Cheng Dali, Wang Kai, Roques-Carmes Charles, Lustig Eran, Long Olivia Y, Wang Heming, Fan Shanhui
Edward L. Ginzton Laboratory, Stanford University, Stanford, CA, USA.
Department of Electrical Engineering, Stanford University, Stanford, CA, USA.
Nature. 2025 Jan;637(8044):52-56. doi: 10.1038/s41586-024-08259-2. Epub 2025 Jan 1.
Non-Abelian gauge fields provide a conceptual framework to describe particles having spins, underlying many phenomena in electrodynamics, condensed-matter physics and particle physics. Lattice models of non-Abelian gauge fields allow us to understand their physical implications in extended systems. The theoretical importance of non-Abelian lattice gauge fields motivates their experimental synthesis and explorations. Photons are fundamental particles for which artificial gauge fields can be synthesized, yet the demonstration of non-Abelian lattice gauge fields for photons has not been achieved. Here we demonstrate SU(2) lattice gauge fields for photons in the synthetic frequency dimensions, a playground to study lattice physics in a scalable and programmable way. In our lattice model, we theoretically observe that homogeneous non-Abelian lattice gauge potentials induce Dirac cones at time-reversal-invariant momenta in the Brillouin zone. We experimentally confirm the presence of non-Abelian lattice gauge fields by two signatures: linear band crossings at the Dirac cones, and the associated direction reversal of eigenstate trajectories. We further demonstrate a non-Abelian scalar lattice gauge potential that lifts the degeneracies of the Dirac cones. Our results highlight the implications of non-Abelian lattice gauge fields in topological physics, and provide a starting point for demonstrations of emerging non-Abelian physics in the photonic synthetic dimensions. Our results may also benefit photonic technologies by providing controls of photon spins and pseudo-spins in topologically non-trivial ways.
非阿贝尔规范场提供了一个描述具有自旋粒子的概念框架，是电动力学、凝聚态物理和粒子物理中诸多现象的基础。非阿贝尔规范场的晶格模型使我们能够理解它们在扩展系统中的物理意义。非阿贝尔晶格规范场的理论重要性推动了其实验合成与探索。光子是可以合成人工规范场的基本粒子，但尚未实现光子的非阿贝尔晶格规范场的证明。在此，我们在合成频率维度上展示了光子的SU(2)晶格规范场，这是一个以可扩展和可编程方式研究晶格物理的平台。在我们的晶格模型中，我们从理论上观察到均匀的非阿贝尔晶格规范势在布里渊区的时间反演不变动量处诱导出狄拉克锥。我们通过两个特征实验证实了非阿贝尔晶格规范场的存在：狄拉克锥处的线性能带交叉以及本征态轨迹的相关方向反转。我们进一步展示了一个非阿贝尔标量晶格规范势，它消除了狄拉克锥的简并。我们的结果突出了非阿贝尔晶格规范场在拓扑物理中的意义，并为在光子合成维度中展示新兴的非阿贝尔物理提供了一个起点。我们的结果还可能通过以拓扑非平凡的方式控制光子自旋和赝自旋而使光子技术受益。
