Phonon Dynamics and Damping in Three-Dimensional Acoustic Bandgap Cavity-Optomechanical Resonators

Mechanical resonators are used in a wide variety of technical applications, from precision time keeping and sensing, to the delay and filtering of microwave signals in mobile communication systems. Critical to many of these applications is the ability of a mechanical object to store vibrational energy at a well defined frequency of oscillation and with minimal damping. Energy damping can occur through acoustic radiation into the resonator support structure, or through impurities and defects in the resonator material, and is highly dependent on the temperature of operation due to the inherent anharmonic motion of atoms within solid-state materials. Here, we present optical measurements down to milliKelvin temperatures of the acoustic mode properties of a crystalline silicon nanobeam cavity incorporating a three-dimensional phononic bandgap support structure for acoustic confinement. Utilizing pulsed laser light to excite a co-localized optical mode of the optomechanical crystal (OMC) device, we are able to measure the dynamics of the internal cavity acoustic modes which are coupled to the light field via radiation pressure. These measurements represent an almost ideal scenario in which the ringdown occurs free of any additional mechanical or probe field contact, and where elastic scattering or radiation of the acoustic field does not lead to energy damping due to the full bandgap shield. The resulting ringdown measurements for the fundamental 5 GHz acoustic mode of the cavity show an exponential increase in phonon lifetime versus phononic shield period number, which at a bath temperature of 35 milliKelvin saturates above six periods to a value as long as 1.5 seconds. This ultra-long lifetime, corresponding to an effective phonon propagation length of several kilometers, is found at the lowest temperatures to be consistent with damping from non-resonant tunneling states whose energy lies below the acoustic shield phononic bandgap, and which are most likely present in the amorphous etch-damaged region of the silicon surface. Other, more rapid forms of damping such as resonant tunneling state damping or three-phonon scattering are suppressed due to the phononic bandgap shield and the reduced density of phonon states in the effectively one-dimensional nanobeam geometry. Prospects for newapplications of ultra-coherent nanoscale mechanical resonators include tests of various collapse models of quantum mechanics, or, if appropriately integrated with microwave superconducting quantum circuits, as miniature quantum memory or processing units with potentially many-orders of magnitude longer coherence time than their electromagnetic counterparts.