The precise knowledge of the atomic masses of light atomic nuclei, e.g. the proton, deuteron, triton and helion, is of great importance for several fundamental tests in physics. However, the latest high-precision measurements of these masses carried out at different mass spectrometers indicate an inconsistency of five standard deviations. To determine the masses of the lightest ions with a relative precision of a few parts per trillion and investigate this mass problem a cryogenic multi-Penning trap setup, LIONTRAP (Light ION TRAP), was constructed. This allows an independent and more precise determination of the relevant atomic masses by measuring the cyclotron frequency of single trapped ions in comparison to that of a single carbon ion. In this paper the measurement concept and the first doubly compensated cylindrical electrode Penning trap, are presented. Moreover, the analysis of the first measurement campaigns of the proton's and oxygen's atomic mass is described in detail, resulting in mp = 1.007 276 466 598 (33) u and m(16O)= 15.994 914 619 37 (87) u. The results on these data sets have already been presented in [F. Heisse et al., Phys. Rev. Lett. 119, 033001 (2017)]. For the proton's atomic mass, the uncertainty was improved by a factor of three compared to the 2014 CODATA value.
We have built a vacuum double crystal spectrometer, which coupled to an electron-cyclotron resonance ion source, allows to measure low-energy x-ray transitions in highly-charged ions with accuracies of the order of a few parts per million. We describe in detail the instrument and its performances. Furthermore, we present a few spectra of transitions in Ar$^{14+}$, Ar$^{15+}$ and Ar$^{16+}$. We have developed an ab initio simulation code that allows us to obtain accurate line profiles. It can reproduce experimental spectra with unprecedented accuracy. The quality of the profiles allows the dire…
We study the ions dynamics inside an Electrostatic Ion Beam Trap (EIBT) and show that the stability of the trapping is ruled by a Hill's equation. This unexpectedly demonstrates that an EIBT, in the reference frame of the ions works very similar to a quadrupole trap. The parallelism between these two kinds of traps is illustrated by comparing experimental and theoretical stability diagrams of the EIBT. The main difference with quadrupole traps is that the stability depends only on the ratio of the acceleration and trapping electrostatic potentials, not on the mass nor the charge of the ions. A…
We report on the design and performance of a double-sided coincidence velocity map imaging spectrometer optimized for electron-ion and ion-ion coincidence experiments studying inner-shell photoionization of gas-phase molecules with soft X-ray synchrotron radiation. The apparatus employs two microchannel plate detectors equipped with delay-line anodes for coincident, time- and position-resolved detection of photo- and Auger electrons with kinetic energies up to 300\,eV on one side of the spectrometer and photoions up to 25\,eV per unit charge on the opposite side. We demonstrate its capabilitie…
Trapping molecular ions that have been sympathetically cooled with laser-cooled atomic ions is a useful platform for exploring cold ion chemistry. We designed and characterized a new experimental apparatus for probing chemical reaction dynamics between molecular cations and neutral radicals at temperatures below 1 K. The ions are trapped in a linear quadrupole radio-frequency trap and sympathetically cooled by co-trapped, laser-cooled, atomic ions. The ion trap is coupled to a time-of-flight mass spectrometer to readily identify product ion species, as well as to accurately determine trapped i…
The novel five-Penning trap mass spectrometer PENTATRAP is developed at the Max-Planck-Institut für 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 β-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 ion…
The photodissociation cross-section of SrCl$^+$ is measured in the spectral range of 36000 -- 46000 cm$^{-1}$ using a modular time-of-flight mass spectrometer (TOF-MS). By irradiating a sample of trapped SrCl$^+$ molecular ions with a pulsed dye laser, X$^1Σ^+$ state molecular ions are electronically excited to the repulsive wall of the A$^1Π$ state, resulting in dissociation. Using the TOF-MS, the fragments are detected and the photodissociation cross-section is determined for a broad range of photon energies. Detailed $\textit{ab initio}$ calculations of the molecular potentials and spectros…
In this article we describe the design, construction and implementation of our ion-atom hybrid system incorporating a high resolution time of flight mass spectrometer (TOFMS). Potassium atoms ($^{39}$K) in a Magneto Optical Trap (MOT) and laser cooled calcium ions ($^{40}$Ca$^+$) in a linear Paul trap are spatially overlapped and the combined trap is integrated with a TOFMS for radial extraction and detection of reaction products. We also present some experimental results showing interactions between $^{39}$K$^+$ and $^{39}$K, $^{40}$Ca$^+$ and $^{39}$K$^+$ as well as $^{40}$Ca$^+$ and $^{39}$…
We report on the design, commissioning, and initial measurements of a Transition-edge Sensor (TES) x-ray spectrometer for the Electron Beam Ion Trap (EBIT) at the National Institute of Standards and Technology (NIST). Over the past few decades, the NIST EBIT has produced numerous studies of highly charged ions in diverse fields such as atomic physics, plasma spectroscopy, and laboratory astrophysics. The newly commissioned NIST EBIT TES Spectrometer (NETS) improves the measurement capabilities of the EBIT through a combination of high x-ray collection efficiency and resolving power. NETS utili…
Significant systematic errors in high-precision Penning trap mass spectrometry can result from electric and magnetic field imperfections. An experimental procedure to minimize these uncertainties is presented for the on-line Penning trap mass spectrometer ISOLTRAP, located at ISOLDE/CERN. The deviations from the ideal magnetic and electric fields are probed by measuring the cyclotron frequency and the reduced cyclotron frequency, respectively, of stored ions as a function of the time between the ejection of ions from the preparation trap and their capture in the precision trap, which influence…
The electron beam ion trap (EBIT) at the National Institute of Standards and Technology was used to produce highly-charged ions of hafnium, tantalum and gold with an open 3d shell. The extreme-ultraviolet (EUV) spectra from these ions were recorded with a flat-field grazing-incidence spectrometer in the wavelength range of 4.5 nm to 25 nm. A total of 133 new spectral lines, primarily due to magnetic-dipole transitions within the ground-state $3d^n$ configurations of the Co-like to K-like ions, were identified by comparing energy-dependent experimental spectra with a detailed collisional-radiat…
We measured the ground-state hyperfine splitting of trapped ${}^{113}$Cd${}^{+}$ ions to be 15199862855.02799(27) Hz with a fractional uncertainty of $1.8\times10^{-14}$. The ions were trapped and laser-cooled in a linear quadrupole Paul trap. The fractional frequency stability was measured to be ${4.2} \times 10^{-13}/\sqrtτ $, obtained from Ramsey fringes of high signal-to-noise ratio and taken over a measurement time of nearly 5 hours, which is close to the short-term stability limit estimated from the Dick effect. Our result is consistent with previous reported values, but the measurement …
We review recent experiments on HD$^+$ spectroscopy. The reduced proton-deuteron mass to electron mass ratio, $μ_{pd}/m_e$, is inferred from the comparison of theory and experiment. Theoretical issues related to the calculations of the spin structure, which are currently the main limiting factor of theoretical accuracy, are discussed.
We have conceived, built and operated a 'half-open' cylindrical Penning trap for the confinement and laser spectroscopy of highly charged ions. This trap allows fluorescence detection employing a solid angle which is about one order of magnitude larger than in conventional cylindrical Penning traps. At the same time, the desired electrostatic and magnetostatic properties of a closed-endcap cylindrical Penning trap are preserved in this congfiuration. We give a detailed account on the design and confinement properties, a characterization of the trap and show first results of light collection wi…
We consider transitions of electron holes (vacancies in otherwise filled shells of atomic systems) in multiply-charged ions that, due to level-crossing of the holes, have frequencies within the range of optical atomic clocks. Strong E1 transitions provide new options for laser-cooling and trapping, while narrow transitions can be used for high-precision spectroscopy and tests of fundamental physics. We show that hole transitions can have extremely high sensitivity to alpha-variation due to large relativistic corrections, and propose candidate transitions that have much larger alpha-sensitiviti…
Expectation values of the Breit operators and the $Q$ terms are calculated for HD$^+$ with the vibrational number $v=0-4$ and the total angular momentum $L=0-4$. Relativistic and radiative corrections to some ro-vibrational transition frequencies are determined. Numerical uncertainty in $R_{\infty}α^2$ order correction is reduced to sub kHz or smaller. Our work provides an independent verification of Korobov's calculations [Phys. Rev. A {\bf74}, 052506 (2006); {\bf77}, 022509 (2008)].
This work presents a multifaceted experimental study of collisions of Na$^{+}$ and K$^{+}$ ions in the energy range 0.5 -- 10 keV with He and Ar atoms. Absolute cross sections for charge-exchange, ionization, stripping and excitation were measured using a refined version of the transfer electric field method, angle- and energy-dependent collection of product ions, energy loss, and optical spectroscopy. The experimental data and the schematic correlation diagrams have been employed to analyze and determine the mechanisms for these processes.
We present an experimental concept and setup for laser-microwave double-resonance spectroscopy of highly charged ions in a Penning trap. Such spectroscopy allows a highly precise measurement of the Zeeman splittings of fine- and hyperfine-structure levels due the magnetic field of the trap. We have performed detailed calculations of the Zeeman effect in the framework of quantum electrodynamics of bound states as present in such highly charged ions. We find that apart from the linear Zeeman effect, second- and third-order Zeeman effects also contribute to the splittings on a level of 10^-4 and …
In Penning traps electromagnetic forces are used to confine charged particles under well-controlled conditions for virtually unlimited time. Sensitive detection methods have been developed to allow observation of single stored ions. Various cooling methods can be employed to reduce the energy of the trapped particle to nearly at rest. In this review we summarize how highly charged ions offer unique possibilities for precision measurements in Penning traps. Precision atomic and nuclear masses as well as magnetic moments of bound electrons allow among others to determine fundamental constants li…
We report measurements of electron-impact excitation cross sections for the strong K-shell n=2-1 transitions in S XV using the LLNL EBIT-I electron beam ion trap, two crystal spectrometers, and the EBIT Calorimeter Spectrometer. The cross sections are determined by direct normalization to the well known cross sections of radiative electron capture, measured simultaneously. Using contemporaneous polarization measurements with the two crystal spectrometers, whose dispersion planes are oriented parallel and perpendicular to the electron beam direction, the polarization of the direct excitation li…
The hyperfine structures of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states of the $^7$Be$^{2+}$ and $^9$Be$^{2+}$ ions are investigated within the framework of the nonrelativistic quantum electrodynamics (NRQED). The uncertainties of present hyperfine splitting results of $^9$Be$^{2+}$ are in the order of several tens of ppm, where two orders of magnitude improvement over the previous theory and experiment values has been achieved. The contribution of nuclear electric quadrupole moment to hyperfine splitting of $^7$Be$^{2+}$ has been studied. A scheme for determining the properties of Be nuclei in t…
We report on the fragmentation dynamics of triply charged, diatomic, molecular ions of NO and CO. Dissociative fragmentation after multiple ionization of NO and CO is studied under the impact of 200 keV proton beam using recoil-ion momentum spectrometer. Kinetic Energy Release distributions (KERDs) for various fragmentation channels were obtained. We have also calculated the potential energy curves (PECs) for ground and several excited states of NO^{3+} and CO^{3+} molecular ion. The obtained KERDs are discussed in the background of the calculated PECs as well as the simple Coulomb excitation …
In a joint experimental and theoretical endeavour, photoionization of metastable C4+(1s 2s 3S1) ions via intermediate levels with hollow, double-K-vacancy configurations 2s2p, 2s3p, 2p3s, 2p3d, 2s4p, 2p4s and 2p4d has been investigated. High-resolution photon-ion merged-beams measurements were carried out with the resolving power reaching up to 25,000 which is sufficient to separate the leading fine-structure components of the 2s2p 3P term. Many-body perturbation theory was employed to determine level-to-level cross sections for K-shell excitation with subsequent autoionization. The resonance …
In this paper we present a technique for the precise measurement of electric dipole allowed transitions in trapped ions. By applying a probe and a cooling laser in quick succession, the full transition can be probed without causing distortion from heating the ion. In addition, two probes can be utilized to measure a dispersion-like signal, which is well suited to stabilizing the laser to the transition. We have fully characterized the parameters for the measurement and find that it is possible to measure the transition frequency to better than 100kHz with an interrogation time of 30s. The long…
The static and dynamic electric multipolar polarizabilities and second hyperpolarizabilities of the H$_2^+$, D$_2^+$, and HD$^+$ molecular ions in the ground and first excited states are calculated nonrelativistically using explicitly correlated Hylleraas basis sets. The calculations are fully nonadiabatic; the Born-Oppenheimer approximation is not used. Comparisons are made with published theoretical and experimental results, where available. In our approach, no derivatives of energy functions nor derivatives of response functions are needed. In particular, we make contact with earlier calcul…
Resonance fluorescence of laser-driven highly charged ions is studied in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynamic phenomena and nuclear effects by applying coherent light with x-ray frequencies. Atomic dipole or multipole moments may be determined to unprecedented accuracy by measuring the interference-narrowed fluoresce…
Optical atomic clocks using highly-charged ions hold an intriguing promise of metrology at the 19th significant figure. Here we study transitions within the $4f^{12}$ ground-state electronic configuration of highly charged ions. We consider isotopes lacking hyperfine structure and show that the detrimental effects of coupling of electronic quadrupole moments to gradients of trapping electric field can be effectively reduced by using specially chosen virtual clock transitions. The estimated systematic fractional clock accuracy is shown to be below $10^{-19}$.
We consider the application of a basic principle of quantum theory, the tracelessness of a certain class of hamiltonians, to the precision spectroscopy of the molecular hydrogen ions. We show that it is possible to obtain the spin-averaged transition frequencies between states from a simple weighted sum of experimentally accessible spin-dependent transition frequencies. We discuss the cases ${\rm H}_{2}^{+}$ and ${\rm HD}^{+}$, which are distinct in the multipole character of their rovibrational transitions. Inclusion of additional frequencies permits canceling also the electric quadrupole shi…
Recently, we reported an ion trap experiment with an integrated time-of-flight mass spectrometer (TOFMS) [Phys. Rev. Appl. 2, 034013 (2014)] focussing on the improvement of mass resolution and detection limit due to sample preparation at millikelvin temperatures. The system utilizes a radio-frequency (RF) ion trap with asymmetric drive for storing and manipulating laser-cooled ions and features radial extraction into a compact $275$ mm long TOF drift tube. The mass resolution exceeds $m / Δm = 500$, which provides isotopic resolution over the whole mass range of interest in current experiments…
We report on the design and performance of a velocity map imaging (VMI) spectrometer optimized for experiments using high-intensity extreme ultraviolet (XUV) sources such as laser-driven high-order harmonic generation (HHG) sources and free-electron lasers (FELs). Typically exhibiting low repetition rates and high single-shot count rates, such~experiments do not easily lend themselves to coincident detection of photo-electrons and -ions. In order to obtain molecular frame or reaction channel-specific information, one has to rely on other correlation techniques, such as covariant detection sche…
Recent progresses on quantum control of cold atoms and trapped ions in both the scientific and technological aspects greatly advance the applications in precision measurement. Thanks to the exceptional controllability and versatility of these massive quantum systems, unprecedented sensitivity has been achieved in clocks, magnetometers and interferometers based on cold atoms and ions. Besides, these systems also feature many characteristics that can be employed to facilitate the applications in different scenarios. In this review, we briefly introduce the principles of optical clocks, cold atom…
我们讨论的技术，允许长的相干时间在激光光谱实验与两个被困离子。我们表明，为了这个目的，不仅纠缠的离子中制备的消相干的子空间可以使用，但也是一对离子，不纠缠，但受到相同的相位噪声。我们将此技术应用于测量~（40）Ca ~（++）3d D ~（5/2）态的电四极矩和测量激发一对~（40）Ca ~（++）离子的超稳激光的线宽。
The refractive index of silicon at $γ$-ray energies from 181 - 1959 keV was investigated using the GAMS6 double crystal spectrometer and found to follow the predictions of the classical scattering model. This is in contrast to earlier measurements on the GAMS5 spectrometer, which suggested a sign-change in the refractive index for photon energies above 500 keV. We present a re-evaluation of the original data from 2011 as well as data from a 2013 campaign in which we show that systematic errors due to diffraction effects of the prism can explain the earlier data.
We describe the first precision measurement of the electron's electric dipole moment (eEDM, $d_e$) using trapped molecular ions, demonstrating the application of spin interrogation times over 700 ms to achieve high sensitivity and stringent rejection of systematic errors. Through electron spin resonance spectroscopy on $^{180}{\rm Hf}^{19}{\rm F}^{+}$ in its metastable $^{3}Δ_{1}$ electronic state, we obtain $d_e = (0.9 \pm 7.7_{\rm stat} \pm 1.7_{\rm syst}) \times 10^{-29}\,e\,{\rm cm}$, resulting in an upper bound of $|d_e| < 1.3 \times 10^{-28}\,e\,{\rm cm}$ (90% confidence). Our result pro…
Storage rings have been employed over three decades in various kinds of nuclear and atomic physics experiments with highly charged ions. Storage ring operation and precision physics experiments benefit from the availability of beam cooling which is common to nearly all facilities. The basic aspects of the storage ring components and the operation of the ring in various ion-optical modes as well as the achievable beam conditions are described. Ion storage rings offer unparalleled capabilities for high precision experiments with stable and radioactive beams. The versatile techniques and methods …
Mass spectrometry is used in a wide range of scientific disciplines including proteomics, pharmaceutics, forensics, and fundamental physics and chemistry. Given this ubiquity, there is a worldwide effort to improve the efficiency and resolution of mass spectrometers. However, the performance of all techniques is ultimately limited by the initial phase-space distribution of the molecules being analyzed. Here, we dramatically reduce the width of this initial phase-space distribution by sympathetically cooling the input molecules with laser-cooled, co-trapped atomic ions, improving both the mass …
Molecules and atomic highly charged ions provide powerful low-energy probes of the fundamental laws of physics: Polar molecules possess internal fields suitable to enhance fundamental symmetry violation by several orders of magnitudes, whereas atoms in high charge states can feature large relativistic effects and compressed level structures, ideally posed for high sensitivity to variations of fundamental constants. Polar, highly charged molecules could benefit from both: large internal fields and large relativistic effects. However, a high charge dramatically weakens chemical bonding and drive…
We report a series of measurements of the effect of an electric field on the frequency of the ultranarrow linewidth $^7F_0 \rightarrow$ $^5D_0$ optical transition of $\rm Eu^{3+}$ ions in an $\rm Y_2SiO_5$ matrix at cryogenic temperatures. We provide linear Stark coefficients along two dielectric axes and for the two different substitution sites of the $\rm Eu^{3+}$ ions, with an unprecedented accuracy, and an upper limit for the quadratic Stark shift. The measurements, which indicate that the electric field sensitivity is a factor of seven larger for site 1 relative to site 2 for a particular…
Investigating Roles of Triple Excitations for High-precision Determination of Clock Properties of Alkaline Earth Metal Singly Charged Ions
Atomic, Molecular and Optical Physics Division, Physical Research Laboratory（物理研究实验室原子、分子与光学物理分部）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）
