Simulating topological materials with photonic synthetic dimensions in cavities

Photons play essential roles in fundamental physics and practical technologies. They have become one of the attractive informaiton carriers for quantum computation and quantum simulation. Recently, various photonic degrees of freedom supported by optical resonant cavities form photonic synthetic dimensions, which contribute to all-optical platforms for simulating novel topological materials. The photonic discrete or continuous degrees of freedom are mapped to the lattices or momenta of the simulated topological matter, and the couplings between optical modes are equivalent to the interactions among quasi-particles. Mature optical modulations enable flexible engineering of the simulated Hamiltonian. Meanwhile, the resonant detection methods provide direct approaches to obtaining the corresponding energy band structures, particle distributions and dynamical evolutions. In this Review, we give an overview of the synthetic dimensions in optical cavities, including frequency, orbital angular momentum, time-multiplexed lattice, and independent parameters. Abundant higher-dimensional topological models have been demonstrated in lower dimensional synthetic systems. We further discuss the potential development of photonic synthetic dimensions in the future.