Measurements with a one-electron quantum cyclotron determine the electron magnetic moment, given by $g/2=1.001\hspace{0.5em}159\hspace{0.5em}652\hspace{0.5em}180\hspace{0.5em}73(28)[0.28\mathrm{ppt}]$, and the fine structure constant, $\alpha {}^{-1}=137.035\hspace{0.5em}999\hspace{0.5em}084(51)[0.37\mathrm{ppb}]$. 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.

• Received 3 September 2010

DOI:https://doi.org/10.1103/PhysRevA.83.052122

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