Topological insulator in two synthetic dimensions based on an optomechanical resonator

Abstract

Topological insulators (TIs) implemented in synthetic dimensions have recently emerged as an attractive platform to explore higher-dimensional topological phases in compact systems. Here, we present a two-dimensional TI within a single-ring resonator enabled by acousto-optic interactions and electro-optic modulation. In our system, the synthetic dimensions are represented by the range of discrete optical modes supported by the ring resonator and their azimuthal angular order. Gauge fields responsible for the topological order in the synthetic lattice are realized by an array of racetrack couplers coupled to the resonator. We reveal topological bulk and chiral edge bands in time-resolved absorption/transmission spectra, and we show that the proposed system can support reconfigurable and nonreciprocal frequency conversion controlled by the probe frequency detuning. Interestingly, we also show that realistic phase mismatch and disorder in acousto-optic scattering can enable an amorphous TI phase in synthetic space, demonstrating robust nonreciprocal frequency conversion in this regime.