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The successes of superconducting quantum circuits at local manipulation ofquantum information and photonics technology at long-distance transmission ofthe same have spurred interest in the development of quantum transducers forefficient, low-noise, and bidirectional frequency conversion of photons betweenthe microwave and optical domains. We propose to realize such functionalitythrough the coupling of electrical, piezoelectric, and optomechanicalresonators. The coupling of the mechanical subsystems enables formation of aresonant mechanical supermode that provides a mechanically-mediated, efficientsingle interface to both the microwave and optical domains. The conversionprocess is analyzed by applying an equivalent circuit model that relatesdevice-level parameters to overall figures of merit for conversion efficiency$\eta$ and added noise $N$. These can be further enhanced by proper impedancematching of the transducer to an input microwave transmission line. Theperformance of potential transducers is assessed through finite-elementsimulations, with a focus on geometries in GaAs, followed by considerations ofthe AlN, LiNbO$_3$, and AlN-on-Si platforms. We present strategies formaximizing $\eta$ and minimizing $N$, and find that simultaneously achieving$\eta>50~\%$ and $N < 0.5$ should be possible with current technology. We findthat the use of a mechanical supermode for mediating transduction is a keyenabler for high-efficiency operation, particularly when paired with anappropriate microwave impedance matching network. Our comprehensive analysis ofthe full transduction chain enables us to outline a development path for therealization of high-performance quantum transducers that will constitute avaluable resource for quantum information science.

Microwave-to-optical transduction using a mechanical supermode for coupling piezoelectric and optomechanical resonators