Quantum Electrodynamics Calculations Research Articles

Precision laser spectroscopy experiments on antiprotonic helium

At CERN‘s Antiproton Decelerator (AD) facility, the Atomic Spectroscopyand Collisions Using Slow Antiprotons (ASACUSA) collaboration is carrying out precise laser spectroscopy experiments on antiprotonic helium (p̅He+ ≡ p̅+He2++e−) atoms. By employing buffer-gas cooling techniquesin a cryogenic gas target, samples of atoms were cooled to temperatureT = 1.5–1.7 K, thereby reducing the Doppler width in the single-photon resonance lines. By comparing the results with three-body quantum electrodynamics calculations, the antiproton-to-electron mass ratio was determined as Mp̅/me = 1836.1526734(15). This agreed with the known proton-to-electron mass ratio with a precision of 8 . 1010. Further improvements in the experimental precision are currently being attempted. The high-quality antiproton beam provided by the future Extra Low Energy Antiproton Ring (ELENA) facility should further increase the experimental precision.

Strong van der Waals Adhesion of a Polymer Film on Rough Substrates.

We propose that chemically inert polymeric films can enhance van der Waals (vdW) forces in the same way as nanofabrication of biomimetic adhesive materials. For the vdW adhesion of an ethylene-chlorotrifluoroethylene (ECTFE) film on rough metal and dielectric substrates, we present a model that combines microscopic quantum-chemistry simulations of the polymer response functions and the equilibrium monomer-substrate distance with a macroscopic quantum-electrodynamics calculation of the Casimir force between the polymer film and the substrate. We predict adhesive forces up to 2.22 kN/mm2, where the effect is reduced by substrate roughness and for dielectric surfaces.

Quantum state preparation of homonuclear molecular ions enabled via a cold buffer gas: An ab initio study for the H2+ and the D2+ case

Precision vibrational spectroscopy of the molecular hydrogen ions is of significant interest for determining fundamental constants, for searching for new forces, and for testing quantum electrodynamics calculations. Future experiments can profit from the ability of preparing molecular hydrogen ions at ultralow kinetic energy and in preselected internal states, with respect to vibration, rotation, and spin degrees of freedom. For the homonuclear ions (${\mathrm{H}}_{2}{}^{+}, {\mathrm{D}}_{2}{}^{+}$), direct laser cooling of the rotational degree of freedom is not feasible. We show by quantum calculations that rotational cooling by cold He buffer gas is an effective approach. For this purpose we have computed the energy-dependent cross sections for rotationally elastic and inelastic collisions, ${\mathrm{h}}_{2}{}^{+}(v=0,\phantom{\rule{0.16em}{0ex}}N)+\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow} {\mathrm{h}}_{2}{}^{+}(v=0,\phantom{\rule{0.16em}{0ex}}{N}^{\ensuremath{'}})+\mathrm{He}$ (where $\mathrm{h}=\mathrm{H},\phantom{\rule{0.16em}{0ex}}\mathrm{D})$, using ab initio coupled-channel calculations. We find that rotational cooling to the lowest rotational state is possible within tens of seconds under experimentally realistic conditions. We furthermore describe possible protocols for the preparation of a single quantum state, where also the spin state is well defined.

Long-range tails in van der Waals interactions of excited-state and ground-state atoms

A quantum electrodynamic calculation of the interaction of an excited-state atom with a ground-state atom is performed. For an excited reference state and a lower-lying virtual state, the contribution to the interaction energy naturally splits into a pole term and a Wick-rotated term. The pole term is shown to dominate in the long-range limit, altering the functional form of the interaction from the retarded $1/{R}^{7}$ Casimir-Polder form to a long-range tail---provided by the Wick-rotated term---proportional to $cos[2({E}_{m}\ensuremath{-}{E}_{n})\phantom{\rule{0.16em}{0ex}}R/(\ensuremath{\hbar}c)]/{R}^{2}$, where ${E}_{m}<{E}_{n}$ is the energy of a virtual state, lower than the reference-state energy ${E}_{n}$, and $R$ is the interatomic separation. General expressions are obtained which can be applied to atomic reference states of arbitrary angular symmetry. Careful treatment of the pole terms in the Feynman prescription for the atomic polarizability is found to be crucial in obtaining correct results.

New Precision Measurement of Hyperfine Splitting of Positronium

Positronium is an ideal system for precision tests of bound-state quantum electrodynamics (QED). One of the most precisely tested quantities of positronium is the ground-state hyperfine splitting (HFS). Recent progress on theoretical calculation revealed that there was a 16.0 ± 3.5 ppm (4.5 σ) discrepancy between the old experimental value and the theoretical calculation. We performed a new measurement which took into account the positronium thermalization effect for the first time. The result was HFS = 203.3942 ± 0.0016 (stat., 8.0 ppm) ± 0.0013 (syst., 6.4 ppm) GHz, which was consistent with the QED calculation within 1.1 σ, whereas it disfavored the old experimental values by 2.6 σ. It also showed that the positronium thermalization effect on HFS was as large as 10 ± 2 ppm, which was consistent with the discrepancy level within 1.5 σ, which could be the reason of the discrepancy. We are planning to preform a new experiment which uses a slow positron beam and perform HFS measurement in vacuum, instead of using gas as all of the other precision measurements. It will be completely free from material effect on HFS, including the thermalization effect. In this proceeding, summary of our previous work and details of the future new experiment are discussed.

Quantum Electrodynamical Shifts in Multivalent Heavy Ions

The quantum electrodynamics (QED) corrections are directly incorporated into the most accurate treatment of the correlation corrections for ions with complex electronic structure of interest to metrology and tests of fundamental physics. We compared the performance of four different QED potentials for various systems to access the accuracy of QED calculations and to make a prediction of highly charged ion properties urgently needed for planning future experiments. We find that all four potentials give consistent and reliable results for ions of interest. For the strongly bound electrons, the nonlocal potentials are more accurate than the local potential.

Polarization transfer in Rayleigh scattering of hard x-rays

We report on the first elastic hard x-ray scattering experiment where the linear polarization characteristics of both the incident and the scattered radiation were observed. Rayleigh scattering was investigated in a relativistic regime by using a high-Z target material, namely gold, and a photon energy of 175 keV. Although the incident synchrotron radiation was nearly 100% linearly polarized, at a scattering angle of we observed a strong depolarization for the scattered photons with a degree of linear polarization of only. This finding agrees with second-order quantum electrodynamics calculations of Rayleigh scattering, when taking into account a small polarization impurity of the incident photon beam which was determined to be close to 98%. The latter value was obtained independently from the elastic scattering by analyzing photons that were Compton-scattered in the target. Moreover, our results indicate that when relying on state-of-the-art theory, Rayleigh scattering could provide a very accurate method to diagnose polarization impurities in a broad region of hard x-ray energies.

Atomic many-body effects and Lamb shifts in alkali metals

We present a detailed study of the Flambaum-Ginges radiative potential method which enables the accurate inclusion of quantum electrodynamics (QED) radiative corrections in a simple manner in atoms, ions, and molecules over the range 10<=Z<=120, where Z is the nuclear charge. Calculations are performed for binding energy shifts to the lowest valence s, p, and d waves over the series of alkali atoms Na to E119. The high accuracy of the radiative potential method is demonstrated by comparison with rigorous QED calculations in frozen atomic potentials, with deviations on the level of 1%. The many-body effects of core relaxation and second- and higher-order perturbation theory on the interaction of the valence electron with the core are calculated. The inclusion of many-body effects tends to increase the size of the shifts, with the enhancement particularly significant for d waves; for K to E119, the self-energy shifts for d waves are only an order of magnitude smaller than the s-wave shifts. It is shown that account of many-body effects is essential for an accurate description of the Lamb shift.

Polarization response in extreme nonlinear optics: when can the semiclassical approach be used?

Availability of the semiclassical approach in strong-field physics and extreme nonlinear optics is analyzed. It is found that it is valid for calculation of the emission to the initially populated bound state only if population of this state is close to unity during the pulse and in the after pulse regime. If the initial level is depleted, the semiclassical approach fails and should be replaced by quantum-electrodynamical calculations. Also it is demonstrated that the bremsstrahlung spectrum cannot be correctly described in the frames of the semiclassical approach.

Testing helicity-dependentγγ→γγscattering in the region of MeV

Light-by-light scatterings contain rich information on the photon coupling to virtual and real particle states. In the context of quantum electrodynamics (QED), photons can couple to a virtual $e^+e^-$ pair. Photons may also couple to known resonance states in the context of quantum chromodyanmics and electroweak dynamics in higher energy domains and possibly couple to unknown resonance states beyond the starndard model. The perturbative QED calculations manifestly predict the maximized cross section at the MeV scale, however, any example of the exact real-photon - real-photon scattering has not been observed hitherto. Hence, we propose the direct measurement with the maximized cross-section at the center-of-mass system energy of 1-2 MeV to establish the firm footing at the MeV scale. Given currently state-of-the-art high power lasers, the helicity dependent elastic scattering may be observed at a reasonable rate, if a photon-photon collider exploiting $\gamma$-rays generated by the inverse nonlinear Compton process with electrons delivered from laser-plasma accelerators (LPA) are properly designed. We show that such verification is feasible in a table-top scale collider which may be an unprecedented breakthrough in particle accelerators for basic physics research in contrast to energy frontier colliders.

Lamb Shift of n = 1 and n = 2 States of Hydrogen-like Atoms, 1 ≤ Z ≤ 110

Theoretical energy levels of the n = 1 and n = 2 states of hydrogen-like atoms with the nuclear charge numbers 1 ≤ Z ≤ 110 are tabulated. The tabulation is based on ab initio quantum electrodynamics calculations performed to all orders in the nuclear binding strength parameter Zα, where α is the fine structure constant. Theoretical errors due to various effects are critically examined and estimated.

Single-photon excitation ofKαin heliumlikeKr34+: Results supporting quantum electrodynamics predictions

We study two fundamental transitions from the ground state $^{1}S_{0}$ to $^{1}P_{1}$ ($w$ line) and $^{3}P_{1}$ ($y$ line) in heliumlike ${\mathrm{Kr}}^{34+}$ by resonant single-photon excitation using an electron-beam ion trap and monochromatic x rays at PETRA III. Our results for the transition energies $E(w)=13\phantom{\rule{0.16em}{0ex}}114.47(14)$ eV and $E(y)=13\phantom{\rule{0.16em}{0ex}}026.15(14)$ eV are in excellent agreement with quantum electrodynamics calculations, but disagree for $w$ with the average of the hitherto reported experimental results ${\overline{E}}_{\mathrm{Lit}}(w)=13\phantom{\rule{0.16em}{0ex}}115.15(17)$ eV. Independently of any energy calibration, we obtain a value $E(w)/E(y)=1.006\phantom{\rule{0.16em}{0ex}}780(7)$, also in consistency with predictions.

Theory of Lamb Shift in Muonic Hydrogen

There has been for a while a large discrepancy between the values of the proton charge radius measured by the Lamb shift in muonic hydrogen and by other methods. It has already been clear that theory of muonic hydrogen is reliable at the level of this discrepancy and an error there cannot be a reason for the contradiction. Still the status of theory at the level of the uncertainty of the muonic-hydrogen experiment (which is two orders of magnitude below the discrepancy level) requires an additional clarification. Here, we revisit theory of the 2p − 2s Lamb shift in muonic hydrogen. We summarize all the theoretical contributions in order α5m, including pure quantum electrodynamics (QED) ones as well as those which involve the proton-structure effects. Certain enhanced higher-order effects are also discussed. We basically confirm former QED calculations of other authors, present a review of recent calculations of the proton-structure effects, and treat self-consistently higher-order proton-finite-size corrections. We also overview theory of the 2p states. Eventually, we derive a value of the root-mean-square proton charge radius. It is found to be 0.840 29(55) fm, which is slightly different from that previously published in the literature (0.840 87(39) fm [Antognini et al., Science 339, 417 (2013)]).

First test of O(α) correction on the energy spectrum in the orthopositronium decay

Positronium(Ps) is an ideal system for the precision test of quantum electrodynamics (QED) in bound state. Orthopositronium(o-Ps) decays into three gamma rays dominantly, and their energy spectrum has detail information on bound-state QED. The purpose of this study is to check the spectrum at the O(α) level accuracy. We constructed a setup for the precise measurement. Ps is created at silica aerogel in a vacuum chamber, and its decay gamma rays are measured with a LaBr3 (Ce) scintillator. In this setup, the materials around the Ps assembly and the detector are well-controlled, and all their responses are coded in a GEANT4 simulator in detail. After the measurement for 100 days, the obtained spectrum is compared with the expected spectrum from the QED calculations and the GEANT4 simulator. The obtained spectrum is consistent with O(a) calculation and excludes the lowest- order calculation at 92% C.L.

Constraints on extra dimensions from precision molecular spectroscopy

Accurate investigations of quantum-level energies in molecular systems are shown to provide a testing ground to constrain the size of compactified extra dimensions. This is made possible by recent progress in precision metrology with ultrastable lasers on energy levels in neutral molecular hydrogen (H2, HD, and D2) and molecular hydrogen ions (H2+, HD+, and D2+). Comparisons between experiment and quantum electrodynamics calculations for these molecular systems can be interpreted in terms of probing large extra dimensions, under which conditions gravity will become much stronger. Molecules are a probe of spacetime geometry at typical distances where chemical bonds are effective (i.e., at length scales of an Å). Constraints on compactification radii for extra dimensions are derived within the Arkani-Hamed-Dimopoulos-Dvali framework, while constraints for curvature or brane separation are derived within the Randall-Sundrum framework. Based on the molecular spectroscopy of D2 molecules and HD+ ions, the compactification size for seven extra dimensions (in connection to M-theory defined in 11 dimensions) of equal size is shown to be limited to . While limits on compactification sizes of extra dimensions based on other branches of physics are compared, the prospect of further tightening constraints from the molecular method is discussed.

High-Precision Spectroscopy of the Forbidden2 S13→2 P11Transition in Quantum Degenerate Metastable Helium

We have measured the forbidden 2 (3)S(1)→2 (1)P(1) transition at 887 nm in a quantum degenerate gas of metastable (4)He atoms confined in an optical dipole trap. The determined transition frequency is 338 133 594.4 (0.5) MHz, from which we obtain an ionization energy of the 2 (1)P(1) state of 814 709 148.6 (0.5) MHz. This ionization energy is in disagreement by >3σ with the most accurate quantum electrodynamics calculations available. Our measurements also provide a new determination of the lifetime of the 2 (1)P(1) state of 0.551 (0.004)(stat) ((-0.000)(+0.013))(syst) ns, which is the most accurate determination to date and in excellent agreement with theory.

Development of many‐body perturbation theory: How to combine with quantum electrodynamics

In the first part, a review is made of the development of the many‐body perturbation theory for the last half century. The development of methods for quantum electrodynamics (QED) calculations, which have occurred essentially in parallel, is also briefly reviewed. In the second part, an effort of unifying the two is discussed. The covariant‐evolution‐operator method, developed primarily for QED calculations by the Gothenburg group, can be combined with atomic/molecular many‐body perturbation theory (MBPT) and for the first time making it possible to combine full QED with electron correlation of arbitrary order. The basic idea is to extend the standard procedure of MBPT to a time‐ or energy‐dependent formalism, which makes it possible to include QED perturbations in a rigorous fashion. The procedure has been implemented and as a first test applied to helium like ions. The method can also be applied to dynamical processes. © 2014 Wiley Periodicals, Inc.

Precision Spectroscopy of Atomic Hydrogen

Precise determinations of transition frequencies of simple atomic systems are required for a number of fundamental applications such as tests of quantum electrodynamics (QED), the determination of fundamental constants and nuclear charge radii. The sharpest transition in atomic hydrogen occurs between the metastable 2S state and the 1S ground state. Its transition frequency has now been measured with almost 15 digits accuracy using an optical frequency comb and a cesium atomic clock as a reference [1]. A recent measurement of the 2S – 2P3/2 transition frequency in muonic hydrogen is in significant contradiction to the hydrogen data if QED calculations are assumed to be correct [2, 3]. We hope to contribute to this so-called "proton size puzzle" by providing additional experimental input from hydrogen spectroscopy.

A step toward probing higher-order Feynman diagrams in few-electron highly charged ions

The Lamb shift in medium-heavy H-like and He-like ions has been determined with unprecedented accuracy with a novel x-ray spectroscopy technique. Absolute wavelength measurements of emission lines from trapped highly charged Ar ions thereby achieved uncertainties down to the range of 1.6–2.4 ppm. For the H-like ion Ar17+, the ground state Lamb shift is determined with a 0.4% accuracy, thus excellently confirming quantum electrodynamics (QED) calculations and therefore the hitherto implied suitability of lines from these ionic species as absolute and accurate standards in the x-ray region. Second-order QED terms, i.e. two-electron terms, are also probed for the He-like species Ar16+. Deviations from QED predictions that have recently been claimed are excluded with high significance by the present results.

TWO-PHOTON LASER SPECTROSCOPY OF ANTIPROTONIC HELIUM

The ASACUSA collaboration of CERN has recently carried out two-photon laser spectroscopy of antiprotonic helium atoms. Some nonlinear two-photon transitions of the antiproton at the deep UV wavelengths λ = 139.8–197.0 nm were excited by irradiating the atom with two counterpropagating laser beams. This reduced the thermal Doppler broadening in the observed spectral lines. Three transition frequencies were thus determined with fractional precisions of 2.3–5 parts in 109. By comparing the results with three-body quantum electrodynamics calculations, the antiproton-to-electron mass ratio was derived as 1836.1526736(23). In this paper, we briefly review these recent experimental results.