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