Two-photon nonlinearity in general cavity QED systems

We have investigated the two-photon nonlinearity at general cavity QED systems, which covers both weak and strong coupling regimes and includes radiative loss from the atom. The one- and two-photon propagators are obtained in analytic forms. By surveying both coupling regimes, we have revealed the conditions on the photonic wavepacket for yielding large nonlinearity depending on the cavity Q-value. We have also discussed the effect of radiative loss on the nonlinearity.