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The quantum electrodynamic (QED) description of light-and-matter interaction is one of the most fundamental theories of physics and has been shown to be in excellent agreement with experimental results. Specifically, measurements of the electronic magnetic moment (or $g$ factor) of highly charged ions (HCI) in Penning traps can provide a stringent probe for QED, testing the Standard model in the strongest electromagnetic fields. When studying the difference of isotopes, even the intricate effects stemming from the nucleus can be resolved and tested as, due to the identical electron configuration, many common QED contributions do not have to be considered. Experimentally however, this becomes quickly limited, particularly by the precision of the ion masses or the achievable magnetic field stability. Here we report on a novel measurement technique that overcomes both of these limitations by co-trapping two HCIs in a Penning trap and measuring the difference of their $g$ factors directly. The resulting correlation of magnetic field fluctuations leads to drastically higher precision. We use a dual Ramsey-type measurement scheme with the ions locked on a common magnetron orbit, separated by only a few hundred micrometres, to extract the coherent spin precession frequency difference. We have measured the isotopic shift of the bound electron $g$ factor of the neon isotopes of $^{20}$Ne$^{9+}$ and $^{22}$Ne$^{9+}$ to 0.56 parts-per-trillion ($5.6 \cdot 10^{-13}$) precision relative to their $g$ factors, which is an improvement of more than two orders of magnitude compared to state-of-the-art techniques. This resolves the QED contribution to the nuclear recoil for the very first time and accurately validates the corresponding theory. Furthermore, the agreement with theory allows setting constraints for a fifth-force, resulting from Higgs-portal-type dark-matter interactions., 22 pages, 5 figures

The hyperfine structure splitting in the 6p2 4S3/2 -> 6p27s 4P1/2 transition at 307 nm in atomic 208Bi was measured with collinear laser spectroscopy at ISOLDE, CERN. The hyperfine A and B factors of both states were determined with an order of magnitude improved accuracy. Based on these measurements, theoretical input for the hyperfine structure anomaly, and results from hyperfine measurements on hydrogen-like and lithium-like 209Bi80+,82+, the nuclear magnetic moment of 208Bi has been determined to ��(208Bi) =+4.570(10) ��N . Using this value, the transition energy of the ground-state hyperfine splitting in hydrogen-like and lithium-like 208Bi80+,82+ and their specific difference of ���67.491(5)(148) meV are predicted. This provides a means for an experimental confirmation of the cancellation of nuclear structure effects in the specific difference in order to exclude such contributions as the cause of the hyperfine puzzle, the recently reported 7-�� discrepancy between experiment and bound-state strong-field QED calculations of the specific difference in the hyperfine structure splitting of 209Bi80+,82+.

Jena, Darmstadt : Helmholtz-Institut Jena/GSI Helmholtzzentrum für Schwerionenforschung GmbH 90 p. (2020). doi:10.15120/GSI-2020-00954, Published by Helmholtz-Institut Jena/GSI Helmholtzzentrum für Schwerionenforschung GmbH, Jena, Darmstadt

Jena, Darmstadt : Helmholtz Institut Jena / GSI, 99 p. (2018). doi:10.15120/GSI-2018-00628, Published by Helmholtz Institut Jena / GSI, Jena, Darmstadt

Large-scale relativistic calculations are performed for the transition energy and line strength of the $ 1s^{2} 2s 2p$ $^1P_{1} \,-\ 1s^{2} 2s^{2}$ $^1S_{0} $ transition in Be-like carbon. Based on the multiconfiguration Dirac-Hartree-Fock~(MCDHF) approach, different correlation models are developed to account for all major electron-electron correlation contributions. These correlation models are tested with various sets of the initial and the final state wave functions. The uncertainty of the predicted line strength due to missing correlation effects is estimated from the differences between the results obtained with those models. The finite nuclear mass effect is accurately calculated taking into account the energy, wave functions as well as operator contributions. As a result, a reliable theoretical benchmark of the $E1$ line strength is provided to support high precision lifetime measurement of the $ 1s^{2} 2s 2p$ $^1P_{1} $ state in Be-like carbon.

A recent measurement of the hyperfine splitting in the ground state of Li-like $^{209}$Bi$^{80+}$ has established a "hyperfine puzzle" -- the experimental result exhibits a 7$\sigma$ deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017); J. P. Karr, Nat. Phys. 13, 533 (2017)]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment ($\mu_I$) of $^{209}$Bi. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of $\mu_I(^{209}{\rm Bi})$ and combine it with nuclear magnetic resonance measurements of Bi(NO$_3$)$_3$ in nitric acid solutions and of the hexafluoridobismuthate(V) BiF$_6^-$ ion in acetonitrile. The result clearly reveals that $\mu_I(^{209}{\rm Bi})$ is much smaller than the tabulated value used previously. Applying the new magnetic moment shifts the theoretical prediction into agreement with experiment and resolves the hyperfine puzzle.

Missing Journal / Fehlende Zeitschrift 2(5), 055025 (2018). doi:10.1088/2399-6528/aac445

30th International Conference on Photonic, Electronic and Atomic Collisions, ICPEAC XXX, Cairns, Australia, 26 Jul 2017 - 1 Aug 2017; Journal of physics / Conference Series 875, 052007 (2017). doi:10.1088/1742-6596/875/6/052007, The spin evolution of two spin-1/2 valence electrons, located at two separated ions, is investigated with the help of Breit equation. This evolution that arise solely depends on their dipole-dipole magnetic interaction. Special attention is paid to the effects beyond the leading order of the dipole-dipole magnetic interaction. In contrast to just including the leading order, it is found that the spin-spin interactions flips the spin of both electrons together, while the spin-orbit interactions typically changes the spin of just single electron. As a consequence, different behaviour is observed in the time evolution of two different entangled Bell states., Published by IOP Publ., Bristol

We performed a laser spectroscopic determination of the $2s$ hyperfine splitting (HFS) of Li-like $^{209}\text{Bi}^{80+}$ and repeated the measurement of the $1s$ HFS of H-like $^{209}\text{Bi}^{82+}$. Both ion species were subsequently stored in the Experimental Storage Ring at the GSI Helmholtzzentrum f\"ur Schwerionenforschung Darmstadt and cooled with an electron cooler at a velocity of $\approx 0.71\,c$. Pulsed laser excitation of the $M1$ hyperfine-transition was performed in anticollinear and collinear geometry for $\text{Bi}^{82+}$ and $\text{Bi}^{80+}$, respectively, and observed by fluorescence detection. We obtain $\Delta E^{(1s)}= 5086.3(11)\,\textrm{meV}$ for $\text{Bi}^{82+}$, different from the literature value, and $\Delta E^{(2s)}= 797.50(18)\,\textrm{meV}$ for $\text{Bi}^{80+}$. These values provide experimental evidence that a specific difference between the two splitting energies can be used to test QED calculations in the strongest static magnetic fields available in the laboratory independent of nuclear structure effects. The experimental result is in excellent agreement with the theoretical prediction and confirms the sum of the Dirac term and the relativistic interelectronic-interaction correction at a level of 0.5% confirming the importance of accounting for the Breit interaction., Comment: 5 pages, 2 figures

Studies of the hyperfine splitting in hydrogen are strongly motivated by the level of accuracy achieved in recent atomic physics experiments, which yield finally model-independent informations about nuclear structure parameters with utmost precision. Considering the current status of the determination of corrections to the hyperfine splitting of the ground state in hydrogen, this thesis provides further improved calculations by taking into account the most recent value for the proton charge radius. Comparing theoretical and experimental data of the hyperfine splitting in hydrogen the proton-size contribution is extracted and a relativistic formula for this contribution is derived in terms of moments of the nuclear charge and magnetization distributions. An iterative scheme for the determination of the Zemach and magnetic radii of the proton is proposed. As a result, the Zemach and magnetic radii are determined and the values are compared with the corresponding ones deduced from data obtained in electron-proton scattering experiments. The extraction of the Zemach radius from a rescaled difference between the hyperfine splitting in hydrogen and in muonium is considered as well. Investigations of forbidden radiative transitions in few-electron ions within ab initio QED provide a most sensitive tool for probing the influence of relativistic electron-correlation and QED corrections to the transition rates. Accordingly, a major part of this thesis is devoted to detailed studies of radiative and interelectronic-interaction effects to the transition probabilities. The renormalized expressions for the corresponding corrections in one- and two-electron ions as well as for ions with one electron over closed shells are derived employing the two-time Green's function method. Numerical results for the correlation corrections to magnetic transition rates in He-like ions are presented. For the first time also the frequency-dependent contribution is calculated, which has to be accounted for preserving gauge invariance. One-loop QED corrections to the magnetic-dipole transition amplitude between the fine-structure levels 2p_{3/2} and 2p_{1/2} are calculated to all orders in \alpha Z. Taking into account consistently relativistic, interelectronic-interaction, and QED corrections to the magnetic-dipole transition amplitude allows for predictions of the lifetimes of the states (1s^2 2s^2 2p)^2P_{3/2} in B-like ions and (1s^2 2s 2p)^3P_2 in Be-like ions with utmost precision. The results of corresponding calculations are compared with experimental data obtained in recent measurements at the Heidelberg EBIT. Finally, for He-like ions with nonzero-spin nuclei the effect of hyperfine quenching on the lifetimes of the 2^3P_{0,2} states is investigated and again compared available experimental data.

Jena, Darmstadt : Helmholtz Institut Jena / GSI 96 p. (2019). doi:10.15120/GSI-2019-00643, Published by Helmholtz Institut Jena / GSI, Jena, Darmstadt