Measurement of light shift ratios with a single trapped barium-138(+) ion, and prospects for a parity violation experiment

This thesis describes the development and implementation of a new scheme for observing RF transitions between spin states in a single, trapped Ba + ion. We use optical pumping to place the ion in a selected magnetic sublevel of either the 6S_1/2 ground state or the 5D_3/2 metastable state. The ion is exposed to an RF field, and a spin-sensitive version of the electron shelving method detects the resulting spin state. The precision of this kind of RF spectroscopy is limited only by magnetic-field noise, and with the current apparatus, line widths of about 10 Hz can be achieved.; This scheme is applied to a precision measurement of light shifts (or AC Stark shifts) in Ba+. Zeeman energies are altered by a circularly-polarized, off resonant laser, and the resulting resonance shifts are measured simultaneously in both the 6S_1/2 and 5D_3/2 state. When taking the ratio, light intensity and polarization drop out, and we can determine the ratio of P-D to S-P matrix elements with a precision of <0.5%, with the evaluation of some systematic effects still pending. Motivation for this work comes from the fact that knowledge of P-D matrix elements is essential for precisely calculating parity-violating transition amplitudes.; A measurement of the latter with a single ion is the ultimate experimental goal of this project. Such an experiment could enable comparison with Standard Model predictions at the sub-percent level and provide an independent check to a recent parity violation experiment in Cs. The observable in this measurement is a spin-dependent light shift, induced by a parity-violating E1 transition between the S and D states in either Ba+ or Ra+. The experiment and its systematic problems are analyzed in this thesis. We also propose an alternative scheme using odd isotopes and the E2-forbidden F = 0 ↔ F = 1 transition, along with an initial investigation of its systematic effects.