We propose a scheme that is able to generate the microwave controlled opticaldouble optome-chanical induced transparency (OMIT) in a hybridpiezo-optomechanical cavity system, which a piezoelectric optomechanicalcrystal AlN-nanobeam resonator is placed in a superconducting microwave cavity,and the AlN-nanobeam resonator can be simultaneously driven by both the opticalfield via the radiation pressure and the microwave field via the piezoelectricinteraction. We show that in the presence of a strong pumped optical fieldapplied to the optomechanical crystal cavity through the optical waveguide andan intensely stimulated microwave field applied to the superconductingmicrowave cavity, a double-OMIT window can be observed in the weak output probefield. The mechanism is that a N-type four-level system can be formed by thesystem, when two driving fields and a probe field are applied to thecorresponding levels, under the effect of quantum interference betweendifferent energy level pathways, the third-order nonlinear absorption isenhanced by the constructive quantum interference while the linear absorptionis inhibited by the destruc- tive quantum interference, as a result, thedouble-OMIT window is generated. Our scheme can be applied to realizehigh-speed optical switches, high-resolution spectroscopy, coherent populationtrapping or quantum information processing in the solid state quantum systems.
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