Hybrid cavity mechanics with doped systems

We investigate the dynamics of a mechanical resonator in which is embedded an ensemble of two-level systems interacting with an optical cavity field. We show that this hybrid approach to optomechanics allows for enhanced effective interactions between the mechanics and the cavity field, leading, for instance, to ground-state cooling of the mechanics, even in regimes, like the unresolved sideband regime, in which standard radiation pressure cooling would be inefficient.

Figure 1

Schematics–(a) Hybrid optomechanical setup consisting of a vibrating membrane inside an optical cavity and doped with two-level quantum emitters (TLS) which interact with one cavity field mode. The doping pattern can be tailored to fit vibrational patterns of the membrane and/or the transverse intensity profile of the cavity field. (b) Cavity field susceptibility as a function of frequency, illustrating the bad cavity and good dopant regime in which the cavity linewidth $\kappa$ is much larger than the dopant linewidth $\gamma$. The relevant frequencies and detunings are shown (see text for details).

Figure 2

Final occupation number $n_f$ as a function of atomic detuning ${\Delta }_a$ (blue dots): in (a) the bad $(\kappa /{\omega }_m=10,g/{\omega }_m={10}^{-2})$ and (b) intermediate $(\kappa /{\omega }_m=1,g/{\omega }_m=0.1)$ cavity regimes. Parameters: $\gamma /{\omega }_m={10}^{-2},{\Delta }_c/{\omega }_m=1,{\gamma }_m/{\omega }_m={10}^{-5},G/{\omega }_m={10}^{-2}$, and $n_m={10}^3$. The corresponding standard radiation pressure optomechanical (OM) result (in which case the $x$ axis represents ${\Delta }_c/{\omega }_m$) is shown by the red circles for comparison. Only points corresponding to stable working points are shown.

Figure 3

Final occupation number $n_f$ as a function of cavity detuning ${\Delta }_c$ for a resonant dopant $\left({\Delta }_a=0\right)$. (a) Good cavity limit $\left(\kappa /{\omega }_m=0.1\right)$–Red circles: Standard OM. Blue dots: doped OM with a “weakly” coupled dopant $g/{\omega }_m=0.1$. Yellow squares: doped OM with a “strongly” coupled dopant $g/{\omega }_m=3$. (b) Bad cavity limit $\left(\kappa /{\omega }_m=10\right)$–Red circles: Standard OM. Blue dots: doped OM with a “weakly” coupled dopant $g/{\omega }_m=0.72$. Yellow squares: doped OM with a “strongly” coupled dopant $g/{\omega }_m=4$. Other parameters: ${\gamma }_m/{\omega }_m={10}^{-5},G/{\omega }_m={10}^{-2},\gamma /{\omega }_m={10}^{-2}$, and $n_m={10}^3$. Only points corresponding to stable working points are shown.

Figure 4

Final occupation number $n_f$ as a function of polariton detuning $\Delta$, for various coupling strengths: (a) $g/{\omega }_m=6$, (b) $g/{\omega }_m=0.8$, and (c) $g/{\omega }_m=0.2$. Parameters: $\kappa /{\omega }_m=0.1,\gamma /{\omega }_m={10}^{-2},{\gamma }_m/{\omega }_m={10}^{-5},n_m={10}^3,G/{\omega }_m={10}^{-2}$. The inset in (b) shows the variation of the optomechanical damping rate $\Gamma$, normalized to ${\gamma }_m$.