We have measured the ground-state g-factor of boronlike argon 40 Ar 13+ with a fractional uncertainty of 1.4 × 10 −9 with a single ion in the newly developed Alphatrap double Penning-trap setup. The here obtained value of g = 0.663 648 455 32(93) is in agreement with our theoretical prediction of 0.663 648 12(58). The latter is obtained accounting for quantum electrodynamics, electron correlation, and nuclear effects within the state-of-the-art theoretical methods. Our experimental result distinguishes between existing predictions that are in disagreement, and lays the foundations for an independent determination of the fine-structure constant.

By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.

First ever measurements of the ratios of free cyclotron frequencies of heavy, highly charged ions with Z > 50 with relative uncertainties close to 10 −11 are presented. Such accurate measurements have become realistic due to the construction of the novel cryogenic multi-Penning-trap mass spectrometer PENTATRAP. Based on the measured frequency ratios, the mass differences of five pairs of stable xenon isotopes, ranging from 126 Xe to 134 Xe, have been determined. Moreover, the first direct measurement of an electron binding energy in a heavy highly charged ion, namely of the 37th atomic electron in xenon, with an uncertainty of a few eV is demonstrated. The obtained value agrees with the calculated one using two independent, different implementations of the multiconfiguration Dirac-Hartree-Fock method. PENTATRAP opens the door to future measurements of electron binding energies in highly charged heavy ions for more stringent tests of bound-state quantum electrodynamics in strong electromagnetic fields and for an investigation of the manifestation of light dark matter in isotopic chains of certain chemical elements.

State-of-the-art optical clocks [1] achieve fractional precisions of 10 −18 and below using ensembles of atoms in optical lattices [2, 3] or individual ions in radiofrequency traps [4, 5]. They are used as frequency standards and in searches for possible variations of fundamental constants [6], dark matter detection [7], and physics beyond the Standard Model [8, 9]. Promising candidates for novel clocks are highly charged ions (HCIs) [10] and nuclear transitions [11], which are largely insensitive to external perturbations and reach wavelengths beyond the optical range [12], now becoming accessible to frequency combs [13]. However, insufficiently accurate atomic structure calculations still

QED corrections to the g factor of Li-like and B-like ions in a wide range of nuclear charges are presented. Many-electron contributions as well as radiative effects on the one-loop level are calculated. Contributions resulting from the interelectronic interaction, the self-energy effect, and most of the terms of the vacuumpolarization effect are evaluated to all orders in the nuclear coupling strength Zα. Uncertainties resulting from nuclear size effects, numerical computations, and uncalculated effects are discussed.