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The effects of photon bunching and antibunching correspond to the classicaland quantum features of the electromagnetic field, respectively. No directevidence suggests whether these effects can be potentially related to quantumentanglement. Here we design a cavity quantum electrodynamics model with twoatoms trapped in to demonstrate the connections between the steady-state photonstatistics and the two-atom entanglement . It is found that within the weakdissipations and to some good approximation, the local maximal two-atomentanglements perfectly correspond to not only the quantum feature of theelectromagnetic field---the optimal photon antibunching, but also the classicalfeature---the optimal photon bunching. We also analyze the influence of strongdissipations and pure dephasing. An intuitive physical understanding is alsogiven finally.

Photon statistics on the extreme entanglement