  We propose and analyse a quantum electromechanical system composed of a
monolithic quartz bulk acoustic wave (BAW) oscillator coupled to a
superconducting transmon qubit via an intermediate LC electrical circuit.
Monolithic quartz oscillators offer unprecedentedly high effective masses and
quality factors for the investigation of mechanical oscillators in the quantum
regime. Ground-state cooling of such mechanical modes via resonant
piezoelectric coupling to an LC circuit, which is itself sideband cooled via
coupling to a transmon qubit, is shown to be feasible. The fluorescence
spectrum of the qubit, containing motional sideband contributions due to the
couplings to the oscillator modes, is obtained and the imprint of the
electromechanical steady-state on the spectrum is determined. This allows the
qubit to function both as a cooling resource for, and transducer of, the
mechanical oscillator. The results described are relevant to any hybrid quantum
system composed of a qubit coupled to two (coupled or uncoupled) thermal
oscillator modes.

Quantum Physics;Mesoscale and Nanoscale Physics