Threshold for formation of atom-photon bound states in a coherent photonic band-gap reservoir

•We model a two-level atom embedded in a coherent photonic band-gap (PBG) reservoir.•The threshold for the formation of atom-photon bound (APB) states was studied.•The embedded position of the atom plays an important role in the threshold while the position of the atomic upper level also affects this threshold.•The direct link between the steady-state entanglement and APB states was investigated.

We study the threshold for the formation of atom-photon bound (APB) states from a two-level atom embedded in a coherent photonic band-gap (PBG) reservoir. It is shown that the embedded position of the atom plays an important role in the threshold. By varying the atomic embedded position, a part of formation range of APB states can be moved from inside to outside the band gap. The direct link between the steady-state entanglement and APB states is also investigated. We show that the values of entanglement between reservoir modes reflect the amount of bounded energy caused by APB states. The feasible experimental systems for verifying the above phenomena are discussed. Our results provide a clear clue on how to form and control APB states in PBG materials.