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<p>Topology has emerged as a fundamental property of many systems yet mostly limited to low dimensions. Here, we reveal the hidden topology in entangled states carrying orbital angular momentum (OAM), in arbitrary dimensions. For two-dimensional systems, we demonstrate multiple skyrmion topologies and their equivalence to ’t Hooft-Polyakov magnetic monopoles, experimentally connecting them to the Higgs field. In higher dimensions, we use non-Abelian gauge fields of SU(d) Yang-Mills theory to predict a rich tapestry of topological maps and their invariants, which we confirm experimentally for dimensionality up to seven, showing an underlying topology of 48 dimensions and a topological spectrum spanning over 17000 invariants. In addition to inducing robustness to perturbation, the topological spectrum enables probing them, by observing their emergent signatures in its non-topological spaces. The only degree of freedom we use to construct the topology is OAM, breaking away from the optical paradigm of polarisation-based spin-textured fields and forgoing the need for quantum state engineering. Our theoretical framework can be extrapolated to any dimension and degree of freedom, opening a distinct path for finding topologies in light.</p>

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Revealing the topological nature of entangled orbital angular momentum states of light

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月12日

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  • Robert de Mello Koch,
  • Pedro Ornelas,
  • Neelan Gounden,
  • Bo-Qiang Lu,
  • Isaac Nape,
  • Andrew Forbes

摘要

Topology has emerged as a fundamental property of many systems yet mostly limited to low dimensions. Here, we reveal the hidden topology in entangled states carrying orbital angular momentum (OAM), in arbitrary dimensions. For two-dimensional systems, we demonstrate multiple skyrmion topologies and their equivalence to ’t Hooft-Polyakov magnetic monopoles, experimentally connecting them to the Higgs field. In higher dimensions, we use non-Abelian gauge fields of SU(d) Yang-Mills theory to predict a rich tapestry of topological maps and their invariants, which we confirm experimentally for dimensionality up to seven, showing an underlying topology of 48 dimensions and a topological spectrum spanning over 17000 invariants. In addition to inducing robustness to perturbation, the topological spectrum enables probing them, by observing their emergent signatures in its non-topological spaces. The only degree of freedom we use to construct the topology is OAM, breaking away from the optical paradigm of polarisation-based spin-textured fields and forgoing the need for quantum state engineering. Our theoretical framework can be extrapolated to any dimension and degree of freedom, opening a distinct path for finding topologies in light.