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.

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We investigate the steady-state cooling dynamics of vibrational degrees of freedom related to a nanomechanical oscillator coupled with a laser-pumped quantum dot in an optical resonator. Correlations between phonon-cooling and quantum-dot photon emission processes occur respectively when a photon laser absorption together with a vibrational phonon absorption is followed by photon emission in the optical resonator. Therefore, the detection of photons generated in the cavity mode concomitantly contribute to phonon cooling detection of the nanomechanical resonator.Comment: 4 pages, 3 figure