Conversion of mechanical noise into correlated photon pairs: Dynamical Casimir effect from an incoherent mechanical drive

We show that the dynamical Casimir effect in an optomechanical system can be achieved under incoherent mechanical pumping. We adopt a fully quantum-mechanical approach for both the cavity field and the oscillating mirror. The dynamics is then evaluated using a recently developed master-equation approach in the dressed picture, including both zero- and finite-temperature photonic reservoirs. This analysis shows that the dynamical Casimir effect can be observed even when the mean value of the mechanical displacement is zero. This opens up possibilities for the experimental observation of this effect. We also calculate cavity emission spectra in both the resonant and the dispersive regimes, providing useful information on the emission process.