Efficient engineering of multiatom entanglement through single-photon detections

We propose an efficient scheme to engineer multiatom entanglement by detecting cavity decay through single-photon detectors. In the special case of two atoms, this scheme is much more efficient than previous probabilistic schemes, and insensitive to randomness in the atom's position. More generally, the scheme can be used to prepare arbitrary superpositions of multiatom Dicke states without the requirements of high-efficiency detection and separate addressing of different atoms.