A single photonic cavity with two independent physical synthetic dimensions.

The concept of synthetic dimensions has generated interest in many branches of science ranging from ultracold-atomic physics to photonics, as it provides a versatile platform for realizing effective gauge potentials and topological physics. Previous experiments have augmented the real-space dimensionality by one additional physical synthetic dimension. We endow a single ring resonator with two independent physical synthetic dimensions. Our system consists of a temporally modulated ring resonator with spatial coupling between the clockwise and counterclockwise modes, creating a synthetic Hall ladder along the frequency and pseudospin degrees of freedom for photons propagating in the ring. We observe a wide variety of rich physics, including effective spin-orbit coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase transition, and signatures of topological chiral one-way edge currents, completely in synthetic dimensions. Our experiments demonstrate that higher-dimensional physics can be studied in simple systems by leveraging the concept of multiple simultaneous synthetic dimensions.