Generation of atomic Greenberger-Horne-Zeilinger states and cluster states through cavity-assisted interaction

This paper proposes a scalable scheme to generate $n$-atom GHZ states and cluster states by using the basic building block, i.e., a weak coherent optical pulse $\left\vert \alpha\right\rangle $ being reflected successively from a single-atom cavity. In the schemes, coherent state of light is used instead of single photon source, homodyne measurement on coherent light is done instead of single photon detection, and no need for individually addressing keeps the schemes easy to implement from the experimental point of view. The successful probabilities of our protocols approach unity in the ideal case.