Giant Optical Non-linearity induced by a Single Two-Level System interacting with a Cavity in the Purcell Regime

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.Comment: 40 pages, 16 figures, accepted in Phys. Rev.