In this paper, we describe the preparation and detection of ultracold atoms on a microchip with single-atom sensitivity. The detection scheme is based on multi-photon ionization of atoms and the subsequent guiding of the generated ions by ion optics to a channel electron multiplier. We resolve single atoms with a detection efficiency above 60%. The detector is suitable for real-time observations of static and dynamic processes in ultracold quantum gases. Although the ionization is destructive, sampling a small subset of the atomic distribution is sufficient for the determination of the desired information. We take full high-resolution spectra of ultracold atoms by ionizing only 5% of the atoms. Using an additional microwave near 6.8 GHz, the detection scheme becomes energy, position and state selective. This can be used for in situ determination of the energy distribution and temperature of atom clouds inside the trap and applied for future correlation measurements.
Ultracold collisions of ions with neutral atoms in traps are studied. Recently, ultracold atom-ion systems have become available in experimental setups, where their quantum states can be coherently controlled. This control allows for an implementation of quantum information processing, combining the advantages of charged and neutral particles. The state-dependent dynamics that is a necessary ingredient for quantum computation schemes is provided in this case by the short-range interaction forces that depend on the hyperfine states of both particles. In this work, a theoretical description of spin-state-dependent trapped atom-ion collisions is developed in the framework of a multichannel quantum-defect theory and an effective single-channel model is formulated that reduces the complexity of the problem. Based on this description, a two-qubit phase gate between a
135Ba+ ion and a
87Rb atom is simulated using a realistic combination of the singlet and triplet scattering lengths. The gate process is optimized and accelerated with the help of optimal control techniques. The result is a gate fidelity of $1\ensuremath{-}{10}^{\ensuremath{-}3}$ within
350 $\ensuremath{\mu}$s.