  Nonreciprocal circuit elements form an integral part of modern measurement
and communication systems. Mathematically they require breaking of
time-reversal symmetry, typically achieved using magnetic materials and more
recently using the quantum Hall effect, parametric permittivity modulation or
Josephson nonlinearities. Here, we demonstrate an on-chip magnetic-free
circulator based on reservoir engineered optomechanical interactions.
Directional circulation is achieved with controlled phase-sensitive
interference of six distinct electro-mechanical signal conversion paths. The
presented circulator is compact, its silicon-on-insulator platform is
compatible with both superconducting qubits and silicon photonics, and its
noise performance is close to the quantum limit. With a high dynamic range, a
tunable bandwidth of up to 30 MHz and an in-situ reconfigurability as beam
splitter or wavelength converter, it could pave the way for superconducting
qubit processors with integrated and multiplexed on-chip signal processing and
readout.
