An optical atomic clock based on a highly charged ion.

Optical atomic clocks are the most accurate measurement devices ever constructed and have found many applications in fundamental science and technology1-3. The use of highly charged ions (HCI) as a new class of references for highest-accuracy clocks and precision tests of fundamental physics4-11 has long been motivated by their extreme atomic properties and reduced sensitivity to perturbations from external electric and magnetic fields compared with singly charged ions or neutral atoms. Here we present the realization of this new class of clocks, based on an optical magnetic-dipole transition in Ar13+. Its comprehensively evaluated systematic frequency uncertainty of 2.2 × 10-17 is comparable with that of many optical clocks in operation. From clock comparisons, we improve by eight and nine orders of magnitude on the uncertainties for the absolute transition frequency12 and isotope shift (40Ar versus 36Ar) (ref. 13), respectively. These measurements allow us to investigate the largely unexplored quantum electrodynamic (QED) nuclear recoil, presented as part of improved calculations of the isotope shift, which reduce the uncertainty of previous theory14 by a factor of three. This work establishes forbidden optical transitions in HCI as references for cutting-edge optical clocks and future high-sensitivity searches for physics beyond the standard model.

Hanle Effect for Lifetime Determinations in the Soft X-Ray Regime.

By exciting a series of 1s^{2} ^{1}S_{0}→1snp^{1}P_{1} transitions in heliumlike nitrogen ions with linearly polarized monochromatic soft x rays at the Elettra facility, we found a change in the angular distribution of the fluorescence sensitive to the principal quantum number n. In particular it is observed that the ratio of emission in directions parallel and perpendicular to the polarization of incident radiation increases with higher n. We find this n dependence to be a manifestation of the Hanle effect, which served as a practical tool for lifetime determinations of optical transitions since its discovery in 1924. In contrast to traditional Hanle effect experiments, in which one varies the magnetic field and considers a particular excited state, we demonstrate a "soft x-ray Hanle effect" which arises in a static magnetic field but for a series of excited states. By comparing experimental data with theoretical predictions, we were able to determine lifetimes ranging from hundreds of femtoseconds to tens of picoseconds of the 1snp^{1}P_{1} levels, which find excellent agreement with atomic-structure calculations. We argue that dedicated soft x-ray measurements could yield lifetime data that are beyond current experimental reach and cannot yet be predicted with sufficient accuracy.

Approximate Atomic Green Functions.

In atomic and many-particle physics, Green functions often occur as propagators to formally represent the (integration over the) complete spectrum of the underlying Hamiltonian. However, while these functions are very crucial to describing many second- and higher-order perturbation processes, they have hardly been considered and classified for complex atoms. Here, we show how relativistic (many-electron) Green functions can be approximated and systematically improved for few- and many-electron atoms and ions. The representation of these functions is based on classes of virtual excitations, or so-called excitation schemes, with regard to given bound-state reference configurations, and by applying a multi-configuration Dirac-Hartree-Fock expansion of all atomic states involved. A first implementation of these approximate Green functions has been realized in the framework of Jac, the Jena Atomic Calculator, and will facilitate the study of various multi-photon and/or multiple electron (emission) processes.

High Resolution Photoexcitation Measurements Exacerbate the Long-Standing Fe XVII Oscillator Strength Problem.

For more than 40 years, most astrophysical observations and laboratory studies of two key soft x-ray diagnostic 2p-3d transitions, 3C and 3D, in Fe XVII ions found oscillator strength ratios f(3C)/f(3D) disagreeing with theory, but uncertainties had precluded definitive statements on this much studied conundrum. Here, we resonantly excite these lines using synchrotron radiation at PETRA III, and reach, at a millionfold lower photon intensities, a 10 times higher spectral resolution, and 3 times smaller uncertainty than earlier work. Our final result of f(3C)/f(3D)=3.09(8)(6) supports many of the earlier clean astrophysical and laboratory observations, while departing by five sigmas from our own newest large-scale ab initio calculations, and excluding all proposed explanations, including those invoking nonlinear effects and population transfers.

Interaction of relativistic electron-vortex beams with few-cycle laser pulses.

We study the interaction of relativistic electron-vortex beams (EVBs) with laser light. Exact analytical solutions for this problem are obtained by employing the Dirac-Volkov wave functions to describe the (monoenergetic) distribution of the electrons in vortex beams with well-defined orbital angular momentum. Our new solutions explicitly show that the orbital angular momentum components of the laser field couple to the total angular momentum of the electrons. When the field is switched off, it is shown that the laser-driven EVB coincides with the field-free EVB as reported by Bliokh et al. [Phys. Rev. Lett. 107, 174802 (2011)]. Moreover, we calculate the probability density for finding an electron in the beam profile and demonstrate that the center of the beam is shifted with respect to the center of the field-free EVB.

Strong higher-order resonant contributions to x-ray line polarization in hot plasmas.

We studied angular distributions of x rays emitted in resonant recombination of highly charged iron and krypton ions, resolving dielectronic, trielectronic, and quadruelectronic channels. A tunable electron beam drove these processes, inducing x rays registered by two detectors mounted along and perpendicular to the beam axis. The measured emission asymmetries comprehensively benchmarked full-order atomic calculations. We conclude that accurate polarization diagnostics of hot plasmas can only be obtained under the premise of inclusion of higher-order processes that were neglected in earlier work.

Dominance of the Breit interaction in the x-ray emission of highly charged ions following dielectronic recombination.

The Breit interaction typically appears as a-more or less small-correction to the Coulomb repulsion acting among the electrons. We here propose two x-ray measurements on the angular distribution and linear polarization of the 1s2s(2)2p(1/2) J=1-->1s(2)2s(2) J=0 electric-dipole radiation of high-Z, beryllium-like ions, following the resonant electron capture into initially lithium-like ions, for which the Breit interaction strongly dominates the Coulomb repulsion and leads to a qualitative change in the expected x-ray emission pattern. The proposed measurements are feasible with present-day x-ray detectors and may serve a stringent test on relativistic corrections to the electron-electron interaction in the presence of strong fields.

Unified treatment of even and odd anharmonic oscillators of arbitrary degree.

We present a unified treatment, including higher-order corrections, of anharmonic oscillators of arbitrary even and odd degree. Our approach is based on a dispersion relation which takes advantage of the PT symmetry of odd potentials for imaginary coupling parameter, and of generalized quantization conditions which take into account instanton contributions. We find a number of explicit new results, including the general behavior of large-order perturbation theory for arbitrary levels of odd anharmonic oscillators, and subleading corrections to the decay width of excited states for odd potentials, which are numerically significant.

Application of radiative electron capture for the diagnostics of spin-polarized ion beams at storage rings.

It is proposed to apply the radiative electron capture into high-Z projectiles as a probe process for measuring the spin polarization of the hydrogenlike ions at storage rings. We argue that such polarization measurements are possible since the linear polarization of emitted x-ray photons is greatly sensitive to the spin states of incoming ions with nuclear spin I > 1/2. In particular, for K-shell electron capture into the hydrogenlike ions, the linear polarization of light as measured out of the reaction plane is found to be proportional to the degree of ion polarization. Detailed computations for the dependence of the photon polarization on the ion spin states and projectile energies are carried out for the electron recombination into hydrogenlike Bi 82+ ions.