Optical non-reciprocity, a phenomenon that allows unidirectional flow of optical field is pivoted on the time reversal symmetry breaking. The symmetry breaking happens in the cavity optomechanical system (COS) due to non uniform radiation pressure as a result of light-matter interaction, and is crucial in building non-reciprocal optical devices. In our proposed COS, we study the non-reciprocal transport of optical signals across two ports via three optical modes optomechanically coupled to the mechanical excitations of two nano-mechanical resonators (NMRs) under the influence of strong classical drive fields and weak probe fields. By tuning different system parameters, we discover the conversion of reciprocal to non-reciprocal signal transmission. We reveal perfect nonreciprocal transmission of output fields when the effective cavity detuning parameters are near resonant to the NMRs frequencies. The unidirectional non-reciprocal signal transport is robust to the optomechanical coupling parameters at resonance conditions. Moreover, the cavities photon loss rates play an inevitable role in the unidirectional flow of signal across the two ports. Bidirectional transmission can be fully controlled by the phase changes associated with the incoming probe and drive fields via two ports. Our scheme may provide a foundation for the compact non-reciprocal communication and quantum information processing, thus enabling new devices that route photons in unconventional ways such as all-optical diodes, optical transistors and optical switches.
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