Generation of Atomic Cluster State via Adiabatic Evolution of Dark Eigenstates

We propose a scheme to generate atomic cluster states of arbitraryconfiguration in the cavity quantum electrodynamics (QED) system. Theprocess is achieved via adiabatic evolution of dark states, which onlyrequires 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.