Mechanical resonators are important components of devices that range from gravitational wave detectors to cellular telephones. They serve as high-performance transducers, sensors and filters by offering low dissipation, tunable coupling to diverse physical systems, and compatibility with a wide range of frequencies, materials and fabrication processes. Systems of mechanical resonators typically obey reciprocity, which ensures that the phonon transmission coefficient between any two resonators is independent of the direction of transmission1,2. Reciprocity must be broken to realize devices (such as isolators and circulators) that provide one-way propagation of acoustic energy between resonators. Such devices are crucial for protecting active elements, mitigating noise and operating full-duplex transceivers. Until now, nonreciprocal phononic devices3,4,5,6,7,8,9,10,11 have not simultaneously combined the features necessary for robust operation: strong nonreciprocity, in situ tunability, compact integration and continuous operation. Furthermore, they have been applied only to coherent signals (rather than fluctuations or noise), and have been realized exclusively in travelling-wave systems (rather than resonators). Here we describe a scheme that uses the standard cavity-optomechanical interaction to produce robust nonreciprocal coupling between phononic resonators. This scheme provides about 30 decibels of isolation in continuous operation and can be tuned in situ simply via the phases of the drive tones applied to the cavity. In addition, by directly monitoring the dynamics of the resonators we show that this nonreciprocity can control thermal fluctuations, and that this control represents a way to cool phononic resonators.
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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
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This work is supported by the Air Force Office of Scientific Research grant number FA9550-15-1-0270, the Air Force Office of Scientific Research Multidisciplinary University Research Initiative grant number FA9550-15-1-0029, the Office of Naval Research Multidisciplinary University Research Initiative grant number N00014-15-1-2761 and the Simons Foundation (award number 505450).
Nature thanks Claudiu Genes, Andre Xuereb and the other anonymous reviewer(s) for their contribution to the peer review of this work.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
This data was used to calculate the normalized temperature ratio shown in Fig. 4b. The error bars show the standard error of the mean.
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Xu, H., Jiang, L., Clerk, A.A. et al. Nonreciprocal control and cooling of phonon modes in an optomechanical system. Nature 568, 65–69 (2019). https://doi.org/10.1038/s41586-019-1061-2
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