We propose to demonstrate nonreciprocal conversion between microwave andoptical photons in an electro-optomechanical system where a microwave mode andan optical mode are coupled indirectly via two non-degenerate mechanical modes.The nonreciprocal conversion is obtained in the broken time-reversal symmetryregime, where the conversion of photons from one frequency to the other isenhanced for constructive quantum interference while the conversion in thereversal direction is suppressed due to destructive quantum interference. It isinteresting that the nonreciprocal response between the microwave and opticalmodes in the electro-optomechanical system appears at two different frequencieswith opposite directions. The proposal can be used to realize nonreciprocalconversion between photons of any two distinctive modes with differentfrequencies. Moreover, the electro-optomechanical system can also be used toconstruct a three-port circulator for three optical modes with distinctivelydifferent frequencies by adding an auxiliary optical mode coupled to one of themechanical modes.
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