Artificial Non-Abelian Lattice Gauge Fields for Photons in the Synthetic Frequency Dimension

Non-Abelian gauge fields give rise to nontrivial topological physics. Here we develop a scheme to create an arbitrary SU(2) lattice gauge field for photons in the synthetic frequency dimension using an array of dynamically modulated ring resonators. The photon polarization is taken as the spin basis to implement the matrix-valued gauge fields. Using a non-Abelian generalization of the Harper-Hofstadter Hamiltonian as a specific example, we show that the measurement of the steady-state photon amplitudes inside the resonators can reveal the band structures of the Hamiltonian, which show signatures of the underlying non -Abelian gauge field. These results provide opportunities to explore novel topological phenomena associated with non-Abelian lattice gauge fields in photonic systems.

Automated summary

Non-Abelian gauge fields for photons in the synthetic frequency dimension can be created using dynamically modulated ring resonators, with photon polarization as the spin basis for matrix-valued gauge fields. By measuring the steady-state photon amplitudes inside resonators, the band structures of the Harper-Hofstadter Hamiltonian can be revealed, demonstrating the signatures of the underlying non-Abelian gauge field. These findings open up opportunities for investigating novel topological phenomena in photonic systems.