Phase noise and laser-cooling limits of optomechanical oscillators

The noise from laser phase fluctuation sets a major technical obstacle to cool the nano-mechanical oscillators to the quantum region. We propose a cooling configuration based on the opto-mechanical coupling with two cavity modes to significantly reduce this phase noise by $(2\omega_m/\gamma)^2$ times, where $\omega_m$ is the frequency of the mechanical mode and $\gamma$ is the decay rate of the cavity mode. We also discuss the detection of the phonon number when the mechanical oscillator is cooled near the quantum region and specify the required conditions for this detection.