  We investigate theoretically the model of a cavity-quantum-electrodynamics
(QED) system that consists of two two-level atoms coupled to a single-mode
cavity in the weak coupling regime, where the system is driven by quantum
light. The dynamics behavior of the entire system is tackled in the framework
of a cascaded quantum system. We find that the two-photon blockade with
two-photon bunching and three-photon antibunching can be obtained even when the
strong system dissipation is included. This result shows that our work has
potential for realizing entangled photon pairs in a weakly coupled cavity.
Moreover, we also analyze the photon statistics of the system in the case of
out-of-resonance coupling between cavity and two nonidentical atoms. Here, an
unconventional photon blockade effect with the suppression of two-photon
correlation and enhancement of three-photon correlation can be realized, which
shows many quantum statistical characteristics of cavity QED system in weak
coupling.
