  The demonstration of a quantum link between microwave and optical frequencies
would be an important step towards the realization of a quantum network of
superconducting processors. A major impediment to quantum electro-optic
transduction in all platforms explored to date is noise added by thermal
occupation of modes involved in the transduction process, and it has proved
difficult to realize low thermal occupancy concurrently with other desirable
features like high duty cycle and high efficiency. In this work, we present an
efficient and continuously operating electro-optomechanical transducer whose
mechanical mode has been optically sideband-cooled to its quantum ground state.
The transducer achieves a maximum efficiency of 47% and minimum input-referred
added noise of 3.2 photons in upconversion. Moreover, the thermal occupancy of
the transducer's microwave mode is minimally affected by continuous laser
illumination with power more than two orders of magnitude greater than that
required for optomechanical ground-state cooling.
