  We investigate theoretically two-photon processes in a microcavity containing
one quantum dot in the strong coupling regime. The cavity mode can be tuned to
resonantly drive the two-photon transition between the ground and the biexciton
states, while the exciton states are far-off resonance due to the biexciton
binding energy. We study the steady state of the quantum dot and cavity field
in presence of a continuous incoherent pumping. We identify the regime where
the system acts as two-photon emitter and discuss the feasibility and
performance of realistic single quantum dot devices for two-photon lasing.
