  We consider a system where a waveguide is coupled to a cavity embedded with a
two-level system (TLS), and study the effects when a two-photon quantum state
is injected into the waveguide. The wave function of two outgoing photons is
exactly solved using the Lehmann-Symanzik-Zimmermann (LSZ) reduction formalism.
Our results explicitly exhibit the photon blockade effects in the strong
atom-cavity coupling regime. The quantum statistical characters of the outgoing
photons, including the photon bunching and anti-bunching behaviors, are also
investigated in both the strong and weak coupling regimes. These results agree
with the observations of recent experiments.
