Long-time correlated quantum dynamics of phonon cooling

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 contributes to phonon cooling detection of the nanomechanical resonator.

Figure 1

Schematic model: (a) a laser-pumped two-level quantum dot with transition frequency ${\omega }_0$ is fixed on a nanomechanical resonator vibrating at frequency $\omega$ and is interacting also with the quantized resonator optical mode of frequency ${\omega }_C$, and (b) correlated cooling dynamics occurs when a laser photon absorption together with a vibrational phonon absorption is accompanied by the emission of a cavity photon.

Figure 2

The steady-state mean value of the photon number $\langle a^{†}a\rangle$ as a function of ${\Delta }_1/\gamma$. Here, ${\gamma }_c/\gamma =0.3$, $g/\gamma =2$, $\lambda /\gamma =4$, $\Omega /\gamma =50$, $\omega /\gamma =50$, $\Delta /\left(2\Omega \right)=0.5$, ${\kappa }_a/\gamma =0.01$, and ${\kappa }_b/\gamma =0.001$. The solid line corresponds to $\overline{n}=10$, the long-dashed line corresponds to $\overline{n}=4$, and the short-dashed line corresponds to $\overline{n}=2$.

Figure 3

The same as in Fig. 2 but for the vibrational phonon mean number $\langle b^{†}b\rangle$.