Preparation of four-mode square cluster states in the optical coupled cavity array

We propose a scheme for preparation of four-mode square cluster states. We consider a chain of four single-mode cavities coupled with short fiber, each contains an atomic ensemble. We will show that a four-mode square cluster state can be deterministically prepared by driving the atomic ensembles with suitable laser pulse. The procedure can be extended to the case of multimode and other shape cluster states by choosing right frequencies and phases. (authors)