High-dimensional topological physics synthesized in a photonic ring resonator

Topological physics in three or more dimensions exhibits rich phenomena without lower-dimensional counterparts. To experimentally explore these high-dimensional effects, researchers have introduced the concept of synthetic dimensions, where non-spatial degrees of freedom of particles are utilized to augment the dimensionality of the physical space. An emerging approach involves using a single photonic ring resonator in which longitudinal modes are coupled via electro-optic modulations to create multiple synthetic frequency dimensions. However, previous implementations have only demonstrated high-dimensional Hamiltonians that are topologically trivial. Here, we propose theoretically a general scheme that employs mode-selective modulations and mode conversions within a single ring resonator to realize a wide range of non-trivial, high-dimensional topological physics. As specific examples, we numerically demonstrate a three-dimensional, two-band model with Weyl points and topological insulator phases, and a five-dimensional, four-band model featuring Yang monopoles and Weyl surfaces. We show that the band structures of the models, including topological features such as degeneracies and band gaps, can be extracted from a transmission measurement of the ring resonator. These results pave the way for experimental studies and future applications of topological physics in high dimensions.