Devices that achieve nonreciprocal microwave transmission are ubiquitous inradar and radio-frequency communication systems, and commonly rely onmagnetically biased ferrite materials. Such devices are also indispensable inthe readout chains of superconducting quantum circuits as they protectsensitive quantum systems from the noise emitted by readout electronics. Sinceferrite-based nonreciprocal devices are bulky, lossy, and require largemagnetic fields, there has been significant interest in magnetic-field-freeon-chip alternatives, such as those recently implemented using Josephsonjunctions. Here we realise reconfigurable nonreciprocal transmission betweentwo microwave modes using purely optomechanical interactions in asuperconducting electromechanical circuit. We analyse the transmission as wellas the noise properties of this nonreciprocal circuit. The scheme relies on theinterference in two mechanical modes that mediate coupling between microwavecavities. Finally, we show how quantum-limited circulators can be realized withthe same principle. The technology can be built on-chip without any externalmagnetic field, and is hence fully compatible with superconducting quantumcircuits. All-optomechanically-mediated nonreciprocity demonstrated here canalso be extended to implement directional amplifiers, and it forms the basistowards realising topological states of light and sound.
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