Shelving-style QND phonon-number detection in quantum optomechanics

We propose a new method for optomechanical quantum non-demolition (QND) detection of phonon number, based on a "shelving" style measurement. The scheme uses a two-mode optomechanical system where the frequency splitting of the two photonic modes is near-resonant with the mechanical frequency. The combination of a strong optical drive and the underlying nonlinear optomechanical interaction gives rise to spin-like dynamics which facilitate the measurement. This approach allows phonon number measurement to be accomplished parametrically faster than in other schemes which are restricted to weak driving. The ultimate power of the scheme is controlled by the size of the single photon optomechanical cooperativity.