n-1}$ gives the cooling rate of Eq.\[gamma\]. However, with the exact expressions we can show that the equilibrium mean phonon number is

$$\langle n
\rangle_{PT}=\frac{S_1(\omega_M)+S_2(\omega_M)}{
S_1(-\omega_M)+S_2(-\omega_M)-S_1(\omega_M)-S_2(\omega_M)}.
\label{neq}$$

![(Colour online) Maps of cooling rates calculated from Eq. \[gamma\] for parameters $R=1.0$ and $R=0.5$. Blue corresponds to cooling, yellow/white to heating. The white lines indicate the locus of the single field resonances (where $-\Delta_{1}^x=\omega_M$ or where $-\Delta_{2}^x=\omega_M$). The detunings are given in units of $A$ and are dimensionless. For $R=1$ it is clear that there is a deep, maximum cooling region at a double resonance where the two white lines intersect and both optical fields cool simultaneously. It is also evident that there is a strong cooling resonance for $+\Delta_{1,2\pm}^x=\omega_M$. For $R=0.5$, three cooling resonances $-\Delta_{1\pm}^x=\omega_M$, $-\Delta_{2\pm}^x=\omega_M$ and $+\Delta_{1}^x=\omega_M$ merge to give a very broad strong-cooling [*region*]{}, quite insensitive to detuning $\Delta_2$ over a range of over 1MHz. Here $A=\kappa/2= 0.3$MHz and the input power into mode 1 corresponds to 2mW.[]{data-label="Cool"}](Cool.eps){height="3.3in"}

In Fig. \[Cool\] we show colour maps comparing the cooling and minimum phonon numbers for both $R=0.5$ and $R=1$ respectively. The cooling behaviour was investigated previously in [@Opto1]. In this case, for each fixed detuning $\Delta_1$ there are up to three 