Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions

Non-Abelian gauge fields¹ provide a conceptual framework to describe particles having spins, underlying many phenomena in electrodynamics, condensed-matter physics^2,3 and particle physics^4,5. Lattice models⁶ 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^7-9. Photons are fundamental particles for which artificial gauge fields can be synthesized^10-30, 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^31,32, 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 ways³³.