One-step implementation of an N-qubit quantum phase gate through a double Raman passage

We propose a scheme for controllably implementing anN-qubit phase gate by one step within a ground-state subspace ofN three-state atoms trapped in a cavity through a double Ramanpassage. We can extend our scheme to the realisation of an arbitraryN-qubit phase gate by appropriately adjusting coupling strengthsand detunings between atoms and external driving fields. Theadvantage of this one-step scheme is its robustness againstdecoherence.