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There is a growing interest in high-precision spectroscopy and frequency metrology for fundamental studies using sympathetically cooled highly charged ions (HCIs) embedded in Coulomb crystals of laser-cooled ions. In order to understand how their strong repulsion affects the crystal structure and dynamics, we study the thermal motion and rearrangement of small mixed linear and homogeneous crystals by both measurements and simulations. Co-crystallized HCIs form superlattices and divide the crystal into domains, where different reordering rates, melting points and localized phase transitions are observed due to decoupling of motional modes across boundaries. These results improve our understanding of homogeneous and inhomogeneous ion strings over a wide range of charge-to-mass ratios. This allows us to test our own simulations of the dynamic behavior of ion strings and gives us confidence in their suitability for applications related to quantum simulation as well as computing and the search for new physics., Comment: 19 pages, 15 figures

We propose In-like Pr10+ as a candidate for the development of a high-accuracy optical clock with high sensitivity to a time variation of the fine-structure constant, (\dot alpha}/alpha, as well as favorable experimental systematics. We calculate its low-lying energy levels by combining the configuration interaction and the coupled cluster method, achieving uncertainties as low as 0.1%, and improving previous work. We benchmark these results by comparing our calculations for the (5s^2 5p 2P_1/2) - (5s^2 5p 2P_3/2) transition in Pr10+ with a dedicated measurement and for Pr9+ with a recent experiment, respectively. In addition, we report calculated hyperfine-structure constants for the clock and logic states in Pr10+., Comment: 9 pages, 2 figures

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond $10^{15}\,\text{V}/\text{cm}$ for the innermost electrons. 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 last decades. Another approach is the measurement of $g$ factors in highly charged ions. However, so far, either experimental accuracy or small field strength in low-$Z$ ions limited the stringency of these QED tests. Here, we report on our high-precision, high-field test of QED in hydrogenlike $^{118}$Sn$^{49+}$. The highly charged ions were produced with the Heidelberg-EBIT (electron beam ion trap) and injected into the ALPHATRAP Penning-trap setup, where the bound-electron $g$ factor was measured with a precision of 0.5 parts-per-billion. 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 via the Lamb shift and, with anticipated advances in the $g$-factor theory, surpass them by more than an order of magnitude.

The last decade has seen unprecedented effort in dark matter model building at all mass scales coupled with the design of numerous new detection strategies. Transformative advances in quantum technologies have led to a plethora of new high-precision quantum sensors and dark matter detection strategies for ultralight ($<10\,$eV) bosonic dark matter that can be described by an oscillating classical, largely coherent field. This white paper focuses on searches for wavelike scalar and vector dark matter candidates., Comment: Snowmass 2021 White Paper

A key requirement for the correct interpretation of high-resolution X-ray spectra is that transition energies are known with high accuracy and precision. We investigate the K-shell features of Ne, CO$_2$, and SF$_6$ gases, by measuring their photo ion-yield spectra at the BESSY II synchrotron facility simultaneously with the 1s-np fluorescence emission of He-like ions produced in the Polar-X EBIT. Accurate ab initio calculations of transitions in these ions provide the basis of the calibration. While the CO$_2$ result agrees well with previous measurements, the SF$_6$ spectrum appears shifted by ~0.5 eV, about twice the uncertainty of the earlier results. Our result for Ne shows a large departure from earlier results, but may suffer from larger systematic effects than our other measurements. The molecular spectra agree well with our results of time-dependent density functional theory. We find that the statistical uncertainty allows calibrations in the desired range of 1-10 meV, however, systematic contributions still limit the uncertainty to ~40-100 meV, mainly due to the temporal stability of the monochromator energy scale. Combining our absolute calibration technique with a relative energy calibration technique such as photoelectron energy spectroscopy will be necessary to realize its full potential of achieving uncertainties as low as 1-10 meV., Comment: 13 pages, 7 figures

The detection of variations of fundamental constants of the Standard Model would provide us with compelling evidence of new physics, and could lift the veil on the nature of dark matter and dark energy. In this work, we discuss how a network of atomic and molecular clocks can be used to look for such variations with unprecedented sensitivity over a wide range of time scales. This is precisely the goal of the recently launched QSNET project: A network of clocks for measuring the stability of fundamental constants. QSNET will include state-of-the-art atomic clocks, but will also develop next-generation molecular and highly charged ion clocks with enhanced sensitivity to variations of fundamental constants. We describe the technological and scientific aims of QSNET and evaluate its expected performance. We show that in the range of parameters probed by QSNET, either we will discover new physics, or we will impose new constraints on violations of fundamental symmetries and a range of theories beyond the Standard Model, including dark matter and dark energy models.

We present a novel ultrastable superconducting radio-frequency (RF) ion trap realized as a combination of an RF cavity and a linear Paul trap. Its RF quadrupole mode at 34.52 MHz reaches a quality factor of $Q\approx2.3\times 10^5$ at a temperature of 4.1 K and is used to radially confine ions in an ultralow-noise pseudopotential. This concept is expected to strongly suppress motional heating rates and related frequency shifts which limit the ultimate accuracy achieved in advanced ion traps for frequency metrology. Running with its low-vibration cryogenic cooling system, electron beam ion trap and deceleration beamline supplying highly charged ions (HCI), the superconducting trap offers ideal conditions for optical frequency metrology with ionic species. We report its proof-of-principle operation as a quadrupole mass filter with HCI, and trapping of Doppler-cooled ${}^9\text{Be}^+$ Coulomb crystals., Comment: 16 pages, 19 figures

We have developed an extreme ultraviolet (XUV) frequency comb for performing ultra-high precision spectroscopy on the many XUV transitions found in highly charged ions (HCI). Femtosecond pulses from a 100 MHz phase-stabilized near-infrared frequency comb are amplified and then fed into a femtosecond enhancement cavity (fsEC) inside an ultra-high vacuum chamber. The low-dispersion fsEC coherently superposes several hundred incident pulses and, with a single cylindrical optical element, fully compensates astigmatism at the $w_0=15\mu$m waist cavity focus. With a gas jet installed there, intensities reaching $\sim10^{14}$ W/cm$^2$ generate coherent high harmonics with a comb spectrum at 100 MHz rate. We couple out of the fsEC harmonics from the 7th up to the 35th (42 eV; 30 nm) to be used in upcoming experiments on HCI frequency metrology., Comment: 12 pages, 6 figures

Electron beam ion traps (EBIT) are ideal tools for both production and study of highly charged ions (HCI). In order to reduce their construction, maintenance, and operation costs we have developed a novel, compact, room-temperature design, the Heidelberg Compact EBIT (HC-EBIT). Four already commissioned devices operate at the strongest fields (up to 0.86 T) reported for such EBITs using permanent magnets, run electron beam currents up to 80 mA and energies up to 10 keV. They demonstrate HCI production, trapping, and extraction of pulsed Ar$^{16+}$ bunches and continuous 100 pA ion beams of highly charged Xe up to charge state 29+, already with a 4 mA, 2 keV electron beam. Moreover, HC-EBITs offer large solid-angle ports and thus high photon count rates, e. g., in x-ray spectroscopy of dielectronic recombination in HCIs up to Fe$^{24+}$, achieving an electron-energy resolving power of $E/\Delta E > 1500$ at 5 keV. Besides traditional on-axis electron guns, we have also implemented a novel off-axis gun for laser, synchrotron, and free-electron laser applications, offering clear optical access along the trap axis. We report on its first operation at a synchrotron radiation facility demonstrating resonant photoexcitation of highly charged oxygen., Comment: 20 pages, 18 figures, 1 table

Precision spectroscopy of atomic systems is an invaluable tool for the advancement of our understanding of fundamental interactions and symmetries. Recently, highly charged ions (HCI) have been proposed for sensitive tests of physics beyond the Standard Model and as candidates for high-accuracy atomic clocks. However, the implementation of these ideas has been hindered by the parts-per-million level spectroscopic accuracies achieved to date. Here, we cool a trapped HCI to the lowest reported temperatures, and introduce coherent laser spectroscopy on HCI with an eight orders of magnitude leap in precision. We probe the forbidden optical transition in $^{40}$Ar$^{13+}$ at 441 nm using quantum-logic spectroscopy and measure both its excited-state lifetime and $g$-factor. Our work ultimately unlocks the potential of HCI, a large, ubiquitous atomic class, for quantum information processing, novel frequency standards, and highly sensitive tests of fundamental physics, such as searching for dark matter candidates or violations of fundamental symmetries., Comment: Accepted manuscript

We demonstrate a widely applicable technique to absolutely calibrate the energy scale of x-ray spectra with experimentally well-known and accurately calculable transitions of highly charged ions, allowing us to measure the K-shell Rydberg spectrum of molecular O$_2$ with 8 meV uncertainty. We reveal a systematic $\sim$450 meV shift from previous literature values, and settle an extraordinary discrepancy between astrophysical and laboratory measurements of neutral atomic oxygen, the latter being calibrated against the aforementioned O$_2$ literature values. Because of the widespread use of such, now deprecated, references, our method impacts on many branches of x-ray absorption spectroscopy. Moreover, it potentially reduces absolute uncertainties there to below the meV level., Comment: Accepted by PRL. Main article: 7 pages, 3 figures. Supplemental Material: 3 pages, 5 figures

Recent theoretical works have proposed atomic clocks based on narrow optical transitions in highly charged ions. The most interesting candidates for searches of new physics are those which occur at rare orbital crossings where the shell structure of the periodic table is reordered. There are only three such crossings expected to be accessible in highly charged ions, and hitherto none have been observed as both experiment and theory have proven difficult. In this work we observe an orbital crossing in highly charged ions for the first time, in a system chosen to be tractable from both sides: Pr$^{9+}$. We present electron beam ion trap measurements of its spectra, including the inter-configuration lines that reveal the sought-after crossing. The proposed nHz-wide clock line, found to be at 452.334(1) nm, proceeds through hyperfine admixture of its upper state with an E2-decaying level. With state-of-the-art calculations we show that it has a very high sensitivity to new physics and extremely low sensitivity to external perturbations, making it a unique candidate for proposed precision studies., Comment: Director's Cut

In-vacuo cryogenic environments are ideal for applications requiring both low temperatures and extremely low particle densities. This enables reaching long storage and coherence times for example in ion traps, essential requirements for experiments with highly charged ions, quantum computation, and optical clocks. We have developed a novel cryostat continuously refrigerated with a pulse-tube cryocooler and providing the lowest vibration level reported for such a closed-cycle system with 1 W cooling power for a <5 K experiment. A decoupling system suppresses vibrations from the cryocooler by three orders of magnitude down to a level of 10 nm peak amplitudes in the horizontal plane. Heat loads of about 40 W (at 45 K) and 1 W (at 4 K) are transferred from an experimental chamber, mounted on an optical table, to the cryocooler through a vacuum-insulated massive 120 kg inertial copper pendulum. The 1.4 m long pendulum allows installation of the cryocooler in a separate, acoustically isolated machine room. In the laser laboratory, we measured the residual vibrations using an interferometric setup. The positioning of the 4 K elements is reproduced to better than a few micrometer after a full thermal cycle to room temperature. Extreme high vacuum on the $10^{-15}$ mbar level is achieved. In collaboration with the Max-Planck-Intitut f\"ur Kernphysik (MPIK), such a setup is now in operation at the Physikalisch-Technische Bundesanstalt (PTB) for a next-generation optical clock experiment using highly charged ions.

We present a comprehensive experimental and theoretical study on superfluorescence in the extreme ultraviolet wavelength regime. Focusing a high-intensity free-electron laser pulse in a cell filled with Xe or Kr gas, the medium is quasi instantaneously population-inverted by inner-shell ionization on the giant resonance followed by Auger decay. On the timescale of 100 ps a macroscopic polarization builds up in the medium, resulting in superfluorescent emission of several Xe and Kr lines in the forward direction. As the number of emitters in the system is increased by either raising the pressure or the pump-pulse energy, the emission shows an exponential growth of over 4 orders of magnitude and reaches saturation. With increasing yield, we observe line broadening, a manifestation of superfluorescence in the spectral domain. Our novel theoretical approach, based on a full quantum treatment of the atomic system and the irradiated field, shows quantitative agreement with the experiment and supports our interpretation.

Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. These systems have enabled relative frequency uncertainties at a level of a few parts in $10^{-18}$. This accomplishment not only allows for extremely accurate time and frequency measurements, but also to probe our understanding of fundamental physics, such as variation of fundamental constants, violation of the local Lorentz invariance, and forces beyond the Standard Model of Physics. In addition, novel clocks are driving the development of sophisticated technical applications. Crucial for applications of clocks in fundamental physics are a high sensitivity to effects beyond the Standard Model and Einstein's Theory of Relativity and a small frequency uncertainty of the clock. Highly charged ions offer both. They have been proposed as highly accurate clocks, since they possess optical transitions which can be extremely narrow and less sensitive to external perturbations compared to current atomic clock species. The selection of highly charged ions in different charge states offers narrow transitions that are among the most sensitive ones for a change in the fine-structure constant and the electron-to-proton mass ratio, as well as other new physics effects. Recent advances in trapping and sympathetic cooling of highly charged ions will in the future enable high accuracy optical spectroscopy. Progress in calculating the properties of selected highly charged ions has allowed the evaluation of systematic shifts and the prediction of the sensitivity to the "new physics" effects. This article reviews the current status of theory and experiment in the field., Comment: 53 pages, 16 figures, submitted to RMP

We analyze the complex level structure of ions with many-valence-electron open [Kr] 4$d^\textrm{m}$ sub-shells ($\textrm{m}$=7-4) with ab initio calculations based on configuration-interaction many-body perturbation theory (CI+MBPT). Charge-state-resolved optical and extreme ultraviolet (EUV) spectra of Sn$^{7+}$-Sn$^{10+}$ ions were obtained using an electron beam ion trap. Semi-empirical spectral fits carried out with the orthogonal parameters technique and Cowan code calculations lead to 90 identifications of magnetic-dipole transitions and the determination of 79 energy ground-configuration levels, questioning some earlier EUV-line assignments. Our results, the most complete data set available to date for these ground configurations, confirm the ab initio predictive power of CI+MBPT calculations for the these complex electronic systems., Comment: 18 pages, 5 figures

We experimentally re-evaluate the fine structure of Sn$^{11+...14+}$ ions. These ions are essential in bright extreme-ultraviolet (EUV) plasma-light sources for next-generation nanolithography, but their complex electronic structure is an open challenge for both theory and experiment. We combine optical spectroscopy of magnetic dipole $M1$ transitions, in a wavelength range covering 260\,nm to 780\,nm, with charge-state selective ionization in an electron beam ion trap. Our measurements confirm the predictive power of \emph{ab initio} calculations based on Fock space coupled cluster theory. We validate our line identification using semi-empirical Cowan calculations with adjustable wavefunction parameters. Available Ritz combinations further strengthen our analysis. Comparison with previous work suggests that line identifications in the EUV need to be revisited., Comment: 13 pages, 6 figures

An in-trap decay spectroscopy setup has been developed and constructed for use with the TITAN facility at TRIUMF. The goal of this device is to observe weak electron-capture (EC) branching ratios for the odd-odd intermediate nuclei in the $\beta\beta$ decay process. This apparatus consists of an up-to 6 Tesla, open-access spectroscopy ion-trap, surrounded radially by up to 7 planar Si(Li) detectors which are separated from the trap by thin Be windows. This configuration provides a significant increase in sensitivity for the detection of low-energy photons by providing backing-free ion storage and eliminating charged-particle-induced backgrounds. An intense electron beam is also employed to increase the charge-states of the trapped ions, thus providing storage times on the order of minutes, allowing for decay-spectroscopy measurements. The technique of multiple ion-bunch stacking was also recently demonstrated, which further extends the measurement possibilities of this apparatus. The current status of the facility and initial results from a $^{116}$In measurement are presented., Comment: Proceedings for the 2nd International Conference on Advances in Radioactive Isotope Science (ARIS2014)

This article presents an upgraded in-trap decay spectroscopy apparatus which has been developed and constructed for use with TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). This device consists of an open-access electron-beam ion-trap (EBIT), which is surrounded radially by seven low-energy planar Si(Li) detectors. The environment of the EBIT allows for the detection of low-energy photons by providing backing-free storage of the radioactive ions, while guiding charged decay particles away from the trap centre via the strong (up to 6 T) magnetic field. In addition to excellent ion confinement and storage, the EBIT also provides a venue for performing decay spectroscopy on highly-charged radioactive ions. Recent technical advancements have been able to provide a significant increase in sensitivity for low-energy photon detection, towards the goal of measuring weak electron-capture branching ratios of the intermediate nuclei in the two-neutrino double beta ($2\nu\beta\beta$) decay process. The design, development, and commissioning of this apparatus are presented together with the main physics objectives. The future of the device and experimental technique are discussed., Comment: Submitted to Nuclear Instruments and Methods in Physics Research Section A

Photoabsorption by and fluorescence of the K{\alpha} transitions in highly charged iron ions are essential mechanisms for X-ray radiation transfer in astrophysical environments. We study photoabsorption due to the main K{\alpha} transitions in highly charged iron ions from heliumlike to fluorinelike (Fe 24+...17+) using monochromatic X-rays around 6.6 keV at the PETRA III synchrotron photon source. Natural linewidths were determined with hitherto unattained accuracy. The observed transitions are of particular interest for the understanding of photoexcited plasmas found in X-ray binaries and active galactic nuclei., Comment: Revised version

Dielectronic and higher-order resonant electron recombination processes including a K-shell excitation were systematically measured at high resolution in electron beam ion traps. Storing highly charged Ar, Fe, and Kr ions, the dependence on atomic number Z of the contribution of these processes to the total recombination cross section was studied and compared with theoretical calculations. Large higher-order resonant recombination contributions are found, especially for systems with 10

We present a method to measure the decay rate of the first excited vibrational state of simple polar molecular ions being part of a Coulomb crystal in a cryogenic linear Paul trap. Specifically, we have monitored the decay of the $|\nu$=$1,J$=$1 \rangle_X$ towards the $|\nu$=$0,J$=$0 \rangle_X$ level in MgH$^+$ by saturated laser excitation of the $|\nu$=$0,J$=$2 \rangle_X$-$|\nu$=$1,J$=$1 \rangle_X$ transition followed by state selective resonance enhanced two-photon dissociation out of the $|\nu$=$0,J$=$2 \rangle_X$ level. The technique enables the determination of decay rates, and thus absorption strengths, with an accuracy at the few percent level., Comment: 5 pages, 4 figures

The novel five-Penning trap mass spectrometer PENTATRAP is developed at the Max-Planck-Institut f\"ur Kernphysik (MPIK), Heidelberg. Ions of interest are long-lived highly charged nuclides up to bare uranium. PENTATRAP aims for an accuracy of a few parts in 10^12 for mass ratios of mass doublets. A physics program for PENTATRAP includes Q-values measurements of \beta-transitions relevant for neutrino physics, stringent tests of quantum electrodynamics in the regime of extreme electric fields, and a test of special relativity. Main features of PENTATRAP are an access to a source of highly charged ions, a multi-trap configuration, simultaneous measurements of frequencies, a continuous precise monitoring of magnetic field fluctuations, a fast exchange between different ions, and a highly sensitive cryogenic non-destructive detection system. This paper gives a motivation for the new mass spectrometer PENTATRAP, presents its experimental setup, and describes the present status.

Penning trap mass measurements of short-lived nuclides have been performed for the first time with highly-charged ions (HCI), using the TITAN facility at TRIUMF. Compared to singly-charged ions, this provides an improvement in experimental precision that scales with the charge state q. Neutron-deficient Rb-isotopes have been charge bred in an electron beam ion trap to q = 8 - 12+ prior to injection into the Penning trap. In combination with the Ramsey excitation scheme, this unique setup creating low energy, highly-charged ions at a radioactive beam facility opens the door to unrivalled precision with gains of 1-2 orders of magnitude. The method is particularly suited for short-lived nuclides such as the superallowed {\beta} emitter 74Rb (T1/2 = 65 ms). The determination of its atomic mass and an improved QEC-value are presented., Comment: 5 pages, 3 figures

In the presence of a neighboring atom, electron-ion recombination can proceed resonantly via excitation of an electron in the atom, with subsequent relaxation through radiative decay. It is shown that this two-center dielectronic process can largely dominate over single-center radiative recombination at internuclear distances as large as several nanometers. The relevance of the predicted process is demonstrated by using examples of water-dissolved alkali cations and warm dense matter., Comment: 4 pages, 3 figures

We investigate the formation of nano-sized hillocks on the (111) surface of CaF$_2$ single crystals by impact of slow highly charged ions. Atomic force microscopy reveals a surprisingly sharp and well-defined threshold of potential energy carried into the collision of about 14 keV for hillock formation. Estimates of the energy density deposited suggest that the threshold is linked to a solid-liquid phase transition (``melting'') on the nanoscale. With increasing potential energy, both the basal diameter and the height of the hillocks increase. The present results reveal a remarkable similarity between the present predominantly potential-energy driven process and track formation by the thermal spike of swift ($\sim$ GeV) heavy ions., Comment: 10 pages, 2 figures

A novel technique to identify small fluxes of mixed highly charged ion beams extracted from an Electron Beam Ion Trap (EBIT) is presented and practically demonstrated. The method exploits projectile charge state dependent potential emission of electrons as induced by ion impact on a metal surface to separate ions with identical or very similar mass-to-charge ratio., Comment: 8 pages, 5 figures

The magnetic-dipole transition probabilities between the fine-structure levels (1s^2 2s^2 2p) ^2P_1/2 - ^2P_3/2 for B-like ions and (1s^2 2s 2p) ^3P_1 - ^3P_2 for Be-like ions are calculated. The configuration-interaction method in the Dirac-Fock-Sturm basis is employed for the evaluation of the interelectronic-interaction correction with negative-continuum spectrum being taken into account. The 1/Z interelectronic-interaction contribution is derived within a rigorous QED approach employing the two-time Green function method. The one-electron QED correction is evaluated within framework of the anomalous magnetic-moment approximation. A comparison with the theoretical results of other authors and with available experimental data is presented.

The isotope shifts of forbidden transitions in Be- and B-like argon ions are calculated. It is shown that only using the relativistic recoil operator can provide a proper evaluation of the mass isotope shift, which strongly dominates over the field isotope shift for the ions under consideration. Comparing the isotope shifts calculated with the current experimental uncertainties indicates very good perspectives for a first test of the relativistic theory of the recoil effect in middle-Z ions.