Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system

We propose to cool a mechanical resonator close to its ground state via an electromagnetically-induced-transparency (EIT)-like cooling mechanism in a double-cavity optomechanical system, where an additional cavity couples to the original one in the standard optomechanical system. By choosing optimal parameters such that the cooling process of the mechanical resonator corresponds to the maximum value of the optical fluctuation spectrum and the heating process to the minimum one, the mechanical resonator can be cooled with the final mean phonon number less than that at the absence of the additional cavity. And we show the mechanical resonator may be cooled close to its ground state via such an EIT-like cooling mechanism even when the original resolved sideband condition is not fulfilled.

Figure 1

The schematic of the double-cavity optomechanical system with the possible realization in the system based on (a) Fabry-Pérot cavities and (b) whispering-gallery cavities.

Figure 2

The optical fluctuation spectrum $S_{FF}\left(\omega \right)$ (in arbitrary units) as a function of the frequency $\omega$ with four different optical coupling coefficients $J$. The effective detuning of the first cavity mode ${\Delta }_1={\omega }_m$ and its decay rate is ${\kappa }_1=3{\omega }_m$, while the detuning of the second cavity mode is ${\Delta }_2=-{\omega }_m$ and the corresponding decay rate is ${\kappa }_2=0.1{\omega }_m$.

Figure 3

The optical fluctuation spectrum $S_{FF}\left(\omega \right)$ (in arbitrary units) with four different decay rates ${\kappa }_2$ at the given optical effective detuning ${\Delta }_1=-3{\omega }_m$ and optimal detuning ${\Delta }_2=-{\omega }_m$ and corresponding optimal optical coupling coefficient $J=2\sqrt{2}{\omega }_m$. Here ${\kappa }_1=3{\omega }_m$.

Figure 4

The cooling rate ${\gamma }_c$ as a function of the optical coupling coefficient $J$ with different decay rates ${\kappa }_2$. Here we fix $g=0.2{\omega }_m$, and take ${\Delta }_2=-{\omega }_m,{\kappa }_1=3{\omega }_m$, and the optimal detuning ${\Delta }_1$ satisfying Eq. (16).

Figure 5

The mean phonon number $n_f$ as a function of the dimensionless optimal optical coupling coefficient $J$ with different decay rates ${\kappa }_2$. For the parameters, see the text.