We present absolute-frequency measurements for the transitions from the 6s$_{1/2}$ ground state of $^{133}$Cs to $n$p$_{1/2}$ and $n$p$_{3/2}$ Rydberg states. The transition frequencies are determined by one-photon UV spectroscopy in ultracold samples of Cs atoms using a narrowband laser system referenced to a frequency comb. From a global fit of the ionization energy $E_\mathrm{I}$ and the quantum defects of the two series we determine an improved value of $E_\mathrm{I} = h c \cdot 31 406.467 732 5(14)$ cm$^{-1}$ for the ionization energy of Cs with a relative uncertainty of $5\times10^{-11}$. We also report improved values for the quantum defects of the $n$p$_{1/2}$, $n$p$_{3/2}$, $n$s$_{1/2}$, and $n$d$_{5/2}$ series.
A complete set of spectroscopic data is indispensable when using Rydberg states of trapped ions for quantum information processing. We carried out Rydberg series spectroscopy for $nS_{1/2}$ states with $38 \leq n \leq 65$ and for $nD_{5/2}$ states with $37\leq n \leq 50$ on a single trapped $^{40}$Ca$^+$ ion. From a nonlinear regression to resonance frequencies, we determined the ionization energy of 2 870 575.582(15) GHz, measured 60 times more accurately as compared to the accepted value and contradicting it by 7.5 standard deviations. We confirm quantum defect values of $δ_{S_{1/2}}=1.80299…
Ionization of an atom or molecule presents surprising richness beyond our current understanding: strong-field ionization with low-frequency fields recently revealed unexpected kinetic energy structures (1, 2). A solid grasp on electron dynamics is however pre-requisite for attosecond-resolution recollision imaging (3), orbital tomography (4), for coherent sources of keV light (5), or to produce zeptosecond-duration x-rays (6). We present a methodology that enables scrutinizing strong-field dynamics at an unprecedented level. Our method provides high-precision measurements only 1 meV above the …
We present absolute-frequency measurements in ultracold 39K samples of the transitions from the ground state to np Rydberg states. A global nonlinear regression of the np1/2 and np3/2 term values yields an improved wave number of 35009.8139710(22)(sys)(3)(stat) cm-1 for the first ionization threshold of 39K and the quantum defects of the np1/2 and np3/2 series. In addition, we report the frequencies of selected one-photon transitions n's <- np3/2, n'd <- np3/2, n'f <- nd and n'g <- nf and two-photon transitions nf <- np determined by millimeter-wave spectroscopy. By combining the results from …
Molecular helium represents a benchmark system for testing $\textit{ab initio}$ calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the $a\,^3Σ_u^+$ state of He$_2$, corresponding to the energy interval between the $a\,^3Σ_u^+$ ($v''=0$, $N''=1$) state of He$_2$ and the $X^+\,^2Σ_u^+$ ($v^+=0$, $N^+=1$) state of He${_2}^+$, and of the lowest rotational interval of He${_2}^+$. These measurements rely on the excitation of metastable He$_2$ molecules to high Rydberg states using frequency-comb-calibrated continuous-wave UV radiation in a co…
The classical-quantum hybrid Variational Quantum Eigensolver algorithm is the most widely used approach in the Noisy Intermediate Scale Quantum era to obtain ground state energies of atomic and molecular systems. In this work, we extend the scope of properties that can be calculated using the algorithm by computing the first ionization energies of Lithium and Boron atoms. We check the precision of our ionization energies and the observed many-body trends and compare them with the results from calculations carried out on traditional computers.
We report measurements of electron impact ionization (EII) for Fe^13+, Fe^16+, and Fe^17+ over collision energies from below threshold to above 3000 eV. The ions were recirculated using an ion storage ring. Data were collected after a sufficiently long time that essentially all the ions had relaxed radiatively to their ground state before data were collected. For single ionization of $\fethirteen$ we find that previous single pass experiments are more than 40% larger than our results. Compared to our work, the theoretical cross section recommended by Arnaud & Raymond (1992) is more than 30% la…
Selective field ionization is used to determine the state or distribution of states to which a Rydberg atom is excited. By evolving a small perturbation to the ramped electric field using a genetic algorithm, the shape of the time-resolved ionization signal can be controlled. This allows for separation of signals from pairs of states that would be indistinguishable with unperturbed selective field ionization. Measurements and calculations are presented that demonstrate this technique and shed light on how the perturbation directs the pathway of the electron to ionization. Pseudocode for the ge…
An ionization-induced plasma grating can be formed by spatially selective ionization of gases by the interference of two intersecting ultra-short laser pulses. The density modulation of a plasma grating can approach unity since the plasma is produced only where the two pulses constructively interfere and ionization does not occur in destructive interference regions. Such a large density modulation leads to efficient Thomson scattering of a second ultra-short probe pulse once the Bragg condition is satisfied. By measuring the scattering efficiency, it is possible to determine the absolute elect…
We present experimental measurements and theoretical calculations of photoionization time delays from the $3s$ and $3p$ shells in Ar in the photon energy range of 32-42 eV. The experimental measurements are performed by interferometry using attosecond pulse trains and the infrared laser used for their generation. The theoretical approach includes intershell correlation effects between the 3s and 3p shells within the framework of the random phase approximation with exchange (RPAE). The connection between single-photon ionization and the two-color two-photon ionization process used in the measur…
We have measured the forbidden 2 3S1 - 2 1P1 transition at 887 nm in a quantum degenerate gas of metastable He-4 atoms confined in an optical dipole trap. The determined transition frequency is 338 133 594.4 (0.5) MHz, from which we obtain an ionization energy of the 2 1P1 state of 814 709 148.6 (0.5) MHz. This ionization energy is in disagreement by > 3 sigma with the most accurate quantum electrodynamics (QED) calculations available. Our measurements also provide a new determination of the lifetime of the 2 1P1 state of 0.551 (0.004)stat (+ 0.013,- 0.000)syst ns, which is the most accurate d…
To have a better understanding of a physical process, a comparison of ex-perimental data with theoretical values is mandatory. The comparison ismeaningful if the uncertainty in the experiment is accounted well. However,it is seldom seen, especially for a complex phenomenon. We take a test casethrough L subshell ionization of atoms by particle impact. Experimentally,x-ray production cross-sections are measured, but ionization cross-sectionsare calculated theoretically. Furthermore, the uncertainty of the x-ray pro-duction cross-section is mainly statistics and detector-efficiency driven. Bution…
We study resonant two-color two-photon ionization of Helium via the 1s3p 1P1 state. The first color is the 15th harmonic of a tunable titanium sapphire laser, while the second color is the fundamental laser radiation. Our method uses phase-locked high-order harmonics to determine the {\it phase} of the two-photon process by interferometry. The measurement of the two-photon ionization phase variation as a function of detuning from the resonance and intensity of the dressing field allows us to determine the intensity dependence of the transition energy.
We have measured electron impact ionization (EII) for Fe 7+ from the ionization threshold up to 1200 eV. The measurements were performed using the TSR heavy ion storage ring. The ions were stored long enough prior to measurement to remove most metastables, resulting in a beam of 94% ground state ions. Comparing with the previously recommended atomic data, we find that the Arnaud & Raymond (1992) cross section is up to about 40\% larger than our measurement, with the largest discrepancies below about 400~eV. The cross section of Dere (2007) agrees to within 10%, which is about the magnitude of …
We report ionization cross section measurements for electron impact single ionization (EISI) of Fe^11+$ forming Fe^12+ and electron impact double ionization (EIDI) of Fe^11+ forming Fe^13+. The measurements cover the center-of-mass energy range from approximately 230 eV to 2300 eV. The experiment was performed using the heavy ion storage ring TSR located at the Max-Planck-Institut fur Kernphysik in Heidelberg, Germany. The storage ring approach allows nearly all metastable levels to relax to the ground state before data collection begins. We find that the cross section for single ionization is…
An apparatus for production of various atomic and molecular ions inside a linear Paul trap has been set up. The system applies a custom-made, low energy, pulsed electron gun to produce ions in electron impact process. Such ionization method can find some interesting possible applications such as derivation of ions inaccessible other-ways, which can be used in molecular ion experiments. The technique allows also for determination of cross sections for various collisional processes. As a feasibility study, the apparatus was used for determination of ionization integral cross section of calcium i…
Photoionization spectra of Se have been studied by step-wise resonance laser ionization. The Rydberg series 4s$^2$4p$^3$($^4$S)np $^3$P$_{0,1,2}$ and 4s$^2$4p$^3$($^4$S)np $^5$P$_{1,2,3}$ were measured via different excitation schemes. Using the Rydberg series 4s$^2$4p$^3$($^4$S)np $^3$P$_2$ with n=15-33, the ionization potential of Se was determined with improved precision to 76658.15(2)$_{stat}$(4)$_{sys}$ cm$^{-1}$, which resolved the discrepancy in previous literatures. Autoionizing (AI) spectra between the IP and two neighboring converging limits of the Se ionic states 4s$^2$4p$^3$($^2$D$…
The first ionization potential of neutral atoms is determined from thresholds of laser-induced optical breakdown. Bulk material ablation plasma of aluminum, silver, lead, indium and copper is created in laboratory air with focused, 5-ns pulsed Nd:YAG, 1064 nm IR radiation. At fixed spot size of 2 $\pm$ 0.1 mm, the laser fluence is varied from 16 to 3 J/cm$^2$. The first ionization potentials of the lines Al I 396.2, Ag I 520.9, Pb I 405.8 and 406.2, In I 410.2 and Cu I 515.3 nm are measured to amount to 5.9 $\pm$ 0.2, 7.6 $\pm$ 0.3, 7.4 $\pm$ 0.2, 5.8 $\pm$ 0.1 and 7.7 $\pm$ 0.2 eV, respective…
We propose an attosecond XUV-pump IR-probe photoionization protocol that employs pairs of counter-rotating consecutive harmonics and angularly resolved photoelectron detection, thereby providing direct measurement of ionization phases. The present method, which we call circular holographic ionization-phase meter (CHIP), gives also access to the phase of photoemission amplitudes of even-parity continuum states from a single time-delay measurement, since the relative phase of one- and two-photon ionization pathways is imprinted in the photoemission anisotropy. The method is illustrated with \emp…
This work reports on the application of a novel electric field-ionization setup for high-resolution laser spectroscopy measurements on bunched fast atomic beams in a collinear geometry. In combination with multi-step resonant excitation to Rydberg states using pulsed lasers, the field ionization technique demonstrates increased sensitivity for isotope separation and measurement of atomic parameters over non-resonant laser ionization methods. The setup was tested at the Collinear Resonance Ionization Spectroscopy experiment at ISOLDE-CERN to perform high-resolution measurements of transitions i…
Matter-wave interferometry with atoms and molecules has attracted a rapidly growing interest over the past two decades, both in demonstrations of fundamental quantum phenomena and in quantum-enhanced precision measurements. Such experiments exploit the non-classical superposition of two or more position and momentum states which are coherently split and rejoined to interfere. Here, we present the experimental realization of a universal near-field interferometer built from three short-pulse single-photon ionization gratings. We observe quantum interference of fast molecular clusters, with a com…
Resolving in time the dynamics of light absorption by atoms and molecules, and the electronic rearrangement this induces, is among the most challenging goals of attosecond spectroscopy. The attoclock is an elegant approach to this problem, which encodes ionization times in the strong-field regime. However, the accurate reconstruction of these times from experimental data presents a formidable theoretical challenge. Here, we solve this problem by combining analytical theory with ab-initio numerical simulations. We apply our theory to numerical attoclock experiments on the hydrogen atom to extra…
We investigate the ionization dynamics of Argon atoms irradiated by an ultrashort intense laser of a wavelength up to 3100 nm, addressing the momentum distribution of the photoelectrons with near-zero-energy. We find a surprising accumulation in the momentum distribution corresponding to meV energy and a \textquotedblleft V"-like structure at the slightly larger transverse momenta. Semiclassical simulations indicate the crucial role of the Coulomb attraction between the escaping electron and the remaining ion at extremely large distance. Tracing back classical trajectories, we find the tunneli…
The energy distribution of an ultracold rubidium ion beam, which is intended to be used as the source for a focused ion beam instrument, is measured with a retarding field analyzer. The ions are created from a laser-cooled and compressed atomic beam by two-step photoionization in which the ionization laser power is enhanced in a build-up cavity. Particle tracing simulations are performed to ensure the analyzer is able to resolve the distribution. The lowest achieved full width 50% energy spread is $\left(0.205\pm0.006\right)$ eV. The energy spread originates from the variation in the ionizatio…
Rate coefficients for photorecombination (PR) and cross sections for electron-impact ionization (EII) of Fe$^{14+}$ forming Fe$^{13+}$ and Fe$^{15+}$, respectively, have been measured by employing the electron-ion merged-beams technique at a heavy-ion storage ring. Rate coefficients for PR and EII of Fe$^{14+}$ ions in a plasma are derived from the experimental measurements. Simple parametrizations of the experimentally derived plasma rate coefficients are provided for use in the modeling of photoionized and collisionally ionized plasmas. In the temperature ranges where Fe$^{14+}$ is expected …
Accurate cross section data for electron impact ionization (EII) are needed in order to interpret the spectra of collisionally ionized plasmas both in astrophysics and in the laboratory. Models and spectroscopic diagnostics of such plasmas rely on accurate ionization balance calculations, which depend, in turn, on the underlying rates for EII and electron-ion recombination. EII measurements have been carried out using the TSR storage ring located at the Max-Planck-Institut fuer Kernphysik in Heidelberg, Germany. Storage ring measurements are largely free of metastable contamination, resulting …
We investigate the carrier-envelope phase and intensity dependence of the longitudinal momentum distribution of photoelectrons resulting from above-threshold ionization of argon by few-cycle laser pulses. The intensity of the pulses with a center wavelength of 750\,nm is varied in a range between $0.7 \times 10^{14}$ and $\unit[5.5 \times 10^{14}]{W/cm^2}$. Our measurements reveal a prominent maximum in the carrier-envelope phase-dependent asymmetry at photoelectron energies of 2\,$U_\mathrm{P}$ ($U_\mathrm{P}$ being the ponderomotive potential), that is persistent over the entire intensity ra…
Study on ionization process of molecules in an intense infrared laser field is of paramount interest in strong-field physics and constitutes the foundation of imaging of molecular valence orbitals and attosecond science. We show measurement of alignment-dependent ionization probabilities of the lower-lying orbitals of the molecules by experimentally detecting alignment-dependence of fluorescence emission from tunnel ionized carbon dioxide molecules. The experimental measurements are compared with the theoretical calculations of strong field approximation (SFA) and molecular ADK models. Our res…
Ionization energies for Rydberg $^4 \mathrm{He}$ ($1snp\,^{1,3}P$) states using the correlated B-spline basis function method
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新院）；University of Chinese Academy of Sciences（中国科学院大学）
Elliptically polarized laser pulses (EPLPs) are widely applied in many fields of ultrafast sciences, but the ellipticity~($\varepsilon$) has never been in situ measured in the interaction zone of the laser focus. In this work, we propose and realize a robust scheme to retrieve the $\varepsilon$ by temporally overlapping two identical counter-rotating EPLPs. The combined linearly electric field is coherently controlled to ionize Xe atoms by varying the phase delay between the two EPLPs. The electron spectra of the above-threshold ionization and the ion yield are sensitively modulated by the pha…
This publication describes a re-analysis of previously published data on neutral carbon (C I) utilizing critically examined and improved values for the line energies of the absorption spectrum of molecular iodine to calibrate the transition energies of C I absorption lines originating from the 1s22s22p3s 3P°2) level and terminating on highly excited Rydberg states of the 1s22s22pnp 3D3 series, which converges on the first excited fine-structure level of the ionic ground configuration. Additional use of improved energy values for the 1s22s22p3s 3P°2 level, the fine-structure interval of the ion…
Testing Exotic Electron-Electron Interactions with the Helium Ionization-Energy Anomaly
Helmholtz Institute Mainz（亥姆霍兹马因茨研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI重离子研究中心有限公司）；Johannes Gutenberg University（约翰内斯·古腾堡大学）；Faculty of Mathematics, University of Vienna（维也纳大学数学学院）；Gravitational Physics Group, University of Vienna（维也纳大学引力物理组）；Department of Physics, University of California at Berkeley（加州大学伯克利分校物理系）
Measurement of the $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ interval in positronium using field-ionization of Rydberg states
To measure and control the electron motion in atoms and molecules by the strong laser field on the attosecond time scale is one of the research frontiers of atomic and molecular photophysics. It involves many new phenomena and processes and raises a series of questions of concepts, theories and methods. Recent studies show that the Coulomb potential can cause the ionization time lag (about 100 attoseconds) between instants of the field maximum and the ionization-rate maximum. This lag can be understood as the response time of the electronic wave function to the strong-field-induced ionization …
Trapping cold, chemically important molecules with electromagnetic fields is a useful technique to study small molecules and their interactions. Traps provide long interaction times that are needed to precisely examine these low density molecular samples. However, the trapping fields lead to non-uniform molecular density distributions in these systems. Therefore, it is important to be able to experimentally characterize the spatial density distribution in the trap. Ionizing molecules in different locations in the trap using resonance enhanced multiphoton ionization (REMPI) and detecting the re…
We report new frequency-comb-based measurements of Ca Rydberg energy levels. Counter-propagating laser beams at 390 nm and 423 nm excite Ca atoms from the $4s^2~^1\mbox{S}_0$ ground state to $4sns~^1\mbox{S}_0$ Rydberg levels with $n$ ranging from 40 to 110. Near-resonant two-photon two-color excitation of atoms in a thermal beam makes it possible to eliminate the first-order Doppler shift. The resulting lineshapes are symmetric and Gaussian. We verify laser metrology and absolute accuracy by reproducing measurements of well-known transitions in Cs, close to the fundamental wavelengths of our …
We consider electron impact single ionization of an atom at large energy-momentum transfer in the nearly Bethe-ridge kinematics. For evaluation of the ionization amplitude, a plane wave Born series is employed. A regularization procedure is utilized in circumventing typical divergence problems associated with the higher-order Born terms. The regularized Born series for the ionization amplitude is derived. On this basis, renormalized analogs of the traditional plane wave Born and impulse approximations are developed. These renormalized first-order models resemble the traditional plane wave impu…
We have studied ionizing collisions in a BEC of He*. Measurements of the ion production rate combined with measurements of the density and number of atoms for the same sample allow us to estimate both the 2 and 3-body contributions to this rate. A comparison with the decay of the number of condensed atoms in our magnetic trap, in the presence of an rf-shield, indicates that ionizing collisions are largely or wholly responsible for the loss. Quantum depletion makes a substantial correction to the 3-body rate constant.
The dissociation energy of H$_2$ represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the EF $^1Σ_g^+(v=0,N=1)$ state and the 54p1$_1$ Rydberg state of H$_2$. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy $D_0^{N=1}$ of ortho-H$_2$ that has, for the first time, reached a level of uncertainty that is three times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 359…
We study photoionization of argon atoms excited by attosecond pulses using an interferometric measurement technique. We measure the difference in time delays between electrons emitted from the $3s^2$ and from the $3p^6$ shell, at different excitation energies ranging from 32 to 42 eV. The determination of single photoemission time delays requires to take into account the measurement process, involving the interaction with a probing infrared field. This contribution can be estimated using an universal formula and is found to account for a substantial fraction of the measured delay.
We present a measurement of the lifetime of ground state atomic carbon, C(^3P), against ionization processes in interplanetary space and compare it to the lifetime expected from the dominant physical processes likely to occur in this medium. Our measurement is based on analysis of a far ultraviolet (FUV) image of comet C/2004 Q2 (Machholz) recorded by the Galaxy Evolution Explorer (GALEX) on 2005 March 1. The bright CI 1561 A and 1657 A multiplets dominate the GALEX FUV band. We used the image to create high S/N radial profiles that extended beyond one million km from the comet nucleus. Our me…
