Tests Of Quantum Electrodynamics Research Articles

Precision Measurement of the n=2 Triplet P J=1 to J=0 Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields.

Increasing accuracy of the theory and experiment of the n=2 ^{3}P fine structure of helium has allowed for increasingly precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant α, and limitations on possible beyond the standard model physics. Here we present a 2ppb measurement of the J=1 to J=0 interval. The measurement is performed using frequency-offset separated-oscillatory fields. Our result of 29 616 955 018(60)Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved.

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.

Fitting for the energy levels of hydrogen

Atomic hydrogen energy levels calculated to high precision are required to assist experimental researchers working on spectroscopy in the pursuit of testing quantum electrodynamics (QEDs) and probing for physics beyond the Standard Model. There are two important parts to the problem of computing these levels: an accurate evaluation of contributions from QED and using an accurate value for the proton charge radius as an input. Recent progress on QED corrections to the fine structure, as well as increasing evidence that a proton charge radius in the range of 0.84 fm is favored over the previously adopted larger value in the 0.88 fm range, has advanced the field, yet several state-of-the-art measurements remain in contradiction with this smaller value. Motivated by on-going and future work in this area, we present here a simple parameterization for the energy levels of hydrogen at the level of hyperfine structure using the so-called relativistic Ritz approach. The fitting of a finite sample of QED-generated levels at low to intermediate principal quantum number, n, gives a generally applicable formula for all values of n for each distinct angular momentum channel, given in this work up to orbital angular momentum number . We also provide a simple linear parameterization for the shift in hydrogen energy levels as a function of the proton radius, providing a useful cross check for extant and future measured energy intervals.

Stimulated Raman scattering metrology of molecular hydrogen

Frequency combs have revolutionized optical frequency metrology, allowing one to determine highly accurate transition frequencies of a wealth of molecular species. These progresses have only marginally benefited infrared-inactive transitions, due to their inherently weak cross-sections. Here we overcome this limitation by introducing stimulated-Raman-scattering metrology, where a frequency comb is exploited to calibrate the frequency detuning between the pump and Stokes excitation lasers. We apply this approach to the investigation of molecular hydrogen, which is a recognized benchmark for tests of quantum electrodynamics and of theories that describe physics beyond the standard model. Specifically, we measure the transition frequency of the Q(1) fundamental line of H2 around 4155 cm−1 with few parts-per-billion uncertainty, which is comparable to the theoretical benchmark of ab initio calculations and more than a decade better than the experimental state of the art. Our comb-calibrated stimulated Raman scattering spectrometer extends the toolkit of optical frequency metrology as it can be applied, with simple technical changes, to many other infrared-inactive transitions, over a 50-5000 cm−1 range that covers also purely rotational bands.

Toward XUV frequency comb spectroscopy of the 1 S–2 S transition in hbox {He}^+

The energy levels of hydrogen-like atoms and ions are accurately described by bound-state quantum electrodynamics (QED). hbox {He}^{+} ions have a doubly charged nucleus, which enhances the higher-order QED contributions and makes them interesting for precise tests of QED. Systematic effects that currently dominate the uncertainty in hydrogen spectroscopy, such as the second-order Doppler shift and time-of-flight broadening, are largely suppressed by performing spectroscopy on trapped and cooled hbox {He}^{+} ions. Measuring a transition in hbox {He}^{+} will extend the test of QED beyond the long-studied hydrogen. In this article, we describe our progress toward precision spectroscopy of the 1 S–2 S two-photon transition in hbox {He}^{+}. The transition can be excited by radiation at a wavelength of 60.8 nm generated by a high-power infrared frequency comb using high-order harmonic generation (HHG). The hbox {He}^{+} ions are trapped in a Paul trap and sympathetically cooled with laser-cooled hbox {Be}^{+} ions. Our recently developed signal detection scheme based on secular-scan spectrometry is capable of detecting hbox {He}^{+} excitation with single-event sensitivity.Graphic abstract

Lack of hyperfine shifts in Doppler-limited spectra of molecular hydrogen

Accurate spectroscopy of molecular hydrogen isotopologues is used for testing quantum electrodynamics and searching for physics beyond the standard model. Recent measurements of energies of rovibrational resonances in the ground electronic state have reached a level of uncertainty lower than the magnitude of the hyperfine splitting. The underlying hyperfine components of the resonance clearly perturb sub-Doppler saturation spectra. The extent to which hyperfine structure influences the Doppler-limited spectra is not fully understood, as there are two contradicting experimental works that show either a 350 kHz shift or lack of any deviation from the central frequency of the resonance in the HD molecule. Here, we address this problem theoretically. Using the spherical tensor approach, we prove that the barycenter of all hyperfine-resolved spectra corresponds to the unperturbed transition frequency (the first moment of the hyperfine-resolved spectra vanishes). This property is directly transferred to Doppler-limited spectra: we show that there is no detectable shift due to the hyperfine structure unless the ratio of the Doppler width to the root-mean-square hyperfine splitting is less than 50.

Prospect for attosecond laser spectra of highly charged ions

The spectra of highly charged ions (HCIs) are of great significance for astronomical observation, astrophysical model establishment, and test of quantum electrodynamics (QED) theory. However, the transitions of HCI are mostly in the extreme ultraviolet or even X-ray range, the excitation spectra of HCI measured by laser spectroscopy in laboratory are very limited due to lack of the suitable light source. Up to now, only few experiments on the spectra of HCIs performed on synchrotron radiation, free electron laser or heavy-ions storage ring have been reported, which are summarized in this work. With the development of attosecond technology, several attosecond light source facilities have been built, such as extreme light infrastructure attosecond light pulse source (ELI-ALPS) and synergetic extreme condition user facility (SECUF), which have high photon energy and ultra-short pulse duration in the extreme ultraviolet and even soft X-ray range, providing new opportunities for laboratory research on HCI spectra and ultra short energy level lifetimes. Electron beam ion trap (EBIT), electron cyclotron resonance (ECR), and heavy-ion storage ring are usually used to generate ion target. But it is difficult to combine the attosecond laser source with large scale facility of HCI, for none of laboratories has both these two facilities now. Thus, two possible experimental schemes for attosecond spectrum of HCIs are proposed in this work. One scheme is that an EBIT can be designed as a terminal of attosecond laser facility, such as ELI-ALPS and SECUF, which can output different laser beams with high photon energy, ultra-short pulse duration or high flux. Another scheme is that a table-top HHG system pumped by an all-solid-state femtosecond laser or fiber femtosecond laser with high power can be combined with heavy-ion storage ring, such as ESR, CSRe, HIAF, and FAIR. Owing to high energy of ions in storage ring, the measurable energy levels of HCIs can even be extended to keV by the Doppler shift. Three different measurement methods: fluorescence detection, ion detection and attosecond absorption spectroscopy, can be used to obtain the HCI spectrum. Finally, a preliminary experimental setup for attosecond laser spectrum of HCI is proposed. The proposal on combining extreme ultraviolet attosecond light source with HCI target is discussed, and the feasibility of attosecond time-resolved precision spectrum for HCI is analyzed according to the typical parameters of attosecond light source and the known excitation cross-section and detection efficiency, which can provide a new platform for implementing ion level structure calculation, QED theory high-precision test and astronomical spectroscopic observation. It can be used to measure the ultra-short lifetime, low excitation cross-section ionic energy level, and even some transitions with large energy interval. We hope that this work can provide a reference for the experimental measuring of HCI spectrum and ion energy level lifetime in future.

Scientific Opportunities at the ARIEL Electron Linac

This paper gives an overview of the scientific opportunities at the ARIEL electron accelerator identified in open discussion at the workshop, including applications in hadron structure, astrophysical processes, tests of quantum electrodynamics, dark matter and other BSM physics, and material science.

Measurement of a helium tune-out frequency: an independent test of quantum electrodynamics.

Despite quantum electrodynamics (QED) being one of the most stringently tested theories underpinning modern physics, recent precision atomic spectroscopy measurements have uncovered several small discrepancies between experiment and theory. One particularly powerful experimental observable that tests QED independently of traditional energy level measurements is the "tune-out" frequency, where the dynamic polarizability vanishes and the atom does not interact with applied laser light. In this work, we measure the tune-out frequency for the 23S1 state of helium between transitions to the 23P and 33P manifolds and compare it with new theoretical QED calculations. The experimentally determined value of 725,736,700(260) megahertz differs from theory [725,736,252(9) megahertz] by 1.7 times the measurement uncertainty and resolves both the QED contributions and retardation corrections.

Towards perfectly linearly polarized x-rays

In recent years, high-precision x-ray polarimeters have become a key method for the investigation of fundamental physical questions from solid-state physics to quantum optics. Here, we report on the verification of a polarization purity of better than $8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ at an x-ray free-electron laser, which implies a suppression of the incoming photons to the noise level in the crossed polarizer setting. This purity provides exceptional sensitivity to tiny polarization changes and offers intriguing perspectives for fundamental tests of quantum electrodynamics.

Improved ionization and dissociation energies of the deuterium molecule

The ionization energy of D$_2$ has been determined experimentally from measurements involving two-photon Doppler-free vacuum-ultraviolet pulsed laser excitation and near-infrared continuous-wave laser excitation to yield $E_\mathrm{I}(\mathrm{D}_2)=124\,745.393\,739(26)$ \wn. From this value, the dissociation energy of D$_2$ is deduced to be $D_0$(D$_2$) = 36\,748.362\,282(26) \wn, representing a 25-fold improvement over previous values, and found in good agreement (at $1.6\sigma$) with recent ab initio calculations of the 4-particle nonadiabatic relativistic energy and of quantum-electrodynamic corrections up to order $m\alpha^6$. This result constitutes a test of quantum electrodynamics in the molecular domain, while a perspective is opened to determine nuclear charge radii from molecules.

Benchmark Calculations of the Energy Spectra and Oscillator Strengths of the Beryllium Atom

In this work, we present a series of benchmark variational calculations for the ground and 19 lowest bound excited singlet S and P states of the beryllium atom. The nonrelativistic wave functions of the states that represent the motion of the nucleus and the four electrons around the center of mass of the atom are expanded in terms of up to 17 000 all-particle explicitly correlated Gaussians. The Gaussians are optimized independently for each state. The leading relativistic corrections to the energy levels are computed in the framework of the perturbation theory and they explicitly include the nuclear recoil effects. We also calculate the leading quantum electrodynamics (QED) corrections for each considered state. Using the obtained energy levels and the corresponding wave functions, we compute the transition frequencies, transition dipole moments, and oscillator strengths. A comparison with the available experimental data shows very good agreement. The results of this most comprehensive set of calculations of spectroscopic accuracy for Be to date may open up new applications pertinent to the precision tests of QED, determination of the nuclear charge radius, and modeling matter-radiation equilibria of the beryllium gas that has relevance to the physics of interstellar media.

Atom-surface physics: A review

An atom in front of a surface is one of the simplest and fundamental problem in physics. Yet, it allows testing quantum electrodynamics, while providing potential platforms and interfaces for quantum technologies. Despite its simplicity, combined with strong scientific and technological interests, atom-surface physics, at its fundamental level, remains largely unexplored mainly because of challenges associated with precise control of the atom-surface distance. Nevertheless, substantial breakthroughs have been made over the last two decades. With the development of cold and quantum atomic gases, one has gained further control on atom-surface position, naturally leading to improved precision in the Casimir–Polder interaction measurement. Advances have also been reported in finding experimental knobs to tune and even reverse the Casimir–Polder interaction strength. So far, this has only been achieved for atoms in short-lived excited states, however, the rapid progresses in material sciences, e.g., metamaterials and topological materials has inspired new ideas for controlling the atom-surface interaction in long-lived states. In addition, combining nano-photonic and atom-surface physics is now envisioned for applications in quantum information processing. The first purpose of this Review is to give a general overview on the latest experimental developments in atom-surface physics. The second main objective is to sketch a vision of the future of the field, mainly inspired by the abundant theoretical works and proposals available now in the literature.

Hyperfine structure of the EFΣg+1 state in H2

Calculations of hyperfine splittings in ${\mathrm{H}}_{2}$ are needed for an accurate experimental determination of frequencies of rovibrational transitions and the dissociation energy in ${\mathrm{H}}_{2}$, which are used for experimental tests of quantum electrodynamics for molecules and for searches for new physics beyond the standard model. While the hyperfine structure of the ground electronic $X^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ state in ${\mathrm{H}}_{2}$ has been studied in detail, there are no theoretical or experimental data regarding the excited electronic $^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ states. Here, we report the first investigation of the hyperfine structure of rovibrational levels in the excited double-well $EF^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$ state in the hydrogen molecule. We provide hyperfine splittings and coupling constants for several low-lying rovibrational levels. The hyperfine splittings in the inner well are approximately 1 order of magnitude larger than those in the outer well and 2 times smaller than those in the ground electronic state.

Three-body QED test and fifth-force constraint from vibrations and rotations of HD+

We present a parts-per-million test of quantum electrodynamics (QED) in the HD + molecular hydrogen ion, improving on previous tests based on vibrational and rotational transitions by factors of 76 and 1.4, respectively. The test is performed following a unified statistical approach that also produces improved constraints on physics beyond the standard model. We furthermore show how individual constraints derived from the various degrees of freedom in HD + and antiprotonic helium can be combined to enhance the sensitivity, thus ruling out “fifth forces” on the Angstrom scale that are 10 11 times weaker than the electromagnetic interaction.

Hyperfine structure of rovibrational quadrupole transitions in HD

We perform a theoretical investigation of hyperfine structure of all rovibrational quadrupole transitions in the ground electronic 1Σ+ state of the HD molecule. We determine positions and intensities of 185 631 hyperfine components of 7 251 quadrupole rovibrational transitions from the O, Q and S branches. Moreover, we provide a list of hyperfine splittings of all bound states in the six isotopologues of hydrogen which we considered in previous papers. The results reported here are necessary for a reliable interpretation of accurate experimental studies of rovibrational transition frequencies in the HD isotopologue, which are useful for tests of quantum electrodynamics for molecules and searches for new physics beyond the Standard Model.

Testing Quantum Electrodynamics with Exotic Atoms.

Precision study of few-electron, high-Z ions is a privileged field for probing high-field, bound-state quantum electrodynamics (BSQED). However, the accuracy of such tests is plagued by nuclear uncertainties, which are often larger than the BSQED effects under investigation. We propose an alternative method with exotic atoms and show that transitions may be found between circular Rydberg states where nuclear contributions are vanishing while BSQED effects remain large. When probed with newly available quantum sensing detectors, these systems offer gains in sensitivity of 1 to 2 orders of magnitude, while the mean electric field largely exceeds the Schwinger limit.

Hyperfine components of rovibrational dipole transitions in HT and DT

We report a list of positions and intensities of 331 892 hyperfine components of all 18 585 rovibrational dipole transitions in the HT and DT isotopologues of molecular hydrogen. Apart from the study of hyperfine structure, we investigate the intensities of all rovibrational dipole transitions in the two isotopologues, which were not known prior to this work. The results presented here are crucial for a reliable interpretation of accurate measurements of rovibrational transition frequencies in the tritium-bearing isotopologues of hydrogen, which are useful for tests of quantum electrodynamics for molecules and searches for new physics beyond the Standard Model.

Hadronic vacuum-polarization contribution to various QED observables

Due to precision tests of quantum electrodynamics (QED), determination of accurate values of fundamental constants, and constraints on new physics, it is important in a consistent way to evaluate a number of QED observables such as the Lamb shift in hydrogen-like atomic systems. Even in a pure leptonic case, those QED variables are in fact not pure QED ones since hadronic effects are involved through intermediate states while accounting for higher-order effects. One of them is hadronic vacuum polarization (hVP). Complex evaluations often involve a number of QED quantities, for which treatment of hVP is not consistent. The highest accuracy for a calculation of the hVP term is required for the anomalous magnetic moment of a muon. However, a standard data-driven treatment of hVP, based on a dispersion integration of experimental data on electron-positron annihilation to hadrons and some other phenomena, leads to a contradiction with the experimental value of a_mu . This experimental value can be considered as an indirect determination of the hVP contribution to a_mu and the scatter of theory and experiment allows one to obtain a conservative estimation of the related hVP contribution. In this paper, we derive exact and approximate relations between the leading-order (LO) hVP contributions to various observables. Using those relations, we obtain for them a consistent set of the results, based on the scatter of a_mu values. While calculating the LO hVP term, we have to remember that next-to-LO (NLO) hVP corrections are often comparable with the uncertainty of the LO term. Special attention is payed to hVP contribution to simple atoms. In particular, we discuss the NLO contribution to the Lamb shift in ordinary and muonic hydrogen and other two-body atoms for Zle 10. We also consider the NLO contribution of the muonic vacuum polarization to the Lamb shift in hydrogen-like atoms. With the a_mu puzzle unresolved, one may still require present-days values of the hVP contributions to various observable for comparison to experiment etc. the presence of contradicting values and a lack of consistency means an additional uncertainty for a_mu and for key contributions to it, including the LO hVP one. We present here an estimation of such a propagated uncertainty in hVP contributions to different QED observables and recommend a consistent set of the related LO hVP contributions.Graphic

Hyperfine structure of ro-vibrational transition of HD in magnetic field

The precise measurement of the infrared transition of hydrogen-deuterium (HD) molecule is used to test quantum electrodynamics and determine the proton-to-electron mass ratio. The saturated absorption spectrum of the R(1) line in the first overtone (2–0) band of HD molecule has been measured by the comb locked cavity ring-down spectroscopy (CRDS) method in Hefei [Tao L G, et al. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1103/PhysRevLett.120.153001"> 2018 <i>Phys. Rev. Lett.</i> <b>120</b> 153001</ext-link>], and also by the noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) method in Amsterdam [Cozijn F M J, et al. <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1103/PhysRevLett.120.153002">2018 <i>Phys. Rev. Lett.</i> <b>120</b> 153002 </ext-link>]. However, there is a significant difference between the line center positions obtained in these two studies. Later the discrepancy was found to be due to unexpected asymmetry in the line shape of the saturated absorption spectrum of the HD molecule. A possible reason is the superposition of multiple hyperfine splitting peaks in the saturated spectrum. However, this model strongly depends on the population transfer caused by intermolecular collisions, which is a lack of experimental and theoretical support. In this paper, the hyperfine structures of the ro-vibrational transition of HD are calculated in the coupled and uncoupled representations. The hyperfine structures of the R(0), P(1) and R(1) lines in the (2–0) band of HD molecule under different external magnetic fields are calculated. The corresponding spectral structures at a temperature of 10 K are simulated. The results show that the transition structure of HD molecule changes significantly with the externally applied magnetic field. The frequency shift of each hyperfine transition line also increases with the intensity of external magnetic field increasing. When the intensity of the external magnetic field is sufficiently high, the hyperfine lines are clearly divided into two branches, and they can be completely separated from each other. Because the dynamic effect of intermolecular collision and the energy level population transfer are very sensitive to the energy level structure, the comparison between experiment and theory will help us to analyze the mechanism of the observed special profiles. It will allow us to obtain accurate frequencies of these transitions, which can be used for testing the fundamental physics.