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

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.

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Cited by in corpus (11)

• Non-Abelian lattice gauge fields in the photonic synthetic frequency dimension
• A comprehensive review on developments of synthetic dimensions
• Multi-dimensional band structure spectroscopy in the synthetic frequency dimension
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Synthetic non-Abelian Electric Fields and Spin-Orbit Coupling in Photonic Synthetic Dimensions
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• Quantized topological phases beyond square lattices in Floquet synthetic dimensions
• Quantum walk with coherent multiple translations induces fast quantum gate operations
• Topological quantum electrodynamics in synthetic non-Abelian gauge fields
• Non-Abelian gauge field optics in the time domain