Strong coupling between single photons in semiconductor microcavities

We discuss the observability of strong coupling between single photons in semiconductor microcavities coupled by a chi((2)) nonlinearity. We present two schemes and analyze the feasibility of their practical implementation in three systems: photonic crystal defects, micropillars, and microdisks, fabricated out of GaAs. We show that, if a weak coherent state is used to enhance the chi((2)) interaction, the strong coupling regime between two modes at different frequencies occupied by a single photon is within reach of current technology. The unstimulated strong coupling of a single photon and a photon pair is very challenging and will require an improvement in mirocavity quality factors of 2-4 orders of magnitude to be observable.