Generation of entangled states in cavity QED

We propose a scheme to generate four Bell states and a four-atom entangled cluster state in a thermal cavity. The photon-number-dependent parts in the effective Hamiltonian are canceled with the assistance of a strong classical field. The cavity field 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 decay and the thermal field. The scheme can also be used to generate the cluster state for the trapped ions.