  The concept of an acoustical analog of the optical laser has been developed
recently both in theoretical as well as experimental works. We discuss here a
model of a coherent phonon generator with a direct signature of quantum
properties of the sound vibrations. The considered setup is made of a laser
driven quantum dot (QD) embedded in an acoustical nanocavity. The system's
dynamics is solved for a single phonon mode in the steady-state and in the
strong QD-phonon coupling regime beyond the secular approximation. We
demonstrate that the phonon statistics exhibits quantum features, i.e.
sub-Poissonian phonon statistics.
