  We report the observation of coupling between a 3D microwave cavity mode and
a bulk mechanical resonator mediated by piezoelectric and radiation pressure
effects. The system is composed of a quartz bulk acoustic wave resonator placed
inside a microwave re-entrant cavity, which is designed to act as both the
electrodes for piezoelectric actuation as well as a 3D resonator. The cavity
electromagnetic mode is modulated by a 5 MHz bulk acoustic wave shear mode,
which is modeled and experimentally verified using the input-output formalism.
Through finite element method simulations, we calculate the various
contributions to the electromechanical coupling and discuss the potential of
the system to reach high cooperativities as well as suitable applications.
