$g$ Factor of Hydrogenlike ${}^{28}\mathrm{Si}^{13+}$

We determined the experimental value of the $g$ factor of the electron bound in hydrogenlike ${}^{28}\mathrm{Si}^{13+}$ by using a single ion confined in a cylindrical Penning trap. From the ratio of the ion’s cyclotron frequency and the induced spin flip frequency, we obtain $g=1.9953489587(5)(3)(8)$. It is in excellent agreement with the state-of-the-art theoretical value of 1.995 348 958 0(17), which includes QED contributions up to the two-loop level of the order of $(Z\alpha {)}^2$ and $(Z\alpha {)}^4$ and represents a stringent test of bound-state quantum electrodynamics calculations.

Figure 1

Sketch of the triple Penning trap. For details, see the text.

Figure 2

Change in the axial ion’s oscillation frequency upon induced spin flips in the analysis trap. The calculated frequency difference is 240 mHz in a total frequency of 420 kHz in fair agreement with the observation. Between the left and right periods, the ion was transported into the precision trap where a spin flip was successfully induced by irradiation with microwaves.

Figure 3

Number of observed axial frequency jumps normalized to the total number of attempts to induce a spin flip. As the abscissa we plot the ratio $\Gamma ={\nu }_{\mathrm{MW}}/{\nu }_c$ of the simultaneously measured cyclotron frequency ${\nu }_c$ and the microwave frequency ${\nu }_{\mathrm{MW}}$. The data are fitted with a Gaussian by using the maximum-likelihood method, avoiding the need for data binning. The light gray area indicates the 68% prediction band for the measurement data distribution, while the dark gray area is the confidence band of the fit. The fractional statistical uncertainty of the resonance center of this single resonance is $4\times {10}^{-10}$.