g-Factor experiments on hydrogen-like highly charged ions

The magnetic moment of the electron bound in hydrogenlike systems, expressed by the g-factor, differs from that of the free electron by different contributions: The binding to the nucleus leads to relativistic shifts, which are analytically known, bound state quantum-electrodynamic (BSQED) corrections are 3 orders of magnitude smaller, finally nuclear structure and recoil corrections are small for low values of the nuclear charge Z but become comparable in size to the BSQED part for higher Z. Our experiments aim at a determination of these corrections and a comparison to BSQED theory. After a determination of the g factor in hydrogen-like carbon C in 2000 [1], we completed a similar experiment on oxygen O. A single O ion was confined in a Penning trap and its motional frequencies were measured for accurate calibration of the trap's magnetic field. A superimposed Bfield inhomogeneity serves for determination of the electron ́s spin direction [2]. From a measurement of the induced spin flip frequency we derived the g-factor to g=2.000 047 025 4 (15)(44), where the first error is our combined statistical and systematical error, while the second one reflects the uncertainty of the electron ́s mass [3]. The result agrees within the limits of error to a theoretical calculation: gtheo=2.000 047 020 2 (6) [4]. Attempts to reduce the experimental uncertainty have led to a new method of detecting the cyclotron resonance of the stored ion: An additional radio-frequency field at the difference of the axial and cyclotron oscillation frequencies leads to coupling of the two motional modes and a splitting of the ion ́s axial resonance into two components. From a measurement of the split frequency the cyclotron frequency can be determined. Compared to our previous method of direct excitation of the cyclotron mode, now the ion's radial energy is much smaller and reduces the linewidth of the g-factor resonance. Test measurements have demonstrated that this method has the potential for further improvement in accuracy [5]. Preparations have started to extend the experiments to hydrogen-like ions with larger values of Z, particularly for Ca. Extension to heavier masses, however, is limited by our method of detecting induced electron spin flips. It relies on the observation of small frequency differences in the ion ́s axial oscillation. For Ca it would require detection of 0.2 Hz frequency changes in a total oscillation frequency of 370 kHz. This is below the present limit of sensitivity. Therefore a new method has been developed which determines phase differences between the axial oscillation frequencies [6]. The present limit of sensitivity corresponds to a frequency difference of 0.09 Hz and thus is sufficient for the planned experiments on Ca (fig. 1). Further improvements may increase the sensitivity to a level where g-factor experiments on single protons are possible. Future plans to perform similar experiments on single stored antiprotons may represent a test of CPT invariance [7].