Improving the cooling performance of a mechanical resonator with two-level-system defects

We study the cooling performance of a realistic mechanical resonator containing defects. The normal cooling method through an optomechanical system does not work efficiently due to those defects. We show that, by employing periodical ${\sigma }_z$ pulses, we can eliminate the interaction between defects and their surrounding heat baths up to the first order of time. Compared with the cooling performance of the no ${\sigma }_z$ pulses case, much better cooling results are obtained. Moreover, this pulse sequence has the ability to improve the cooling performance of the resonator with different defect energy gaps and different defect damping rates.

Figure 1

Residual phonon number $\left(\langle n_{\mathrm{osc}}\rangle \right)$ vs different numbers of ${\sigma }_z$ pulses. Blue solid, $N=0$; red dashed, $N=9$; green dotted, $N=19$; black dotted-dashed, $N=49$; purple circle dot, $N=99$ (a) Master equation based on polariton doublets. (b) Simple approach. Parameters are ${\omega }_m=200$ MHz, ${\omega }_z/{\omega }_m=0.9,\kappa /{\omega }_m=0.15,{\gamma }_m/{\omega }_m={10}^{-6},{\gamma }_{\tau }/{\omega }_m=2.5\times {10}^{-4},g/{\omega }_m=0.05,\lambda /{\omega }_m=0.05,{\Delta }_L/{\omega }_m=-1$, and $T=0.1$ K.

Figure 2

Residual phonon number $\left(\langle n_{\mathrm{osc}}\rangle \right)$ vs different numbers of ${\sigma }_z$ pulses $(N$=0, 99, and 199). Parameters are ${\omega }_m=200$ MHz, $\kappa /{\omega }_m=0.15,{\gamma }_m/{\omega }_m={10}^{-6},{\gamma }_{\tau }/{\omega }_m=2.5\times {10}^{-4},g/{\omega }_m=0.05,\lambda /{\omega }_m=0.05,{\Delta }_L/{\omega }_m=-1$, and $T=0.1$ K. From top to bottom, ${\omega }_z/{\omega }_m$ is 0.6, 0.8, and 0.95.

Figure 3

Residual phonon number $\left(\langle n_{\mathrm{osc}}\rangle \right)$ vs ${\gamma }_{\tau }$. Different numbers of ${\sigma }_z$ pulses $(N$ = 0 and 99) are applied. The value of $\langle n_{\mathrm{osc}}\rangle$ is chosen at time $t=200{\omega }_m^{-1}$, where the residual phonon number has been stable already. Parameters are ${\omega }_m=200$ MHz, $\kappa /{\omega }_m=0.15,{\gamma }_m/{\omega }_m={10}^{-6},g/{\omega }_m=0.05,\lambda /{\omega }_m=0.05,{\Delta }_L/{\omega }_m=-1$, and $T=0.1$ K.