Methods for, and limitations to, the generation of entangled states of trapped atomic ions are examined. As much as possible, state manipulations are described in terms of quantum logic operations since the conditional dynamics implicit in quantum logic is central to the creation of entanglement. Keeping with current interest, some experimental issues in the proposal for trappedion quantum computation by J. I. Cirac and P. Zoller (University of Innsbruck) are discussed. Several possible decoherence mechanisms are examined and what may be the more important of these are identified. Some potential applications for entangled states of trapped-ions which lie outside the immediate realm of quantum computation are also discussed.

We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound 9 Be 1 ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion.

A "Schrodinger cat"-like state of matter was generated at the single atom level. A trapped 9Be+ ion was laser-cooled to the zero-point energy and then prepared in a superposition of spatially separated coherent harmonic oscillator states. This state was created by application of a sequence of laser pulses, which entangles internal (electronic) and external (motional) states of the ion. The Schrodinger cat superposition was verified by detection of the quantum mechanical interference between the localized wave packets. This mesoscopic system may provide insight into the fuzzy boundary between the classical and quantum worlds by allowing controlled studies of quantum measurement and quantum decoherence.

We demonstrate the operation of a two-bit "controlled-NOT" quantum logic gate, which, in conjunction with simple single-bit operations, forms a universal quantum logic gate for quantum computation. The two quantum bits are stored in the internal and external degrees of freedom of a single trapped atom, which is first laser cooled to the zero-point energy. Decoherence effects are identified for the operation, and the possibility of extending the system to more qubits appears promising.

We have investigated motional heating of laser-cooled 9 Be + ions held in radio-frequency (Paul) traps. We have measured heating rates in a variety of traps with different geometries, electrode materials, and characteristic sizes.The results show that heating is due to electric-field noise from the trap electrodes which exerts a stochastic fluctuating force on the ion. The scaling of the heating rate with trap size is much stronger than that expected from a spatially uniform noise source on the electrodes (such as Johnson noise from external circuits), indicating that a microscopic uncorrelated noise source on the electrodes (such as fluctuating patch-potential fields) is a more likely candidate for the source of heating.