Creating high-dimensional topological physics using a single ring resonator

The property of a physical system is highly dependent on its dimensionality. Topological physics in three or more dimensions exhibits rich phenomena without lower-dimensional counterparts. In this paper, the authors propose a scheme to implement such high-dimensional topological physics in a single photonic ring resonator, where the model of interest can be arbitrarily high dimensional and arbitrarily multi-band. The frequency modes in the resonator, coupled via electro-optic modulation, are used to create a high-dimensional lattice, and the spatial modes are used as the pseudo-spin degree of freedom within each lattice site. The band structure of the model can be measured from the transmission spectrum of the ring resonator. The authors numerically demonstrate as examples a three-dimensional, two-band model and a five-dimensional, four-band model. This paper establishes a versatile and programmable platform for high-dimensional topological physics, paving the way for its experimental studies and future applications.