Effects of laser linewidth on the back-action cooling of optomechanical resonators

The effects of laser linewidth on the final temperature of a dynamical back-action cooled mirror in a Fabry-P\'{e}rot resonator coupled to an external phonon bath are examined. Classical Monte-Carlo techniques are used to model the colored laser noise with correlation function $<\phi $(t) $\phi $(t')$>$=exp(-$\vert $t-t'$\vert $/$\tau )$ and mean $<\phi $(t)$>$=0. We present results of an analytical and numerical analysis that quantifies the final temperature of the mirror as a function of laser linewidth for experimentally realizable parameters.