High-Precision Determination of $g$ Factors and Masses of ${{}^{20}\mathrm{Ne}}^{9+}$ and ${{}^{22}\mathrm{Ne}}^{9+}$

We present the measurements of individual bound electron $g$ factors of ${{}^{20}\mathrm{Ne}}^{9+}$ and ${{}^{22}\mathrm{Ne}}^{9+}$ on the relative level of 0.1 parts per billion. The comparison with theory represents the most stringent test of bound-state QED in strong electric fields. A dedicated mass measurement results in $m({}^{20}\mathrm{Ne})=19.99244016877(9)\mathrm{u}$, which improves the current literature value by a factor of 18, disagrees by 4 standard deviations, and represents the most precisely measured mass value in atomic mass units. Together, these measurements yield an electron mass on the relative level of 0.1 ppb with $m_{\mathrm{e}}=5.48579909099(59)\times {10}^{-4}\mathrm{u}$ as well as a factor of seven improved $m({}^{22}\mathrm{Ne})=21.9913850982(26)\mathrm{u}$.

Figure 1

Sectional views of the cylindrical Penning-trap setups of Alphatrap [24] (left) and Pentatrap [25] (right). Both trap towers are built from gold-plated copper ring electrodes which are isolated by sapphire and quartz rings. The connected superconducting tank circuits, the amplifiers for the axial detection systems, and the RF excitation lines are shown. At the Alphatrap experiment, ${\nu }_{\mathrm{c}}$ is measured simultaneously to the irradiation of the microwave drive in the Precision trap. The CoFe alloy central ring electrode in the analysis trap produces a strong magnetic bottle, allowing a nondestructive spin-state detection with close to 100% fidelity. Here, a different spin orientation changes the axial force resulting from the magnetic moment inside the inhomogeneous magnetic field leading to axial frequency jumps of the ion (${}^{20,22}{\mathrm{Ne}}^{9+}$ yield jumps of 1.8 Hz and 1.6 Hz, respectively) [40]. At the Pentatrap setup, both ions’ ${\nu }_{\mathrm{c}}$ are measured successively in each measurement trap, resulting in one cyclotron frequency ratio per trap. The ion species are effectively swapped in the measurement traps by adiabatically transporting all ions to the respective neighboring trap and back (position 1 and 2). The different trapping potential depths ($\varphi$) in the two measurement traps are due to different resonance frequencies of the axial detection circuits.

Figure 2

(a) Exemplary ${\nu }_{\mathrm{c}}$ data from traps 2 and 3. (b) Determined ${\mathcal{R}}^{\mathrm{CF}}$ for different ${({\rho }_{+}^{\mathrm{exc}})}^2$ including the corresponding least-square fits and $1\sigma$ confidence bands with ${\chi }_{\mathrm{red}}^2=1.11$ and 0.65 for traps 2 and 3, respectively. Higher-order shifts $\propto {({\rho }_{+}^{\mathrm{exc}})}^3$ and ${({\rho }_{+}^{\mathrm{exc}})}^4$ are estimated to be negligible. The ${\mathcal{R}}^{\mathrm{CF}}$ of each trap is extracted from the fit at ${({\rho }_{+}^{\mathrm{exc}})}^2=0\mathrm{\mu }{\mathrm{m}}^2$. This extrapolation reduces the relativistic shift and all other shifts that are proportional to ${({\rho }_{+}^{\mathrm{exc}})}^2$.

Figure 3

$\mathrm{\Gamma }$ resonance for ${{}^{20}\mathrm{Ne}}^{9+}$ containing 425 cycles and fitted via the Maximum-likelihood method with a three-parameter Gaussian line shape (red line), since asymmetric effects shift the resonance center far below the ppt level [32, 57, 58]. The $1\text{−}\sigma$ confidence band of the fit is displayed in grey. The black binned data points with binomial error bars are presented to guide the eye. The grey shadows at the top are observed spin flips in the PT for the respective $\mathrm{\Gamma }$, whereas the ones at the bottom are no spin flips.