Sub-Poissonian phonon statistics in an acoustical resonator coupled to a pumped two-level emitter

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.