Figure 1

(a) Noise spectrum of the photon number in a driven cavity as a function of frequency when the drive is detuned from the resonance by $\Delta =+5\kappa$ (leading to heating: dashed line) and $\Delta =-5\kappa$ (cooling: solid line). (b) Effective noise temperature $T_{\mathrm{eff}}$ as a function of the detuning, see Eq. (5), for a cantilever frequency matching the detuning: ${\omega }_M=|\Delta |$. The noise temperature is positive on the left side of the resonance, where optomechanical cooling produces a minimum reachable cantilever phonon number ${\overline{n}}_M^O$ (black line) corresponding to $T_{\mathrm{eff}}$, see Eqs. (5, 7).Reuse & Permissions

Figure 2

The steady-state phonon number ${\overline{n}}_M$ obtained through cavity sideband cooling as a function of detuning, with $\Delta =-{\omega }_M$. Thick lines represent the weak-coupling quantum noise result, Eq. (9), for three different laser powers (expressed via constant ${\overline{n}}_{\max }$, so the actual photon number $\overline{n}$ increases towards smaller ${\omega }_M$). The bath temperature corresponds to ${\overline{n}}_M^T=100$ phonons, and the optomechanical coupling has been fixed to yield a realistic ratio ${\Gamma }_{\mathrm{opt}}(\overline{n}=1,{\omega }_M\to \infty )/{\Gamma }_M=0.1$. The dotted red line shows ${\overline{n}}_M^O=[\kappa /(4{\omega }_M){]}^2$ from Eq. (7). The dashed (dash-dotted) lines show the results of the exact input-output equations, for ${\Gamma }_M/\kappa ={10}^{-4}({10}^{-5})$ and ${\overline{n}}_{\max }={10}^6$. They were obtained by integrating the exact spectrum $S_{cc}(\omega )$, Eq. (13), which is shown in the inset as a density plot, for ${\Gamma }_M/\kappa ={10}^{-4}$ (arrow indicates splitting of resonance; “unstable” regime does not permit $\Delta =-{\omega }_M$). The weak-coupling limit is recovered for ${\Gamma }_M/\kappa \to 0$.Reuse & Permissions