QUANTUM INFORMATION PROCESSING (QIP) is a promising interdisciplinary field of Forschung with significant impact on future fundamental as well as applied Forschung. In our experiments electrodynamically trapped ions that can be individually addressed serve as elementary switching units (qubits) for quantum logic operations. While studying questions related to the experimental implementation of a quantum computer, new insight is gained also into fundamental aspects of quantum theory, for instance, regarding entangled states, decoherence, and the problem of measurement in quantum mechanics. QIP with individual trapped ions is scalable in principle, while nuclear magnetic resonance (NMR) with macroscopic ensembles (which has already been used elsewhere to implement complete quantum algorithms) will probably remain restricted to the manipulation of relatively few qubits. We have proposed concepts for spin resonance with trapped ions where methods and techniques that have been successfully used in NMR experiments are applied to individual trapped ions. The use of designed ion "molecules" in a trap will at the same time help to overcome difficulties of the two most successful experimental implementations of QIP. In addition, such a system may serve for the investigation of new physics related, for example, to Solid State Physics. The concept of a state is a central ingredient of quantum theory, and the estimation of the state of a quantum system is of fundamental and practical importance. We have implemented a self-learning strategy for state estimation of the hyperfine qubit of Yb+. In this context, arbitrary single qubit gates have been demonstrated with high precision and very long coherence times. We have also implemented and characterized prototypes of different quantum channels. This will allow for the systematic investigation of the impact of imperfections and decoherence on QIP, for instance, on the performance of error correcting codes.

COHERENT OPTICAL EXCITATION of the electric quadrupole transition S1/2 - D5/2 in Ba+ as well as in Yb+ has been demonstrated. For conditional quantum dynamics with several ions cooling of the common vibrational motion of the ions to its ground state is advantageous, but not always necessary. We have investigated laser cooling of two Ba+ ions experimentally and theoretically and have demonstrated efficient and robust Raman cooling with undemanding laser sources. Cooling of all vibrational modes - not only of the one used as a "bus-qubit" - is necessary for QIP. For this purpose we have developed a new scheme.

QUANTUM ZENO PARADOX. In connection with the interpretation of quantum mechanics E. Schrödinger wrote in 1952: "... we never experiment with just one electron or atom ... In thought-experiments we sometimes assume that we do; this invariably entails ridiculous consequences ..." Taking advantage of modern trapping and cooling methods, repeated measurements on individual quantum systems have become possible, revealing the micro state of a system (as opposed to the ensemble average). In particular, the influence of a measurement on the time development of an individual quantum system can be studied. We have experimentally shown that the correlation between measurement apparatus and quantum system influences the dynamics of the quantum system, even without a direct (in a classical sense) interaction between the two. The information gained in a negative result measurement determines the evolution of the quantum system.

THERMALLY ACTIVATED PROCESSES. Surmounting of a potential barrier assisted by thermal fluctuations is ubiquitous in physics, chemistry, and biology. We carry out experiments using a microscopic prototype system to investigate questions related to reaction rate theory that describes these phenomena: the rate characterising the exchange of the positions of two trapped Ba+ ions is monitored as a function of the particles' temperature. This change of position may take place by surmounting a potential barrier separating two local minima. The potential determining the ions' motion as well as the temperature (determined by laser cooling) are quantitatively well characterised and allow for a direct comparison with theoretical predictions.