Suppression of Stokes scattering and improved optomechanical cooling with squeezed light

We develop a theory of optomechanical cooling with a squeezed input light field. We show that Stokes heating transitions can be \emph{fully} suppressed when the driving field is squeezed below the vacuum noise level at an appropriately selected squeezing phase and for a finite amount of squeezing. The quantum backaction limit to laser cooling can be therefore moved down to zero and the resulting final temperature is then solely determined by the ratio between the thermal phonon number and the optomechanical cooperativity parameter, independently of the actual values of the cavity linewidth and mechanical frequency. Therefore driving with a squeezed input field allows to prepare nanomechanical resonators, even with low resonance frequency, in their quantum ground state with a fidelity very close to one.