Optomechanical Measurements of Ultra-Long-Lived Microwave Phonon Modes in a Phononic Bandgap Cavity*

We present measurements of optomechanical crystal cavity devices (OMCs) based on silicon-on-insulator (SOI) at milliKelvin temperatures engineered with a full three-dimensional phononic bandgap shield. Such devices can exhibit ultra-long-lived phonon modes in the microwave regime, and by optical probing of the phonon dynamics we observe lifetimes as large as τ = 1.21 seconds for the 5 GHz phonon mode in our devices. In addition, we identify several regimes of heating and damping of the high-Q mechanical cavity mode which can be described by coupling to higher frequency phonon baths. With further reduction of these baths caused by unwanted optical absorption heating in our devices, such ultra-long-lived microwave-frequency mechanical modes may become useful in quantum transducers or quantum memory elements incorporating superconducting microwave circuits. To this end, we are developing quasi-2D OMC devices with greatly improved thermal conductance to the milliKelvin environment to enable the study of such microwave phonon modes in the quantum regime.