Parametric Amplification of an Optomechanical Quantum Interconnect

Connecting microwave quantum computing technologies with optical fiber necessitates the conversion of microwave photons to optical photons mediated by strong non-linear coupling between microwave and optical modes. Modern experimental demonstrations exhibit strong coupling between a microwave resonator and an optical cavity mediated through phononic modes in a mechanical oscillator. This paradigmatic transduction experiment is bounded by theoretical efficiency bounds with constant driving amplitudes on the microwave resonator and optical cavity. By adding a parametric drive to the microwave resonator and optical cavity we can amplify the phononic occupation and amplify the converted signal through the quantum transducer. We present a theoretical framework for time-dependent control of the driving lasers based on the input-output formalism of quantum optics, and solve the linear time-varying equation of motion to obtain an analytic expression for the transfer function. The transfer function with the parametric drive results in a simple expression for efficiency gain in a transducer. We illustrate our analytic solution in varying parameter regimes relevant to current transduction experiments using numerical simulation.