A two-level system that is coupled to a high-finesse cavity in the Purcell regime exhibits a giant optical nonlinearity 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 nonlinearity is feasible using semiconductor micropillar cavities containing a single quantum dot in resonance with the cavity mode.
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