  Directional transmission or amplification of microwave signals is
indispensable in various applications involving sensitive measurements. In this
work we show in experiment how to use a generic cavity optomechanical setup to
non-reciprocally amplify microwave signals above 3 GHz in one direction by 9
decibels, and simultaneously attenuate the transmission in the opposite
direction by 21 decibels. We use a device including two on-chip superconducting
resonators and two metallic drumhead mechanical oscillators. Application of
four microwave pump tone frequencies allows for designing constructive or
destructive interference for a signal tone depending on the propagation
direction. The device can also be configured as an isolator with a lossless
nonreciprocal transmission and 18 dB of isolation.
