One studies the quantum statistics of vibrational quanta of a semiconductor multi-layered lattice, which forms an acoustical cavity. A laser driven embedded quantum dot (QD) is acting as a phonon source (see Figure 1). The detuning of the laser’s light from the QD’s transition frequency may allow the creation and annihilation of phonons and, furthermore, lead to the amplification of the phonon field if the QD’s spontaneous emission is considered. The corresponding system’s Hamiltonian is defined by the free QD’s and phonon field terms and by the QD-laser and QD-phonon interaction terms, within a semi-classical laser-QD interaction, i.e., for intense laser fields. The dynamics are solved using the density operator’s master equation including the damping phenomena, i.e., the QD’s spontaneous emission and dephasing processes and the phonon thermal environmental reservoir. We observe a direct signature of quantum features of the sound, i.e., sub-Poissonian distributed phonon fields, via the study of the second-order correlation function (see Figure 2), as it goes under the unity for sub-Poissonian distributed fields [1]. Figure 1. The model Figure 2. Second-order phonon-phonon correlation function (blue curve) and the mean phonon number in the cavity (red dashed curve) as functions of the normalized detuning.