Generation of Atomic Cluster State via Adiabatic Evolution of Dark Eigenstates

We propose a scheme to generate atomic cluster states of arbitrary configuration in the cavity quantum electrodynamics (QED) system. The process is achieved via adiabatic evolution of dark states, which only requires adiabatically increasing or decreasing Rabi frequencies of laser. Thus it allows the robust implementation of entanglement against certain types of errors. Our scheme is relatively decoherence-free in the sense that excited atomic states are never populated and excited cavity photon states can be made negligible in certain conditions.