中国科学技术大学郭光灿团队观测了非厄米合成晶格中的半整数拓扑圈数。2025年6月24日出版的《光：科学与应用》杂志发表了这项成果。

非埃尔米特（NH）系统揭示了埃尔米特对应物中没有观察到的独特拓扑现象，如新的拓扑分类和NH趋肤效应。在周期NH系统中，本征能量变得复杂，并在复平面上表现出绕组，而本征态绕组数在厄米系统中是严格整数，可以取半整数值。然而，直接实验观察NH绕组的本征能量和本征态，特别是半整数绕组，仍然是一个重大挑战。 

在这项工作中，研究组利用轨道角动量（OAM）合成维构建了一个NH拓扑晶格，实现了对本征态和本征能量绕组的直接观测。他们报告了半整数本征态绕组数的首次实验观察，并揭示了NH皮肤动力学方向与本征能量绕组之间的内在关系。此外，通过将OAM链划分为两个半无限链，研究组观察到零边界模，并证明它们的分布是由本征态和本征能量的缠绕数共同决定的。这项工作为NH拓扑结构提供了全面的见解，并为探索NH现象提供了一个新的实验平台。

附：英文原文

Title: Observing half-integer topological winding numbers in non-Hermitian synthetic lattices

Author: Yang, Mu, Liao, Yu-Wei, Zhang, Hao-Qing, Li, Yue, Hao, Zhi-He, Zhou, Zheng-Wei, Luo, Xi-Wang, Xu, Jin-Shi, Li, Chuan-Feng, Guo, Guang-Can

Issue&Volume: 2025-06-24

Abstract: Non-Hermitian (NH) systems have revealed unique topological phenomena that are not observed in Hermitian counterparts, such as novel topology classifications and the NH skin effect. In periodic NH systems, eigenenergies become complex and exhibit windings in the complex plane, while eigenstate winding numbers, which are strictly integers in Hermitian systems, can take half-integer values. However, direct experimental observation of NH winding of both eigenenergies and eigenstates, especially the half-integer winding, remains a significant challenge. In this work, we utilize the orbital angular momentum (OAM) synthetic dimension to construct an NH topological lattice and achieve direct observation of both eigenstate and eigenenergy windings. We report the first experimental observation of a half-integer eigenstate winding number, and reveal the intrinsic relationship between the direction in the NH skin dynamics and eigenenergy windings. Furthermore, by partitioning the OAM chain into two semi-infinite chains, we observe zero boundary modes and demonstrate that their distributions are jointly determined by the winding numbers of both the eigenstates and eigenenergies. This work provides comprehensive insights into NH topologies and offers a new experimental platform for exploring NH phenomena.

DOI: 10.1038/s41377-025-01909-8

Source: https://www.nature.com/articles/s41377-025-01909-8