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.
The Raman-coupled interaction between an atom and a single mode of a cavity field is studied.For the cases in which a light field is initially in a coherent state and in a thermal state separately,we have derived the analytic expressions for the time evolutions of atomic population difference W,modulus B of the Bloch vector,and entropy E.We find that the time evolutions of these quantities are periodic with a period of π.The maxima of W and B appear at the scaled interaction time points τ=kπ(k=0,1,2,...).At these time points,E=0,which shows that the atom and the field are not entangled.Between these time points,E=0,which means that the atom and the field are entangled.When the field is initially in a coherent state,near the maxima,the envelope of W is a Gaussian function with a variance of 1/(4n) (n is the mean number of photons).Under the envelope,W oscillates at a frequency of n/π.When the field is initially in a thermal state,near the maxima,W is a Lorentz function with a width of 1/n.
