Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions

Dali Cheng, Kai Wang, Charles Roques-Carmes, Eran Lustig, Olivia Y. Long, Heming Wang and Shanhui Fan ()
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Dali Cheng: Stanford University
Kai Wang: McGill University
Charles Roques-Carmes: Stanford University
Eran Lustig: Stanford University
Olivia Y. Long: Stanford University
Heming Wang: Stanford University
Shanhui Fan: Stanford University

Nature, 2025, vol. 637, issue 8044, 52-56

Abstract: Abstract Non-Abelian gauge fields1 provide a conceptual framework to describe particles having spins, underlying many phenomena in electrodynamics, condensed-matter physics2,3 and particle physics4,5. 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 explorations7–9. Photons are fundamental particles for which artificial gauge fields can be synthesized10–30, 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 dimensions31,32, 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.

Date: 2025
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DOI: 10.1038/s41586-024-08259-2

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