@PHDTHESIS{,
  author = {Schneider, Christian},
  title = {Towards Scaling Experimental Quantum Simulations with Ions},
  school = {Albert-Ludwigs-Universit\"{a}t Freiburg},
  year = {2012},
  type = {Dissertation},
  month = {jan},
  abstract = {Quantum simulations with trapped ions are an emerging field with great potential for future applications. However, up to now, experiments are restricted to less than ten ions arranged in a linear chain. In this thesis two approaches for scaling quantum simulations with trapped ions are presented and experimentally investigated: One approach aims at radio-frequency (RF) surface electrode traps with optimized electrode shapes providing a two-dimensional micro-trap array. A different approach is based on optical trapping of ions and the first demonstration of an optical confinement of a single ion is presented. First, the approach based on RF surface electrode traps is treated. A theoretical derivation of the toolbox available for quantum simulations is presented and extended to be applicable to more-dimensional arrays of ions. The results are discussed in the context of geometric phase gates and proof-of-principle experiments on the simulation of the quantum Ising Hamiltonian. As a first step towards a two-dimensional array of ions, a basic setup is presented and its operability is demonstrated with a linear surface electrode trap. The trapping results are discussed with regard to future surface electrode traps potentially allowing for two-dimensional arrays of ions. Finally, an outlook on a surface electrode trap with three trapping zones arranged in a triangle is given. This trap has been developed in a collaboration of Roman Schmied (MPQ, University of Basel), the group of Dietrich Leibfried (National Institute of Standards and Technology), Sandia National Laboratories, and us. It is currently fabricated at Sandia National Laboratories and will replace the linear trap in our setup. Second, optically trapped ions are addressed as an alternative approach. Our experiment demonstrates optical trapping of an ion in a single-beam dipole trap superimposed by a static electric potential. The experimental procedures and peculiarities are described in detail. In particular, the static electric potential is of importance, because it can easily prevent successful optical trapping, if its configuration is not chosen carefully. Afterwards, the dipole trap experiments are analysed with different analytic models. According to these models the experimental results agree with recoil heating as the relevant heating effect. To confirm our conclusions, a Monte Carlo simulation has been developed. It reveals a large impact of the static electric potential on the dipole trap experiments in general. While it supports the results of the analytic models for the parameters used in the experiments, the analytic models are no longer valid for significantly different parameters. Finally, technical improvements for future realizations of experiments with optically trapped ions are proposed and possible applications of optical ion traps in quantum simulations and ultracold collisions are presented.}
}