Excitation of spin flips in geonium at small cyclotron quantum numbers: Transition rates and frequency shifts

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Abstract
The most accurate measurements of the electron g factor involve the observation of spin flips of a single electron trapped in a magnetic field and having a cyclotron quantum number very near the ground state. This paper examines the excitation of these flips, finding the following results: The spin-flip rate and the observed shape of the anomaly resonance can be substantially altered when the quantum nature of the cyclotron motion is taken into account. Excitation by rf magnetic field gradient, while in principle the preferable method, may not be feasible at liquid-helium temperatures due to slow transition rates. Excitation by driven oscillations in a static magnetic field gradient is accompanied by several frequency shifts which have not been very important to date but which are likely to significantly affect future measurements.