Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiation-pressure-induced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break time-reversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phase-correlated laser light results in a synthetic magnetic flux, which in combination with dissipative coupling to the mechanical bath, leads to nonreciprocal transport of photons with 35dB of isolation. Additionally, optical pumping with blue-detuned light manifests as a particle non-conserving interaction between photons and phonons, resulting in directional optical amplification of 12dB in the isolator through direction. These results indicate the feasibility of utilizing optomechanical circuits to create a more general class of nonreciprocal optical devices, and further, to enable novel topological phases for both light and sound on a microchip.
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