  Optomechanics experiments are rapidly approaching the regime where the
radiation pressure of a single photon displaces the mechanical oscillator by
more than its zero-point uncertainty. We show that in this limit the power
spectrum has multiple sidebands and that the cavity response has several
resonances in the resolved-sideband limit. Using master-equation simulations,
we also study the crossover from the weak-coupling many-photon to the
single-photon strong-coupling regime. Finally, we find non-Gaussian
steady-states of the mechanical oscillator when multi-photon transitions are
resonant. Our study provides the tools to detect and take advantage of this
novel regime of optomechanics.
