Measurement of the bound-electron g-factor difference in coupled ions

Testing quantum electrodynamics in extreme fields using helium-like uranium

Quantum electrodynamics (QED), the quantum field theory that describes the interaction between light and matter, is commonly regarded as the best-tested quantum theory in modern physics. However, this claim is mostly based on extremely precise studies performed in the domain of relatively low field strengths and light atoms and ions1-6. In the realm of very strong electromagnetic fields such as in the heaviest highly charged ions (with nuclear charge Z ≫ 1), QED calculations enter a qualitatively different, non-perturbative regime. Yet, the corresponding experimental studies are very challenging, and theoretical predictions are only partially tested. Here we present an experiment sensitive to higher-order QED effects and electron-electron interactions in the high-Z regime. This is achieved by using a multi-reference method based on Doppler-tuned X-ray emission from stored relativistic uranium ions with different charge states. The energy of the 1s1/22p3/2 J = 2 → 1s1/22s1/2 J = 1 intrashell transition in the heaviest two-electron ion (U90+) is obtained with an accuracy of 37 ppm. Furthermore, a comparison of uranium ions with different numbers of bound electrons enables us to disentangle and to test separately the one-electron higher-order QED effects and the bound electron-electron interaction terms without the uncertainty related to the nuclear radius. Moreover, our experimental result can discriminate between several state-of-the-art theoretical approaches and provides an important benchmark for calculations in the strong-field domain.

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

We present the measurements of individual bound electron g factors of ^{20}Ne^{9+} and ^{22}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}Ne)=19.992 440 168 77(9)  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_{e}=5.485 799 090 99(59)×10^{-4}  u as well as a factor of seven improved m(^{22}Ne)=21.991 385 098 2(26)  u.

Stringent test of QED with hydrogen-like tin

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond 1015 V cm-1 for the innermost electrons1. Especially in few-electron, highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the past several decades2,3. Another approach is the measurement of gyromagnetic factors (g factors) in highly charged ions4-7. However, so far, either experimental accuracy or small field strength in low-Z ions5,6 limited the stringency of these QED tests. Here we report on our high-precision, high-field test of QED in hydrogen-like 118Sn49+. The highly charged ions were produced with the Heidelberg electron beam ion trap (EBIT)8 and injected into the ALPHATRAP Penning-trap setup9, in which the bound-electron g factor was measured with a precision of 0.5 parts per billion (ppb). For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about 0.012%, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests by means of the Lamb shift and, with anticipated advances in the g-factor theory, surpass them by more than an order of magnitude.

Penning-Trap Mass Measurement of Helium-4

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}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}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.

Limits of Optimization

Optimization is about finding the best available object with respect to an objective function. Mathematics and quantitative sciences have been highly successful in formulating problems as optimization problems, and constructing clever processes that find optimal objects from sets of objects. As computers have become readily available to most people, optimization and optimized processes play a very broad role in societies. It is not obvious, however, that the optimization processes that work for mathematics and abstract objects should be readily applied to complex and open social systems. In this paper we set forth a framework to understand when optimization is limited, particularly for complex and open social systems.

QED Theory of the Nuclear Recoil with Finite Size

We investigate the modification of the transverse electromagnetic interaction between two pointlike particles when one particle acquires a finite size. It is shown that the correct treatment of such interaction cannot be accomplished within the Breit approximation but should be addressed within the QED. The complete QED formula is derived for the finite-size nuclear recoil, exact in the coupling strength parameter Zα. Numerical calculations are carried out for a wide range of Z and verified against the (Zα)^{5} contribution. The comparison with the Zα expansion identifies the contribution of order (Zα)^{6}, which is linear in the nuclear radius and numerically dominates over the lower-order (Zα)^{5} term.