, and <i>M</i> × <i>N</i> 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.</p>

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High-dimensional non-Abelian holonomy in integrated photonics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月17日

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  • Youlve Chen,
  • Yunru Fan,
  • Gulliver Larsonneur,
  • Jinlong Xiang,
  • An He,
  • Guohuai Wang,
  • Xu-Lin Zhang,
  • Guancong Ma,
  • Qiang Zhou,
  • Guangcan Guo,
  • Yikai Su,
  • Xuhan Guo

摘要

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.