Quantum electromechanics of a hypersonic crystal

Radiation pressure within engineered structures has recently been used to couple the motion of nanomechanical objects with high sensitivity to optical and microwave electromagnetic fields. Here, we demonstrate a form of electromechanical crystal for coupling microwave photons and hypersonic phonons by embedding the vacuum-gap capacitor of a superconducting resonator within a phononic crystal acoustic cavity. Utilizing a two-photon resonance condition for efficient microwave pumping and a phononic bandgap shield to eliminate acoustic radiation, we demonstrate large cooperative coupling (\(C \approx 30\)) between a pair of electrical resonances at \(10\)GHz and an acoustic resonance at \(0.425\)GHz. Electrical read-out of the phonon occupancy shows that the hypersonic acoustic mode has an intrinsic energy decay time of \(2.3\)ms and thermalizes close to its quantum ground-state of motion (occupancy \(1.5\)) at a fridge temperature of \(10\)mK. Such an electromechanical transducer is envisioned as part of a hybrid quantum circuit architecture, capable of interfacing to both superconducting qubits and optical photons.