  Synthetic dimensions, which simulate spatial coordinates using non-spatial
degrees of freedom, are drawing interest in topological science and other
fields for modelling higher-dimensional phenomena on simple structures. We
present the first realization of a synthetic frequency dimension on a silicon
ring resonator photonic device fabricated using a CMOS process. We confirm that
its coupled modes correspond to a 1D tight-binding model through acquisition of
up to 280 GHz bandwidth optical frequency comb-like spectra, and by measuring
the first synthetic band structures on an integrated device. Furthermore, we
realized two types of gauge potentials along the frequency dimension, and
probed their effects through the associated band structures. An electric field
analogue was produced via modulation detuning, whereas effective magnetic
fields were induced using synchronized nearest- and second-nearest-neighbor
coupling. Creation of coupled mode lattices and two effective forces on a
monolithic Si CMOS device represents a key step towards wider adoption of
topological principles.
