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.

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.

Higher-Order QED Corrections to the Hyperfine Splitting in

We present a calculation of the hyperfine splitting of the 2^{3}S state in the ^{3}He atom with inclusion of all QED effects up to α^{3}E_{F}, where E_{F} is the Fermi splitting. Using the experimental value of the 1S hyperfine splitting in ^{3}He^{+}, we eliminate uncertainties from the nuclear structure and obtain the theoretical prediction for ^{3}He of ν_{hfs}=-6 739 701 181(41) Hz, which is in perfect agreement with the experimental value -6 739 701 177(16) Hz [S. D. Rosner and F. M. Pipkin, Phys. Rev. A 1, 571 (1970)PLRAAN0556-279110.1103/PhysRevA.1.571]. This result constitutes a 40-fold improvement in precision as compared to the previous value and is the most accurate theoretical prediction ever obtained for a nonhydrogenic system.

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.

Fine structure of heliumlike ions and determination of the fine structure constant.

We report a calculation of the fine-structure splitting in light heliumlike atoms, which accounts for all quantum electrodynamical effects up to order alpha{5} Ry. For the helium atom, we resolve the previously reported disagreement between theory and experiment and determine the fine-structure constant with an accuracy of 31 ppb. The calculational results are extensively checked by comparison with the experimental data for different nuclear charges and by evaluation of the hydrogenic limit of individual corrections.

Electron self-energy in the presence of a magnetic field: hyperfine splitting and g factor.

A high-precision numerical calculation is reported for the self-energy correction to the hyperfine splitting and to the bound-electron g factor in hydrogenlike ions with low nuclear charge numbers. The binding nuclear Coulomb field is treated to all orders, and the nonperturbative remainder beyond the known Zalpha-expansion coefficients is determined. For the 3He+ ion, the nonperturbative remainder yields a contribution of -450 Hz to the normalized difference of the 1S and 2S hyperfine-structure intervals, to be compared with the experimental uncertainty of 71 Hz and with the theoretical error of 50 Hz due to other contributions. In the case of the g factor, the calculation provides the most stringent test of equivalence of the perturbative and nonperturbative approaches reported so far in the bound-state QED calculations.

Nonrelativistic QED approach to the bound-electron g factor.

Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order alpha(Z alpha)(4) to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order alpha(2)(Z alpha)(4)ln([(Z alpha)(-2)] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for the 1S bound-electron g factor and influence the value of the electron mass determined from g-factor measurements.