  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.
