state is approached and thus, for the quantum spectrum, the blue sideband vanishes. At higher pressure there is good agreement between the quantum and classical results. Spectra near double resonance for input power $P_1=7$mW, $A=\kappa=3\times
10^5$Hz, $\Delta_1=-1.5$MHz, $\Delta_2=-0.68$MHz, $R=0.5$. Some hybridization between the mechanical mode and optical mode 1 is seen in the characteristic double-peak sideband structure.[]{data-label="Noise"}](Noise.eps){height="3in"}

![For the broad cooling region formed from three overlapping resonances seen in Fig. \[Cool\](b), we show equilibrium phonon numbers obtained from Eqs. (\[PT\]), (\[qnoise\]) and (\[SSC\]) i.e. perturbation theory, the analytical quantum noise formula and semiclassical Langevin equations respectively. Agreement between quantum and semiclassical results is excellent, less so for perturbation theory at low pressures.[]{data-label="Phonon"}](Phonon.eps){height="3in"}

![Triple mode splitting. For $A=\kappa=3$MHz, even at quite high pressures (here 1mBar), mode splitting is seen in the noise spectra of the optical modes. In all the plots, $\Delta_1 = -1.15$MHz is held fixed while $\Delta_2$ is swept from 0 to -1.6MHz (for an input power of 2mW into mode 1, while $R=0.5$). (a) Shows noise spectra for both optical mode 1 and mode 2. Three way hybridization between the mechanical and both optical modes appears clearly (highlighted in the bold blue line). For clarity, some of the 