  The concept of synthetic dimensions, which has enabled the study of
higher-dimensional physics on lower-dimensional physical structures, has
generated significant recent interest in many branches of science ranging from
ultracold-atomic physics to photonics, since such a concept provides a
versatile platform for realizing effective gauge potentials and novel
topological physics. Previous experiments demonstrating this concept have
augmented the real-space dimensionality by one additional physical synthetic
dimension. Here 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 experimentally
observe a wide variety of rich physics, including effective spin-orbit
coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase
transition, and chiral 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.
