Extremal photon statistics signal the extremal entanglement

Entanglement and photon statistics are investigated in a cavity QED system with three two-level atoms trapped in a modestly driven cavity with weak dissipation. It is shown that the local maximal steady-state entanglement of any two atoms perfectly corresponds to the strongest photon antibunching point. In particular, the local maximal entanglement of two atoms is also consistent with the strongest photon bunching point. It provides a new angle to understand both photon statistics and entanglement. Our work gives strong support for employing extremal photon statistics to signal the extremal atomic entanglement in this system. (paper)