Generation of a four-atom entangled cluster state in cavity QED

We propose a method of generating a four-atom entangled cluster state by considering two kinds of the atoms–cavity field interaction in cavity QED. During the preparation the cavity is only virtually excited no quantum information will be transferred from the atoms to the cavity and thus the scheme is insensitive to the cavity field states and cavity decay. The scheme can also be used to generate the cluster state for the trapped ions.