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A two-level system that is coupled to a high-finesse cavity in the Purcellregime exhibits a giant optical non-linearity due to the saturation of thetwo-level system at very low intensities, of the order of one photon perlifetime. We perform a detailed analysis of this effect, taking into accountthe most important practical imperfections. Our conclusion is that anexperimental demonstration of the giant non-linearity should be feasible usingsemiconductor micropillar cavities containing a single quantum dot in resonancewith the cavity mode.Comment: 40 pages, 16 figures, accepted in Phys. Rev.

Giant optical nonlinearity induced by a single two-level system interacting with a cavity in the Purcell regime