Heather L. Partner

We use laser-cooled ion Coulomb crystals in the well-controlled environment of a harmonic radiofrequency ion trap to investigate phase transitions and defect formation. Topological defects in ion Coulomb crystals (kinks) have been recently proposed for studies of nonlinear physics with solitons and as carriers of quantum information. Defects form when a symmetry breaking phase transition is crossed nonadiabatically. For a second order phase transition, the Kibble-Zurek mechanism predicts that the formation of these defects follows a power law scaling in the rate of the transition. We demonstrate a scaling of defect density and describe kink dynamics and stability. We further discuss the implementation of mass defects and electric fields as first steps toward controlled kink preparation and manipulation.

Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, defects will form with densities predicted to follow a power law scaling in the rate of the transition. The importance of this Kibble-Zurek mechanism (KZM) ranges from cosmology to condensed matter [1-4]. In previous tests in homogeneous systems, defect formation was seen, but weak dependence on the transition rate and limited control of external parameters so far prevented tests of KZM scaling. As recently predicted [5-9], in inhomogeneous systems propagation of the critical front enhances the role of causality and steepens scaling of defect density with the transition rate. We use ion Coulomb crystals in a harmonic trap to demonstrate, for the first time, scaling of the number of topological defects with the transition rate - the central prediction of KZM - in a well-controlled environment.

This dissertation reports on the development of a low-power, high-stability miniature atomic frequency standard based on 171Yb+ ions. The ions are buffer-gas cooled and held in a linear quadrupole trap that is integrated into a sealed, getter-pumped vacuum package, and interrogated on the 12.6 GHz hyperfine transition. We hope to achieve a long-term fractional frequency stability of 10^-14 with a miniature clock that consumes only 50 mW of power and occupies a volume of 5 cm^3. I discuss our progress over several years of work on this project. We began by building a conventional tabletop clock to use as a test bed while developing several designs of miniature ion-trap vacuum packages, while also developing techniques for various aspects of the clock operation, including ion loading, laser and magnetic field stabilization, and a low power ion trap drive. The ion traps were modeled using boundary element software to assist with the design and parameter optimization of new trap geometries. We expect a novel trap geometry that uses a material new to ion traps to lead to an exceptionally small ion trap vacuum package in the next phase of the project. To achieve the long-term stability required, we have also considered the sensitivity of the clock frequency to magnetic fields. A study of the motion of the individual ions in a room-temperature cloud in the trap was performed with the purpose of understanding the effect of both spatially varying and constant magnetic fields on the clock resonance and therefore the operation of the clock. These effects were studied experimentally and theoretically for several traps. In summary, this dissertation is a contribution to the design, development, and testing of a 171Yb+ ion cloud frequency standard and related techniques, including analyses of trap geometries and parameters, modeling of the ion motion, and the practical operation of the clock.