Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension

TL;DR

This paper proposes a method to create and study non-Abelian SU(2) gauge fields for photons in a synthetic frequency dimension using modulated resonators, revealing topological phenomena.

Contribution

The authors develop a scheme to implement arbitrary SU(2) lattice gauge fields for photons in the synthetic frequency dimension using dynamically modulated resonators.

Findings

Measurement of photon amplitudes reveals non-Abelian band structures

Implementation of a non-Abelian Harper-Hofstadter Hamiltonian

Potential to explore topological phenomena in photonic systems

Abstract

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.