Non-Abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate nondispersive modes and show that, when the lattice parameters are slowly modulated, the propagation of the photons bears the fingerprints of the underlying non-Abelian gauge structure. The nondispersive character of the bands enables a high degree of control on photon propagation. Our work paves the way to the generation and detection of non-Abelian gauge fields in photonic and optical lattices.

• Received 30 October 2020
• Revised 24 May 2021
• Accepted 1 June 2021

DOI:https://doi.org/10.1103/PhysRevA.103.063518