  We investigate the feasibility of correlating an optical cavity field and a
vibrational phonon mode. A laser pumped quantum dot fixed on a nano-mechanical
resonator beam interact as a whole with the optical resonator mode. When the
quantum dot variables are faster than the optical and phonon ones, we obtain a
final master equation describing the involved modes only. Increasing the
temperature, that directly affects the vibrational degrees of freedom, one can
as well influence the cavity photon intensity, i.e., the optical and phonon
modes are correlated. Furthermore, the corresponding Cauchy-Schwarz inequality
is violated demonstrating the quantum nature of those correlations.
