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Phononic resonators play important roles in settings that range fromgravitational wave detectors to cellular telephones. They serve ashigh-performance transducers, sensors, and filters by offering low dissipation,tunable coupling to diverse physical systems, and compatibility with a widerange of frequencies, materials, and fabrication processes. Systems of phononicresonators typically obey reciprocity, which ensures that the phonontransmission coefficient between any two resonators is independent of thedirection of transmission. Reciprocity must be broken to realize devices (suchas isolators and circulators) that provide one-way propagation of acousticenergy between resonators. Such devices are crucial for protecting activeelements, mitigating noise, and operating full-duplex transceivers. To date,nonreciprocal phononic devices have not combined the features necessary forrobust operation: strong nonreciprocity, in situ tunability, compactintegration, and continuous operation. Furthermore, they have been applied onlyto coherent signals (rather than fluctuations or noise), and have been realizedexclusively in travelling-wave systems (rather than resonators). Here wedescribe a cavity optomechanical scheme that produces robust nonreciprocalcoupling between phononic resonators. This scheme provides ~ 30 dB of isolationand can be tuned in situ simply via the phases of the drive tones applied tothe cavity. In addition, by directly monitoring the resonators' dynamics weshow that this nonreciprocity can be used to control thermal fluctuations, andthat this control represents a new resource for cooling phononic resonators.

Nonreciprocal control and cooling of phonon modes in an optomechanical system