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^-.
This paper proposes a scheme for entanglement swapping based on cavity QED. The two atoms to be entanglementswapped can be separated over long distance. The scheme is a non-post-selection one with the success probability of 1/2.
