  A two-level system that is coupled to a high-finesse cavity in the Purcell
regime exhibits a giant optical non-linearity due to the saturation of the
two-level system at very low intensities, of the order of one photon per
lifetime. We perform a detailed analysis of this effect, taking into account
the most important practical imperfections. Our conclusion is that an
experimental demonstration of the giant non-linearity should be feasible using
semiconductor micropillar cavities containing a single quantum dot in resonance
with the cavity mode.
