Radio frequency spectroscopy with a trapped Ba⁺ ion: recent progress and prospects for measuring parity violation

We have employed the method of shelving to measure Zeeman resonances of a single trapped Ba⁺ ion in low magnetic fields, and have observed radio frequency transitions with linewidths of 5 Hz, limited by magnetic-field noise. We have also observed the shift in the Zeeman frequency when the ion is illuminated by off-resonant light. A simultaneous measurement of such light shifts in two atomic states of Ba⁺ will permit a precise determination of the ratio of transition matrix elements. Furthermore, using this method with an ion in a standing lightwave, a proposed parity nonconservation (PNC) measurement with Ba⁺ or Ra⁺ could be realized. In this paper we review methods and the status of these experiments and discuss the remaining challenges of the PNC experiment.