  Schemes to achieve strong coupling between mechanical modes of aluminum
nitride microstructures and microwave cavity modes due to the piezoelectric
effect are proposed. We show that the strong coupling regime is feasible for an
on-chip aluminum nitride device that is either enclosed by a three-dimensional
microwave cavity or integrated with a superconducting coplanar resonator.
Combining with optomechanics, the piezomechanical strong coupling permits
coherent conversion between microwave and optical modes with high efficiency.
Hence, the piezomechanical system will be an efficient transducer for
applications in hybrid quantum systems.
