  We analyze the photon statistics of a weakly driven optomechanical system and
discuss the effect of photon blockade under single photon strong coupling
conditions. We present an intuitive interpretation of this effect in terms of
displaced oscillator states and derive analytic expressions for the cavity
excitation spectrum and the two photon correlation function $g^{(2)}(0)$. Our
results predict the appearance of non-classical photon correlations in the
combined strong coupling and sideband resolved regime, and provide a first
detailed understanding of photon-photon interactions in strong coupling
optomechanics.
