Abstract:
A scheme is proposed for measuring the Wigner characteristic function of a cavity field. In the scheme an atom is sent through a slightly detuned cavity and driven by a strong resonant classical field. Then the population of the atom in the ground state directly yields the Wigner characteristic function of the cavity field.

Abstract:
We propose a scheme for implementing nongeometric phase gates fbr two trapped ions via adiabatic passage of dark states. During the operation, the vibrational mode is only virtually excited, thus the scheme is insensitive to heating. Furthermore, the spontaneous emission is suppressed since the ions are always in the electronic ground states. The scheme is robust against small fluctuations of parameters, and the conditional phase is tunable.

Abstract:
A scheme is presented for the cavities. In the scheme, each a coherent state with a small generation of entangled states for two atomic ensembles trapped in two distant atomic sample is initially in a Bloch state and the cavity mode is initially in amplitude. The dispersive dependent phase shift on the atomic system. The detection atomic samples collapse to an entangled Bloch state. atom-cavity interaction leads to a photon-number of a photon leaking from the cavities makes the two

Abstract:
We propose a scheme to prepare Fock states for the vibrational motion of a trapped ion. Unlike previous schemes, the present scheme works in the mediate-excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Thus, the required time is greatly shortened, which is important in view of decoherence.

Abstract:
We propose a quantum nondemolition measurement of the photon-number distribution for a weak cavity field with no more than two photons. The scheme is based on the resonant interaction of atoms with the cavity field, and thus the required interaction time is much shorter than that using dispersive interaction. This is important in view of decoherence. Our scheme can also be used to generate even and odd coherent states for a weak cavity field with resonant atoms.

Abstract:
Two schemes for the implementation of the two-qubit Grover search algorithm in the ion trap system are proposed. These schemes might be experimentally realizable with presently available techniques. The experimental implementation of the schemes would be an important step toward more complex quantum computation in the ion trap system.

Abstract:
A scheme is proposed for the generation of W entangled states for several atoms trapped in a cavity by detecting photon decay. The scheme works in the regime, where the cavity decay rate is larger than the atom-cavity coupling strength. Thus, the requirement for the quality factor of the cavity is greatly loosened, which is of importance in view of experiment. Another advantage of this scheme is that the atoms are always populated in two ground states coupled by Raman transitions, thus the spontaneous emission can also be suppressed.

Abstract:
We propose a scheme to observe the decoherence of a mesoscopic superposition of two coherent states in the motion of a trapped ion. In the scheme the ion is excited by two perpendicular lasers tuned to the ion transition. The decoherence is revealed by the decrease of the correlation between two successive measurements of the internal state of the ion after relevant laser－ion interaction.