Cavity control of a single-electron quantum cyclotron: Measuring the electron magnetic moment

Measurements with a one-electron quantum cyclotron determine the electron magnetic moment, given by g/2=1.001 159 652 180 73(28)[0.28ppt], and the fine structure constant, α^-1=137.035 999 084(51)[0.37ppb]. Announcements of these measurements [Phys. Rev. Lett. 97, 030801 (2006); 100, 120801 (2008)] are supplemented here with a more complete description of the one-electron quantum cyclotron and the measurement methods, a discussion of the cavity control of the radiation field, a summary of the analysis of the measurements, and a fuller discussion of the uncertainties.