Generation of Multiple-Atom Entangled States with Weak Cross-Kerr Nonlinearity

We propose a scheme to generate multiple-atom entangled states in separate cavities. In our scheme, only weak cross-Kerr mediums, homodyne measurement, and some linear elements are employed. With the help of homodyne measurement, four-atom GHZ state can be obtained with high probability and fidelity, and the proposal can be easily scaled to prepare multiple-atom GHZ state. Under ideal conditions, the success probability will not be affected by atomic numbers.