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Optical computing with integrated photonics brings a pivotal paradigm shift to data-intensive computing technologies. However, the scaling of on-chip photonic architectures using spatially distributed schemes faces the challenge imposed by the fundamental limit of integration density. Synthetic dimensions of light offer the opportunity to extend the length of operand vectors within a single photonic component. Here, we show that large-scale, complex-valued matrix-vector multiplications on synthetic frequency lattices can be performed using an ultra-efficient, silicon-based nanophotonic cavity acousto-optic modulator. By harnessing the resonantly enhanced strong electro-optomechanical coupling, we achieve, in a single such modulator, the full-range phase-coherent frequency conversions across the entire synthetic lattice, which constitute a fully connected linear computing layer. Our demonstrations open up the route toward the experimental realizations of frequency-domain integrated optical computing systems simultaneously featuring very large-scale data processing and small device footprints.

Excitons are elementary optical excitation in semiconductors. The ability to manipulate and transport these quasiparticles would enable excitonic circuits and devices for quantum photonic technologies. Recently, interlayer excitons in 2D semiconductors have emerged as a promising candidate for engineering excitonic devices due to their long lifetime, large exciton binding energy, and gate tunability. However, the charge-neutral nature of the excitons leads to weak response to the in-plane electric field and thus inhibits transport beyond the diffusion length. Here, we demonstrate the directional transport of interlayer excitons in bilayer WSe₂driven by the propagating potential traps induced by surface acoustic waves (SAW). We show that at 100 K, the SAW-driven excitonic transport is activated above a threshold acoustic power and reaches 20 μm, a distance at least ten times longer than the diffusion length and only limited by the device size. Temperature-dependent measurement reveals the transition from the diffusion-limited regime at low temperature to the acoustic field-driven regime at elevated temperature. Our work shows that acoustic waves are an effective, contact-free means to control exciton dynamics and transport, promising for realizing 2D materials-based excitonic devices such as exciton transistors, switches, and transducers up to room temperature.