  Efficiently exciting and controlling phonons in diamond nanoresonators
represents a fundamental challenge for quantum applications. Here, we
theoretically demonstrate the possibility to excite mechanical modes within a
double-hybrid-cavity (DHC), formed by adjoining to a diamond cavity a second
cavity, made of aluminum nitride. The latter is piezoelectric and serves as a
microwave-to-phonon transducer, activating mechanical modes in the entire DHC.
We show the process to match the cavities phononic properties, making them work
coordinately in the DHC and obtaining a well confined mode. In the diamond part
of the cavity, this mode replicates the fundamental mode of the individual
diamond cavity, showing that the piezoelectric transducer doesn't alter the
diamond individual fundamental mode. In the piezoelectric part, the strong
confinement of stress and electric field results in a high piezoelectric
coupling rate, demonstrating the effectiveness of a phononic cavity as a
transducer. The study is contextualized in the framework of a quantum
networking application, where the DHC serves as a spin qubit, exploiting the
spin-mechanical coupling within diamond color centers.
