Sven Sturm

Light-Ion Trap (LIONTRAP), a high-precision Penning-trap mass spectrometer, was used to determine the atomic mass of $^{4}$He. Here, we report a 12 parts-per-trillion measurement of the mass of a $^{4}$He$^{2+}$ ion, $m(^{4}\text{He}^{2+}$) = $4.001\:506\:179\:651 (48)$ u. From this, the atomic mass of the neutral atom can be determined without loss of precision: $m(^{4}\text{He})$ = $4.002\:603\:254\:653 (48)$ u. This result is slightly more precise than the current CODATA18 literature value but deviates by 6.6 standard deviations. This is a post-peer-review, pre-copy edit version of an article published in PRL. The final version is available online at https://doi.org/10.1103/PhysRevLett.131.093201.

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.

In Penning traps electromagnetic forces are used to confine charged particles under well-controlled conditions for virtually unlimited time. Sensitive detection methods have been developed to allow observation of single stored ions. Various cooling methods can be employed to reduce the energy of the trapped particle to nearly at rest. In this review we summarize how highly charged ions offer unique possibilities for precision measurements in Penning traps. Precision atomic and nuclear masses as well as magnetic moments of bound electrons allow among others to determine fundamental constants like the mass of the electron or to perform stringent tests of fundamental interactions like bound-state quantum electrodynamics. Recent results and future perspectives in high-precision Penning-trap spectroscopy with highly charged ions will be discussed.

The masses of the lightest atomic nuclei and the electron mass are interlinked and are crucial in a wide range of research fields, with their values affecting observables in atomic, molecular and neutrino physics as well as metrology. The most precise values for these fundamental parameters come from Penning-trap mass spectrometry, which achieves relative mass uncertainties in the range of $10^{-11}$. However, redundancy checks using data from different experiments reveal significant inconsistencies in the masses of the proton ($m_p$), the deuteron ($m_d$) and helion ($m_\text{he}$), amounting to $5$ standard deviations for the term $Δ=m_p+m_d-m_{\text{he}}$, which suggests that the uncertainty of these values may have been underestimated. Here we present results from absolute mass measurements of the deuteron and the ${HD}^+$ molecular ion against $^{12}C$ as a mass reference. Our value for the deuteron $m_d=2.013\,553\,212\,535 (17)$u supersedes the precision of the literature value by a factor of $2.4$ and deviates from this by $4.8$ standard deviations. With a relative uncertainty of $8$ parts per trillion (ppt) this is the most precise mass value measured directly in atomic mass units. Furthermore, the measurement of the ${HD}^+$ molecular ion, $m({HD}^+)=3.021\,378\,241\,561\,(61)$u, not only allows for a rigorous consistency check of our measurements of the masses of the deuteron (this work) and proton, but also establishes an additional link for the masses of tritium and helium-3 to the atomic mass unit. Combined with a recent measurement of the deuteron-to-proton mass ratio the uncertainty of the reference value of $m_p$ can be reduced by a factor of three. This is a post-peer-review, pre-copyedit version of an article published in Nature. The final authenticated version is available online at https://doi.org/10.1038/s41586-020-2628-7

We discuss the coupling of the motion of two ion species in separate Penning traps via a common tank circuit. The enhancement of the coupling assisted by the tank circuit is demonstrated by an avoided crossing behavior measurement of the motional modes of two coupled ions. We propose an intermittent laser cooling method for sympathetic cooling and provide a theoretical description. The technique enables tuning of the coupling strength between two ion species in separate traps and thus allows for efficient sympathetic cooling of an arbitrary type of single ion for high-precision Penning-trap experiments.

State-of-the-art optical clocks achieve fractional precisions of $10^{-18}$ and below using ensembles of atoms in optical lattices or individual ions in radio-frequency traps. Promising candidates for novel clocks are highly charged ions (HCIs) and nuclear transitions, which are largely insensitive to external perturbations and reach wavelengths beyond the optical range, now becoming accessible to frequency combs. However, insufficiently accurate atomic structure calculations still hinder the identification of suitable transitions in HCIs. Here, we report on the discovery of a long-lived metastable electronic state in a HCI by measuring the mass difference of the ground and the excited state in Re, the first non-destructive, direct determination of an electronic excitation energy. This result agrees with our advanced calculations, and we confirmed them with an Os ion with the same electronic configuration. We used the high-precision Penning-trap mass spectrometer PENTATRAP, unique in its synchronous use of five individual traps for simultaneous mass measurements. The cyclotron frequency ratio $R$ of the ion in the ground state to the metastable state could be determined to a precision of $δR=1\cdot 10^{-11}$, unprecedented in the heavy atom regime. With a lifetime of about 130 days, the potential soft x-ray frequency reference at $ν=4.86\cdot 10^{16}\,\text{Hz}$ has a linewidth of only $Δν\approx 5\cdot 10^{-8}\,\text{Hz}$, and one of the highest electronic quality factor ($Q=\fracν{Δν}\approx 10^{24}$) ever seen in an experiment. Our low uncertainty enables searching for more HCI soft x-ray clock transitions, needed for promising precision studies of fundamental physics in a thus far unexplored frontier.

The precise knowledge of the atomic masses of light atomic nuclei, e.g. the proton, deuteron, triton and helion, is of great importance for several fundamental tests in physics. However, the latest high-precision measurements of these masses carried out at different mass spectrometers indicate an inconsistency of five standard deviations. To determine the masses of the lightest ions with a relative precision of a few parts per trillion and investigate this mass problem a cryogenic multi-Penning trap setup, LIONTRAP (Light ION TRAP), was constructed. This allows an independent and more precise determination of the relevant atomic masses by measuring the cyclotron frequency of single trapped ions in comparison to that of a single carbon ion. In this paper the measurement concept and the first doubly compensated cylindrical electrode Penning trap, are presented. Moreover, the analysis of the first measurement campaigns of the proton's and oxygen's atomic mass is described in detail, resulting in mp = 1.007 276 466 598 (33) u and m(16O)= 15.994 914 619 37 (87) u. The results on these data sets have already been presented in [F. Heisse et al., Phys. Rev. Lett. 119, 033001 (2017)]. For the proton's atomic mass, the uncertainty was improved by a factor of three compared to the 2014 CODATA value.

The electron mass in atomic mass units has been determined with a relative uncertainty of $2.8\cdot 10^{-11}$, which represents a 13-fold improvement of the 2010 CODATA value. The underlying measurement principle combines a high-precision measurement of the Larmor-to-cyclotron frequency ratio on a single hydrogen-like carbon ion in a Penning trap with a corresponding very accurate $g$-factor calculation. Here, we present the measurement results in detail, including a comprehensive discussion of the systematic shifts and their uncertainties. A special focus is set on the various sources of phase jitters, which are essential for the understanding of the applied line-shape model for the $g$-factor resonance.