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

We propose a scheme for controllably implementing an N-qubit phase gate by one step within a ground-state subspace of N three-state atoms trapped in a cavity through a double Raman passage. We can extend our scheme to the realisation of an arbitrary N-qubit phase gate by appropriately adjusting coupling strengths and detunings between atoms and external driving fields. The advantage of this one-step scheme is its robustness against decoherence.