José R. Crespo López-Urrutia

We present measurements of K-shell x-ray emission following charge exchange of fully ionized argon with various neutral gaseous targets at small collision energies inside an electron beam ion trap. We also resolve the principal quantum number of electron capture in extreme-ultraviolet spectra from initially bare and hydrogen-like oxygen ions held in the same trap. We analyze discrepancies between these as well as previous measurements with theoretical models based on the multichannel Landau-Zener approach.

Characterization of the trap rf induced a.c. Zeeman shift is essential for achieving high accuracy in optical ion clocks. In this work, we demonstrate the experimental characterization of this shift using highly charged $\mathrm{Ca}^{14+}$. The transverse component of the a.c. magnetic field is measured using the Autler-Townes splitting of the equally-spaced Zeeman components of the $^{3}\mathrm{P}_1$ when the Zeeman splitting is close to resonance with the trap rf drive frequency. We observe the resulting modulation by performing quantum logic spectroscopy using the co-trapped $\mathrm{Be}^{+}$. The longitudinal component is measured from probing the $\mathrm{Be}^{+}$ magnetic field-insensitive hyperfine transition $|F=2,m_F=0 \rangle \rightarrow | F=1,m_F=0 \rangle$. We confirm the small influence of the a.c. Zeeman shift in highly charged ions. The employed techniques can easily be transferred to other multi-level atomic systems.

We present the basic performance and experimental results of an electron beam ion trap (JAXA-EBIT), newly introduced to the Japanese astronomical community. Accurate atomic data are indispensable for the reliable interpretation of high-resolution X-ray spectra of astrophysical plasmas. The JAXA-EBIT generates highly charged ions under well-controlled laboratory conditions, providing experimental benchmarks for atomic data. The JAXA-EBIT shows performance comparable to the Heidelberg compact EBIT through dielectronic recombination measurements of highly charged Ar ions. Furthermore, we conducted resonant photoexcitation spectroscopy of highly charged ions using the soft X-ray beamline BL17SU at the synchrotron radiation facility SPring-8. As a result, we successfully detected resonance transitions of He-like O$^{6+}$ and Ne-like Fe$^{16+}$. These results demonstrate the capability of the JAXA-EBIT for precise measurement of atomic data and show that it serves as a powerful tool for advancing astrophysical research.

Ultraintense pulses from X-ray free-electron lasers can drive, within femtoseconds, multiple processes in the inner shells of atoms and molecules in all phases of matter. The ensuing complex ionization pathways of outer-shell electrons from the neutral to the final highly charged states make a comparison with theory enormously difficult. We resolve these pathways by preparing highly charged ions in an electron beam ion trap before exposing them to the pulsed radiation. This reveals how relativistic fine-structure effects shift electronic energies, largely compensate the core-screening potential, and enable the consecutive, resonant absorption of two quasi-monochromatic X-ray photons that would generally be unfeasible. This doubly-resonant channel enhances the efficiency of two-photon ionization by more than two orders of magnitude, dominating in this regime the nonlinear interaction of light and matter with possible application for future precision X-ray metrology.

Optical transitions of highly charged ions can be very sensitive to hypothetical beyond-the-Standard-Model phenomena. Those near the $5s-4f$ level crossing, where the $5s$ and $4f$ are degenerate are especially promising. We present predictions from atomic theory and measurements of Os$^{15,16,17+}$ at an electron beam ion trap for identification of several transitions suitable for searches for a hypothetical fifth force and possible violations of local Lorentz invariance. The electric quadrupole (E2) transitions of Os$^{16+}$ that were found are especially suitable for frequency metrology due to their small linewidth of 44 $μ$Hz. Our calculations show the need for including enough inner-shell excitations to predict transition rates between configurations, which can otherwise be overestimated. Ultimately, the predicted interconfiguration transitions were too weak to be detected.

We report measurements of the K$α$ emission from the astrophysically very abundant Ca XIX (He-like ion) and its satellite lines resonantly excited by dielectronic recombination (DR). We achieve an electron-energy resolution of 8 eV in a cryogenic electron beam ion trap, and determine the energies of the exciting electrons and the emitted photons up to the KLn ($n\le 8$) manifold with $0.05\%$ and $0.1\%$ respective uncertainties. For the KLL satellites, energies agree very well with our predictions using the Flexible Atomic Code (FAC) and previous state-of-the-art calculations. Our calculations also agree with our experimental direct excitation cross-sections for K$α$ within their $10\%$ uncertainty. We extract DR coefficient rates and find good agreement with values tabulated in the OPEN-ADAS database. As an application, we experimentally benchmark Ca XIX atomic data used to model high-temperature astrophysical plasmas by comparing FAC synthetic spectra with recent XRISM observations revealing the contributions of DR satellites to the Ca XIX lines.

While laser excitation of the nuclear isomeric transition in $^{229}$Th has been recently achieved for thorium atoms embedded in large-bandgap crystals, laser excitation and characterization of the nuclear transition in trapped $^{229}$Th$^{3+}$ ions has not yet been accomplished. To address these experiments, a cryogenic Paul trap setup has been designed, built, and commissioned at LMU Munich. Here, we present the specifications of the new experimental platform and demonstrate its successful operation, showing the extraction, subsequent ion-guiding, mass-purification, and trapping of $^{229}$Th$^{3+}$ and $^{229\text{m}}$Th$^{3+}$ ions from a newly designed buffer-gas stopping cell as well as of $^{88}$Sr$^{+}$ ions from laser ablation of a solid target. Further, we show sympathetic laser cooling of $^{229\text{(m)}}$Th$^{3+}$ by Doppler-cooled $^{88}$Sr$^{+}$ ions and the formation of mixed-species Coulomb crystals.

We report on comprehensive laboratory studies of the K-shell dielectronic recombination (DR) resonances of Fe XXV - XXI ions that prominently contribute to the hard X-ray spectrum of hot astrophysical plasmas. By scanning a monoenergetic electron beam to resonantly excite trapped Fe ions in an electron beam ion trap, and achieving a high electron-ion collision energy resolution of ~7 eV, we resolve their respective KL$n$ satellites up to n'=11. By normalization to known radiative recombination cross sections we also determine their excitation cross sections and that of the continuum with uncertainties below 15%, and verify our results with an independent normalization based on previous measurements. Our experimental data excellently confirm the accuracy and suitability of distorted-wave calculations obtained with the Flexible Atomic Code (FAC) for modeling astrophysical and fusion plasmas.

We measured the $g$-factor of the excited state $^3\text{P}_1$ in $\text{Ca}^{14+}$ ion to be $g = 1.499032(6)$ with a relative uncertainty of $4\times10^{-6}$. The magnetic field magnitude is derived from the Zeeman splitting of a $\text{Be}^+$ ion, co-trapped in the same linear Paul trap as the highly charged $\text{Ca}^{14+}$ ion. Furthermore, we experimentally determined the second-order Zeeman coefficient $C_2$ of the $^3\text{P}_0$ - $^3\text{P}_1$ clock transition. For the $m_J=0\rightarrow m_{J'}=0$ transition, we obtain $C_2 = 0.39\pm0.04\text{HzmT}^{-2}$, which is to our knowledge the smallest reported for any atomic transition to date. This confirms the predicted low sensitivity of highly charged ions to higher-order Zeeman effects, making them ideal candidates for high-precision optical clocks. Comparison of the experimental results with our state-of-the art electronic structure calculations shows good agreement, and demonstrates the significance of the frequency-dependent Breit contribution, negative energy states and QED effects on magnetic moments.

We measure the energy-differential cross sections for collisional excitation of the soft X-ray electric-dipole K$α$ ($x+y+w$) emission from He-like oxygen (O VII), using an electron beam ion trap. Values near their excitation thresholds were extracted from the observed emissivity by rapidly cycling the energy of the exciting electron beam. This allows us to subtract time-dependent contributions of the forbidden $z$-line emission to the multiplet. We develop a time-dependent collisional-radiative model to further demonstrate the method and predict all spectral features. We then compare the extracted $x+y+w$ cross-sections with calculations based on distorted-wave and R-matrix methods from the literature and our own predictions using the Flexible Atomic Code (FAC). All R-matrix results are validated by our measurements of direct and resonant excitation, supporting the use of such state-of-the-art codes for astrophysical and plasma physics diagnostics.

We calculated cross sections for the dielectronic recombination (DR) satellite lines of Fe XVII and benchmarked our predictions with experimental cross sections of Fe XVII resonances that were mono-energetically excited in an electron beam ion trap. We extend the benchmark to all resolved DR and direct electron-impact excitation (DE) channels in the experimental dataset, specifically the $n\geq4$ DR resonances of Fe XVII, complementing earlier investigations of $n=3$ channels. Our predictions overestimate by 20-25$\%$ the DR and DE absolute cross sections for the higher $n$ complexes when using the same methods as in previous works. However, we achieve agreement within $\sim$10$\%$ of the experimental results by an approach in which we "forward fold" the predicted cross sections with the spread of the electron-beam energy and the photon-energy resolution of our experiment. We then calculated rate coefficients from the experimental and theoretical cross sections, finding departures of $10-20\%$ from the rates found in the OPEN-ADAS atomic database.

We improve by a factor of 4-20 the energy accuracy of the strongest soft X-ray transitions of Fe XVII ions by resonantly exciting them in an electron beam ion trap with a monochromatic beam at the P04 beamline of the PETRA III synchrotron facility. By simultaneously tracking instantaneous photon-energy fluctuations with a high-resolution photoelectron spectrometer, we minimize systematic uncertainties down to 10-15 meV, or velocity equivalent $\pm\sim$5 km s$^{-1}$ in their rest energies, substantially improving our knowledge of this key astrophysical ion. Our large-scale configuration-interaction computations include more than four million relativistic configurations and agree with the experiment at a level without precedent for a 10-electron system. Thereby, theoretical uncertainties for interelectronic correlations become far smaller than those of quantum electrodynamics (QED) corrections. The present QED benchmark strengthens our trust in future calculations of many other complex atomic ions of interest to astrophysics, plasma physics, and for the development of optical clocks with highly charged ions.

We implement sympathetic cooling of highly charged ions (HCI) by fully enclosing a linear Paul trap within a superconducting radio-frequency resonator. A quantization magnetic field applied while cooling down into the superconducting state remains present in the trap for centuries and external electromagnetic fluctuations are greatly suppressed. A magnetic field decay rate at the 10$^{-10}$ s$^{-1}$ level is found using trapped Doppler-cooled Be$^+$ ions as hyperfine-structure (hfs) qubits. Ramsey interferometry and spin-echo measurements on magnetically-sensitive hfs transitions yield coherence times of >400 ms, showing excellent passive shielding at frequencies down to DC. For sympathetic cooling of HCI, we extract them from an electron beam ion trap (EBIT) and co-crystallize one together with Doppler-cooled Be$^+$ ions. By subsequently ejecting all but one Be$^+$ ions, we prepare single HCI for quantum logic spectroscopy towards frequency metrology and qubit operations with a great variety of HCI species.

Most ions lack the fast, cycling transitions that are necessary for direct laser cooling. In most cases, they can still be cooled sympathetically through their Coulomb interaction with a second, coolable ion species confined in the same potential. If the charge-to-mass ratios of the two ion types are too mismatched, the cooling of certain motional degrees of freedom becomes difficult. This limits both the achievable fidelity of quantum gates and the spectroscopic accuracy. Here we introduce a novel algorithmic cooling protocol for transferring phonons from poorly- to efficiently-cooled modes. We demonstrate it experimentally by simultaneously bringing two motional modes of a Be$^{+}$-Ar$^{13+}$ mixed Coulomb crystal close to their zero-point energies, despite the weak coupling between the ions. We reach the lowest temperature reported for a highly charged ion, with a residual temperature of only $T\lesssim200~\mathrm{μK}$ in each of the two modes, corresponding to a residual mean motional phonon number of $\langle n \rangle \lesssim 0.4$. Combined with the lowest observed electric field noise in a radiofrequency ion trap, these values enable an optical clock based on a highly charged ion with fractional systematic uncertainty below the $10^{-18}$ level. Our scheme is also applicable to (anti-)protons, molecular ions, macroscopic charged particles, and other highly charged ion species, enabling reliable preparation of their motional quantum ground states in traps.

The Hitomi results for the Perseus cluster have shown that accurate atomic models are essential to the success of X-ray spectroscopic missions, and just as important as knowledge on instrumental calibration and astrophysical modeling. Preparing the models requires a multifaceted approach, including theoretical calculations, laboratory measurements, and calibration using real observations. In a previous paper, we presented a calculation of the electron impact cross sections on the transitions forming the Fe-L complex. In the present work, we systematically test the calculation against cross sections of ions measured in an electron beam ion trap experiment. A two-dimensional analysis in the electron beam energies and X-ray photon energies is utilized to disentangle radiative channels following dielectronic recombination, direct electron-impact excitation, and resonant excitation processes in the experimental data. The data calibrated through laboratory measurements are further fed into global modeling of the Chandra grating spectrum of Capella. We investigate and compare the fit quality, as well as sensitivity of the derived physical parameters to the underlying atomic data and the astrophysical plasma modeling. We further list the potential areas of disagreement between the observation and the present calculations, which in turn calls for renewed efforts in theoretical calculations and targeted laboratory measurements.

State-of-the-art optical clocks achieve fractional precisions of $10^{-18}$ and below using ensembles of atoms in optical lattices or individual ions in radio-frequency traps. Promising candidates for novel clocks are highly charged ions (HCIs) and nuclear transitions, which are largely insensitive to external perturbations and reach wavelengths beyond the optical range, now becoming accessible to frequency combs. However, insufficiently accurate atomic structure calculations still hinder the identification of suitable transitions in HCIs. Here, we report on the discovery of a long-lived metastable electronic state in a HCI by measuring the mass difference of the ground and the excited state in Re, the first non-destructive, direct determination of an electronic excitation energy. This result agrees with our advanced calculations, and we confirmed them with an Os ion with the same electronic configuration. We used the high-precision Penning-trap mass spectrometer PENTATRAP, unique in its synchronous use of five individual traps for simultaneous mass measurements. The cyclotron frequency ratio $R$ of the ion in the ground state to the metastable state could be determined to a precision of $δR=1\cdot 10^{-11}$, unprecedented in the heavy atom regime. With a lifetime of about 130 days, the potential soft x-ray frequency reference at $ν=4.86\cdot 10^{16}\,\text{Hz}$ has a linewidth of only $Δν\approx 5\cdot 10^{-8}\,\text{Hz}$, and one of the highest electronic quality factor ($Q=\fracν{Δν}\approx 10^{24}$) ever seen in an experiment. Our low uncertainty enables searching for more HCI soft x-ray clock transitions, needed for promising precision studies of fundamental physics in a thus far unexplored frontier.

The excitation of the 8 eV $^{229m}$Th isomer through the electronic bridge mechanism in highly charged ions is investigated theoretically. By exploiting the rich level scheme of open $4f$ orbitals and the robustness of highly charged ions against photoionization, a pulsed high-intensity optical laser can be used to efficiently drive the nuclear transition by coupling it to the electronic shell. We show how to implement a promising electronic bridge scheme in an electron beam ion trap starting from a metastable electronic state. This setup would avoid the need for a tunable vacuum ultraviolet laser. Based on our theoretical predictions, determining the isomer energy with an uncertainty of $10^{-5}$ eV could be achieved in one day of measurement time using realistic laser parameters.

This paper reports on the development and testing of a novel, highly efficient technique for the injection of very rare species into electron beam ion traps (EBITs) for the production of highly charged ions (HCI). It relies on in-trap laser-induced desorption of atoms from a sample brought very close to the electron beam resulting in a very high capture efficiency in the EBIT. We have demonstrated a steady production of HCI of the stable isotope $^{165}\mathrm{Ho}$ from samples of only $10^{12}$ atoms ($\sim$ 300 pg) in charge states up to 45+. HCI of these species can be subsequently extracted for use in other experiments or stored in the trapping volume of the EBIT for spectroscopic measurements. The high efficiency of this technique expands the range of rare isotope HCIs available for high-precision nuclear mass and spectroscopic measurements. A first application of this technique is the production of HCI of the synthetic radioisotope $^{163}\mathrm{Ho}$ for a high-precision measurement of the $Q_{\mathrm{EC}}$-value of the electron capture in $^{163}\mathrm{Ho}$ within the Electron Capture in Holmium experiment (ECHo collaboration) ultimately leading to a measurement of the electron neutrino mass with an uncertainty on the sub-eV level.

We determined relative X-ray photon emission cross sections in Fe XVII ions that were mono-energetically excited in an electron beam ion trap. Line formation for the 3s (3s-2p) and 3d (3d-2p) transitions of interest proceeds through dielectronic recombination (DR), direct electron-impact excitation (DE), resonant excitation (RE), and radiative cascades. By reducing the electron-energy spread to a sixth of that of previous works and increasing counting statistics by three orders of magnitude, we account for hitherto unresolved contributions from DR and the little-studied RE process to the 3d transitions, and also for cascade population of the 3s line manifold through forbidden states. We found good agreement with state-of-the-art many-body perturbation theory (MBPT) and distorted-wave (DW) method for the 3s transition, while in the 3d transitions known discrepancies were confirmed. Our results show that DW calculations overestimate the 3d line emission due to DE by ~20%. Inclusion of electron-electron correlation effects through the MBPT method in the DE cross section calculations reduces this disagreement by ~11%. The remaining ~9% in 3d and ~11% in 3s/3d discrepancies are consistent with those found in previous laboratory measurements, solar, and astrophysical observations. Meanwhile, spectral models of opacity, temperature, and turbulence velocity should be adjusted to these experimental cross sections to optimize the accuracy of plasma diagnostics based on these bright soft X-ray lines of Fe XVII.

A cryogenic radio-frequency ion trap system designed for quantum logic spectroscopy of highly charged ions is presented. It includes a segmented linear Paul trap, an in-vacuum imaging lens and a helical resonator. We demonstrate ground state cooling of all three modes of motion of a single $^9$Be$^+$ ion and determine their heating rates as well as excess axial micromotion. The trap shows one of the lowest levels of electric field noise published to date. We investigate the magnetic-field noise suppression in cryogenic shields made from segmented copper, the resulting magnetic field stability at the ion position and the resulting coherence time. Using this trap in conjunction with an electron beam ion trap and a deceleration beamline, we have been able to trap single highly charged Ar$^{13+}$ (Ar XIV) ions concurrently with single Be$^+$ ions, a key prerequisite for the first quantum logic spectroscopy of a highly charged ion.

Theoretical and experimental resonance strengths for KLL dielectronic recombination (DR) into He-, Li-, Be-, and B-like mercury ions are presented, based on state-resolved DR x-ray spectra recorded at the Heidelberg electron beam ion trap. The DR resonance strengths were experimentally extracted by normalizing them to simultaneously recorded radiative recombination signals. The results are compared to state-of-the-art atomic calculations that include relativistic electron-electron correlation and configuration mixing effects. Combining the present data with other existing ones, we derive an improved semi-empirical $Z$-scaling law for DR resonance strength as a function of the atomic number, taking into account higher-order relativistic corrections, which are especially relevant for heavy highly charged ions.

We present a systematic measurement of the X-ray emission asymmetries in the K-shell dielectronic, trielectronic, and quadruelectronic recombination of free electrons into highly charged ions. Iron ions in He-like through O-like charge states were produced in an electron beam ion trap, and the electron-ion collision energy was scanned over the recombination resonances. Two identical X-ray detectors mounted head-on and side-on with respect to the electron beam propagation recorded X-rays emitted in the decay of resonantly populated states. The degrees of linear polarization of X-rays inferred from observed emission asymmetries benchmark distorted-wave predictions of the Flexible Atomic Code (FAC) for several dielectronic recombination satellite lines. The present method also demonstrates its applicability for diagnostics of energy and direction of electron beams inside hot anisotropic plasmas. Both experimental and theoretical data can be used for modeling of hot astrophysical and fusion plasmas.

We report a measurement of $KLL$ dielectronic recombination in charge states from Kr$^{+34}$ through Kr$^{+28}$, in order to investigate the contribution of Breit interaction for a wide range of resonant states. Highly charged Kr ions were produced in an electron beam ion trap, while the electron-ion collision energy was scanned over a range of dielectronic recombination resonances. The subsequent $Kα$ x rays were recorded both along and perpendicular to the electron beam axis, which allowed the observation of the influence of Breit interaction on the angular distribution of the x rays. Experimental results are in good agreement with distorted-wave calculations. We demonstrate, both theoretically and experimentally, that there is a strong state-selective influence of the Breit interaction that can be traced back to the angular and radial properties of the wavefunctions in the dielectronic capture.

The reported observations of an unidentified X-ray line feature at $\sim$3.5 keV have driven a lively discussion about its possible dark matter origin. Motivated by this, we have measured the \emph{K}-shell X-ray spectra of highly ionized bare sulfur ions following charge exchange with gaseous molecules in an electron beam ion trap, as a source of or a contributor to this X-ray line. We produce $\mathrm{S}^{16+}$ and $\mathrm{S}^{15+}$ ions and let them capture electrons in collision with those molecules with the electron beam turned off while recording X-ray spectra. We observed a charge-exchanged-induced X-ray feature at the Lyman series limit (3.47 $\pm$ 0.06 keV). The inferred X-ray energy is in full agreement with the reported astrophysical observations and supports the novel scenario proposed by Gu and Kaastra (A \& A \textbf{584}, {L11} (2015)).

We report linear polarization measurements of x rays emitted due to dielectronic recombination into highly charged krypton ions. The ions in the He-like through O-like charge states were populated in an electron beam ion trap with the electron beam energy adjusted to recombination resonances in order to produce $Kα$ x rays. The x rays were detected with a newly developed Compton polarimeter using a beryllium scattering target and 12 silicon x-ray detector diodes sampling the azimuthal distribution of the scattered x rays. The extracted degrees of linear polarization of several dielectronic recombination transitions agree with results of relativistic distorted--wave calculations. We also demonstrate a high sensitivity of the polarization to the Breit interaction, which is remarkable for a medium-$Z$ element like krypton. The experimental results can be used for polarization diagnostics of hot astrophysical and laboratory fusion plasmas.