Diese Arbeit beschäftigt sich mit der theoretischen Beschreibung eines Hybridsystems eines ultrakalten neutralen Atoms und eines einzelnen Ions. Diese Hybrid-Atom-Ion-Systeme verbinden die wichtigsten Vorteile von ultrakalten neutralen Atomen und Ionen. Neutrale Atome sind leicht skalierbar vor allem und können in großen Stückzahlen vorbereitet werden, wahrend gefangene Ionen über längere Zeiten gelagert werden können und leicht kontrollierbar sind. Einige der vorgeschlagenen Aussichten der hybriden Quantensysteme umfassen die sympathische Kühlung von eingefangenen Ionen, die ultrakalte Chemie, das Quantum Informationsverarbeitung, und Atom-Ionen-Quantensimulatoren. Diese Anwendungen erfordern eine äußerst präzise Steuerung und damit eine sehr genaue theoretische Modellierung. Eine neue Methode, die eine vollständige sechsdimensionale Behandlung von zwei Partikeln ermöglicht In räumlich getrennten dreidimensionalen Fangpotentialen wurde entwickelt. Indem man die raumliche Verschiebung zwischen den Einfangpotentialen erlaubt, ist es möglich, die gesteuerte Bewegung eines einzelnen Ions durch ein optisches Gitterpotential zu beschreiben, das mit neutralen Atomen gefüllt ist. Die Wechselwirkung zwischen dem neutralen Atom und dem geladenen Ion wird durch eine realistische Born-Oppenheimer Potentialkurve beschrieben. Eines der hier diskutierten Hybridsysteme ist 7Li2+ Isotop, das mit der neu entwickelten Methode untersucht wird, dabei wurden vermiedene Kreuzungen im Energiespektrum zwischen molekularen Zuständen und den Schwingungszuständen des Fallenpotentials als Funktion des Abstandes zwischen den beide Fallen beobachtet. Diese vermiedenen Kreuzungen bestatigen die bereits vorhergesagten falleninduzierten Resonanzen, die mithilfe der Quantendefekttheorie bestimmt wurden. Ebenfalls werden die erst kürzlich entdeckten inelastischen falleninduzierten Resonanzen in ultrakalten Atomen auch in den Atom-Ion Systemen beobachtet. / This thesis deals with the theoretical description of a hybrid system of an ultracold neutral atom and a single ion. These hybrid atom-ion systems combine the key advantages of ultracold neutral atoms and ions. In particular, neutral atoms are easily scalable and can be prepared in large numbers, while trapped ions can be stored for much longer times and are easy to control. Some of the proposed prospects of the hybrid quantum systems include sympathetic cooling of trapped ions, ultracold chemistry, quantum information processing, and atom-ion quantum simulators. These applications require extremely precise control and thus very accurate theoretical modeling. A new method that allows for a full 6-dimensional treatment of two particles in spatially separated 3-dimensional trapping potentials was developed. By allowing for the spatial displacement between the trapping potentials, it is possible to describe the controlled motion of a single ion through an optical-lattice potential filled with neutral atoms. The interaction between the neutral atom and the ion is modeled using realistic Born-Oppenheimer potential curves from ab initio quantum chemistry calculations. An application of the developed approach to the hybrid atom-ion system reveals avoided crossings between the molecular bound states and the unbound trap states as a function of the separation between the two traps. These avoided crossings correspond to trap-induced resonances. This finding confirms the trap-induced resonances predicted earlier based on quantum-defect-theory calculations. Also, the recently found inelastic confinement-induced resonances in ultracold neutral atoms are demonstrated to be present in atom-ion systems. These resonances arise due to the coupling between the center-of-mass and relative motions. The inelastic confinement-induced resonances could be used in coherent molecular ion formation and in the determination of atom-ion scattering properties like the scattering lengths.

This thesis describes experimental work towards developing a trapped ion quantum information processor. An existing ion trap apparatus was capable of trapping and laser-cooling single ions or small ion strings of 40 Ca+, and had been used for studies of quantum jumps and natural lifetime measurements in Ca. This thesis describes improvements in this apparatus, which have allowed the stability and the flexibility of experimental control of the ions to be greatly increased. This enabled experiments to read out the spin state of a single trapped ion, and to load ions with isotope selectivity through photoionization. The optical systems were improved by installation of new lasers, optical reference cavities, and a system of acousto-optic modulators for laser intensity switching and frequency control. The photon counting for fluorescence detection was improved, and a new photon time-of-arrival correlation circuit developed. This has permitted rapid and more sensitive detection of micromotion, and hence cancellation of stray fields in the trap. A study of resonant circuits in the low RF, high voltage (10 MHz, 1 kV) regime was carried out with a view to developing a new RF supply for the Paul trap with reduced noise and increased power. A new supply based on a helical resonator was built and used to trap ions. This technique has reduced noise and will permit higher secular frequencies to be attained in the future. A magnetic field B in the ion trap is used to define a quantization axis, and in one series of experiments was required to be of order 100 G to provide a substantial Zeeman splitting. A set of magnetic field coils to control the size and direction of B is described. The design of these posed some problems owing to an unforseen issue with the vacuum chamber. In short, it is magnetizable and acts to first approximation like a magnetic shield. The field coils had to be sufficiently substantial to produce the desired field at the ion even in the presence of this shielding effect, and dark resonance (and other) spectra with Zeeman splitting were obtained to calibrate the field using the ion as a probe. Finally, the thesis describes the successful loading of the ion trap by laser photoionization from a weak atomic beam. This involved two new lasers at 423 nm and 389 nm. Saturated absorption spectroscopy of neutral calcium is first described, then transverse excitation of an atomic beam in our vacuum chamber is used to identify all the main isotopes of calcium and confirm their abundances in our source (a heated sample of natural calcium). Finally, photoionization is used to load the trap. This has three advantages over electron-impact ionization. By avoiding an electron gun, we avoid charging of insulating patches and subsequent electric field drift as they discharge; the flux in the atomic beam and hence calcium (and other) deposits on the electrodes can be greatly reduced; and most importantly, the photoionization is isotope selective. Evidence is presented which suggests that even with an non-enriched source, the rare isotope 43 Ca can be loaded with reasonable efficiency. This isotope is advantageous for quantum information experiments for several reasons, but chiefly because its ground state hyperfine structure can act as a stable qubit.