Rabi-Oscillation Spectroscopy of the Hyperfine Structure of Muonium Atoms

Abstract: As a new method to determine the resonance frequency, Rabi-oscillation spectroscopy has been developed. In contrast to the conventional spectroscopy which draws the resonance curve, Rabi-oscillation spectroscopy fits the time evolution of the Rabi oscillation. By selecting the optimized frequency, it is shown that the precision is twice as good as the conventional spectroscopy with a frequency sweep. Furthermore, the data under different conditions can be treated in a unified manner, allowing more efficient measurements for systems consisting of a limited number of short-lived particles produced by accelerators such as muons. We have developed a fitting function that takes into account the spatial distribution of muonium and the spatial distribution of the microwave intensity to apply the new method to ground-state muonium hyperfine structure measurements at zero field. This was applied to the actual measurement data and the resonance frequencies were determined under various conditions. The result of our analysis gives $\nu_{\rm HFS}=4\ 463\ 301.61 \pm 0.71\ {\rm kHz}$, which is the world's highest precision under zero field conditions.