Theoretical approaches to the photoionization of few-electron atoms are discussed. These include nonequilibrium Greens functions and wave function based approaches. In particular, the Multiconfiguration Time-Dependent Hartree-Fock method is discussed and applied to a model one-dimensional atom with four electrons. We compute ground state energies and the time-dependent photoionization by the field a strong laser pulse with two different frequencies in the ultraviolet.
In a seminal article, Fano predicts that absorption of light occurs preferably with increase of angular momentum. Here we generalize Fano's propensity rule to laser-assisted photoionization, consisting of absorption of an extreme-ultraviolet photon followed by absorption or emission of an infrared photon. The predicted asymmetry between absorption and emission leads to incomplete quantum interference in attosecond photoelectron interferometry. It explains both the angular-dependence of the photoionization time delays and the delay-dependence of the photoelectron angular distributions. Our theo…
We photoionize nitrogen molecules with a train of extreme ultraviolet attosecond pulses together with a weak infrared field. We measure the phase of the two-color two-photon ionization transition (molecular phase) for different states of the ion. We observe a 0.76 $π$ shift for the electrons produced in the ionization channels leading to the X$^2 Σ_g^+$, $v'=1$ and $v'=2$ states. We relate this phase shift to the presence of a complex resonance in the continuum. By providing both a high spectral and temporal resolution, this general approach gives access to the evolution of extremely short liv…
Using extreme-ultraviolet attosecond-pulse-trains, we investigate the photoionization dynamics of a Helium atom in the presence of moderately-strong (~10^12 W/cm^2) femtosecond laser pulses. The electronic structure of a laser-dressed atom is traced in real-time through precision measurements of ion-yields and photo-electron angular distributions. Quantum interferences between photo-excitation paths are interpreted using the Floquet formalism. As the laser pulse intensity ramps on femtosecond timescales, we observe transitions between ionization channels mediated by different atomic resonances…
High-resolution photoionization experiments were carried out using beams of Be-like C$^{2+}$, N$^{3+}$, and O$^{4+}$ ions with roughly equal populations of the $^1$S ground-state and the $^3$P$^o$ manifold of metastable components. The energy scales of the experiments are calibrated with uncertainties of 1 to 10 meV depending on photon energy. Resolving powers beyond 20,000 were reached allowing for the separation of contributions from the individual metastable $^3$P$^o_0$, $^3$P$^o_1$, and $^3$P$^o_2$ states. The measured data compare favourably with semi-relativistic Breit-Pauli R-matrix
We present a quantum kinetic approach for the time-resolved description of many-body effects in photoionization processes in atoms. The method is based on the non-equilibrium Green functions formalism and solves the Keldysh/Kadanoff-Baym equations in second Born approximation. An approximation scheme is introduced and discussed, which provides a complete single-particle description of the continuum, while the atom is treated fully correlated.
Chiral light-matter interactions have been investigated for two centuries, leading to the discovery of many chiroptical processes used for discrimination of enantiomers. Whereas most chiroptical effects result from a response of bound electrons, photoionization can produce much stronger chiral signals that manifest as asymmetries in the angular distribution of the photoelectrons along the light propagation axis. Here we implement a self-referenced attosecond photoelectron interferometry to measure the temporal profile of the forward and backward electron wavepackets emitted upon photoionizatio…
We study the photoionization and autoionization of Helium atom subject to ultrashort laser pulses by using a Feshbach formalism in the time domain. We solve the time-dependent Schrödinger equation in terms of a configuration interaction (CI) spectral method, in which the total wavefunction is expanded with configurations defined within bound-like ($\mathcal{Q}$) and scattering-like ($\mathcal{P}$) halfspaces. The method allowsone to provide accurate descriptions of both the atomic structure (energy positions and widths) and the photodynamics. We illustrate our approach by i) calculating the ti…
We investigate the angle-resolved photoelectron spectra from laser-assisted photoionization for helium and neon atoms using an \textit{ab initio} method based on time-dependent surface flux and configuration interaction singles. We find that the shape of the distributions can be interpreted using a propensity rule, an intrinsic difference in the absorption and emission processes, as well as interference effects between multiple paths to the final angular momentum state. In neon we find that the difference between absorption and emission is hidden in the first sideband due to the multiple compe…
We present a theory of time-resolved photoionisation in the presence of a vortex beam. In a pump-probe setup, an extreme ultraviolet or an x-ray pump pulse triggers ionization, which is probed by a synchronized infrared pulse with non-zero orbital angular momentum. We show, how this property of the probe pulse affects the electron dynamics upon ionization, in a way that is independent of the initial and final angular momentum states of the ionizing system.
We present R-matrix calculations of photoabsorption and photoionization cross sections across the K edge of the Li-like to Ca-like ions stages of Ni. Level-resolved, Breit-Pauli calculations were performed for the Li-like to Na-like stages. Term-resolved calculations, which include the mass-velocity and Darwin relativistic corrections, were performed for the Mg-like to Ca-like ion stages. This data set is extended up to Fe-like Ni using the distorted wave approximation as implemented by AUTOSTRUCTURE. The R-matrix calculations include the effects of radiative and Auger dampings by means of an …
We present the experimental observation of two-center interference in the ionization time delays of Kr2. Using attosecond electron-ion-coincidence spectroscopy, we simultaneously measure the photoionization delays of krypton monomer and dimer. The relative time delay is found to oscillate as a function of the electron kinetic energy, an effect that is traced back to constructive and destructive interference of the photoelectron wave packets that are emitted or scattered from the two atomic centers. Our interpretation of the experimental results is supported by solving the time-independent Schr…
Quantum mechanically, photoionization can be fully described by the complex photoionization amplitudes that describe the transition between the ground state and the continuum state. Knowledge of the value of the phase of these amplitudes has been a central interest in photoionization studies and newly developing attosecond science, since the phase can reveal important information about phenomena such as electron correlation. We present a new attosecond-precision interferometric method of angle-resolved measurement for the phase of the photoionization amplitudes, using two phase-locked Extreme …
We theoretically study time-resolved photoemission in atoms as probed by attosecond streaking. We review recent advances in the study of the photoelectric effect in the time domain and show that the experimentally accessible time shifts can be decomposed into distinct contributions that stem from the field-free photoionization process itself and from probe-field induced corrections. We perform accurate quantum-mechanical as well as classical simulations of attosecond streaking for effective one-electron systems and determine all relevant contributions to the time delay with attosecond precisio…
Characterizing time delays in molecular photoionization as a function of the ejected electron emission direction relative to the orientation of the molecule and the light polarization axis pro-vides unprecedented insights into the attosecond dynamics induced by extreme ultraviolet or X-ray one-photon absorption, including the role of electronic correlation and continuum resonant states. Here, we report completely resolved experimental and computational angular depend-ence of single-photon ionization delays in NO molecules across a shape resonance, relying on synchrotron radiation and time inde…
Using a spectrally resolved electron interferometry technique, we measure photoionization time delays between the $3s$ and $3p$ subshells of argon over a large 34-eV energy range covering the Cooper minima in both subshells. The observed strong variations of the $3s-3p$ delay difference, including a sign change, are well reproduced by theoretical calculations using the Two-Photon Two-Color Random Phase Approximation with Exchange. Strong shake-up channels lead to photoelectrons spectrally overlapping with those emitted from the $3s$ subshell. These channels need to be included in our analysis …
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…
Time-delays in the photoionization of molecules are investigated. As compared to atomic ionization, the time-delays expected from molecular ionization present a much richer phenomenon, with a strong spatial dependence due to the anisotropic nature of the molecular scattering potential. We investigate this from a scattering theory perspective, and make use of molecular photoionization calculations to examine this effect in representative homonuclear and hetronuclear diatomic molecules, nitrogen and carbon monoxide. We present energy and angle-resolved maps of the Wigner delay time for single-ph…
Bichromatic extreme-ultraviolet pulses from a seeded free-electron laser enable us to measure photoelectron angular distribution (PAD) as a function of the relative phase between the different wavelength components. The time-dependent multiconfiguration self-consistent-field (TD-MCSCF) methods are powerful multielectron computation methods to accurately simulate such photoionization dynamics from the first principles. Here we propose a method to evaluate the amplitude and phase of each ionization path, which completely determines the photoionization processes, using TD-MCSCF simulation results…
We revisit the time-resolved photoemission in neon atoms as probed by attosecond streaking. We calculate streaking time shifts for the emission of 2p and 2s electrons and compare the relative delay as measured in a recent experiment by Schultze et al. [Science 328, 1658 (2010)]. The B-spline R-matrix method is employed to calculate accurate Eisenbud-Wigner-Smith time delays from multi- electron dipole transition matrix elements for photoionization. The additional laser field-induced time shifts in the exit channel are obtained from separate, time-dependent simulations of a full streaking proce…
A time-resolved spectroscopic protocol exploiting terahertz-assisted photoionization is proposed to reconstruct transient density matrix. Population and coherence elements are effectively mapped onto spectrally separated peaks in photoionization spectra. The beatings of coherence dynamics can be temporally resolved beyond the pulse duration, and the relative phase between involved states is directly readable from the oscillatory spectral distribution. As demonstrated by a photo-excited multilevel open quantum system, the method shows potential applications for sub-femtosecond time-resolved mea…
Modelling of massive stars and supernovae (SNe) plays a crucial role in understanding galaxies. From this modelling we can derive fundamental constraints on stellar evolution, mass-loss processes, mixing, and the products of nucleosynthesis. Proper account must be taken of all important processes that populate and depopulate the levels (collisional excitation, de-excitation, ionization, recombination, photoionization, bound-bound processes). For the analysis of Type Ia SNe and core collapse SNe (Types Ib, Ic and II) Fe group elements are particularly important. Unfortunately little data is cur…
Propylene oxide, a favorite target of experimental and theoretical studies of circular dichroism, was recently discovered in interstellar space, further amplifying the attention to its role in the current debate on protobiological homochirality. In the present work, a photoelectron-photoion-photoion coincidence technique, using an ion-imaging detector and tunable synchrotron radiation in the 18.0-37.0 eV energy range, permits: (i)-to observe six double-ionization fragmentation channels, their relative yields being accounted for about two-thirds by the couple (C2H4+, CH2O+), one-fifth by (C2H3+…
We investigate the photoionization spectrum of helium by attosecond XUV pulses both in the spectral region of doubly excited resonances as well as above the double ionization threshold. In order to probe for convergence, we compare three techniques to extract photoelectron spectra from the wavepacket resulting from the integration of the time-dependent Schroedinger equation in a finite-element discrete variable representation basis. These techniques are: projection on products of hydrogenic bound and continuum states, projection onto multi-channel scattering states computed in a B-spline clos…
We present a theoretical study of atomic laser-assisted photoionization emission (LAPE). We consider an atom driven by a linearly polarized XUV laser in two different scenarios: i) a single attosecond pulse (in both the streaking and sideband regimes) and ii) an attosecond pulse train. The process takes place assisted by a linearly polarized infrared (IR) laser field. In all these cases the energy and angle-resolved photoelectron spectrum (PES) is determined by a leading contribution, related to the intracycle factor [Gramajo et al., J. Phys. B 51, 055603 (2018)], complemented by other ones, d…
We investigate K-shell ionization of N$_2$ at 40 keV photon energy. Using a COLTRIMS reaction microscope we determine the vector momenta of the photoelectron, the Auger electron and both N$^+$ fragments. These fully differential data show that the dissociation process of the N$_2^{2+}$ ion is significantly modified not only by the recoil momentum of the photoelectron, but also by the photon momentum and the momentum of the emitted Auger electron. We find that the recoil energy introduced by the photon and the photoelectron momentum is partitioned with a ratio of approximately 30/70 between the…
By considering photoionization of the C$_{60}$ fullerene, we elucidate the contributions of various classical and quantum physics phenomena appearing in this process. By comparing the results, based on the {\it ab initio} and model approaches, we map the well-resolved features of the photoabsoprtion spectrum to single-particle and collective excitations which have the different physical nature. It is demonstrated that the peculiarities arising in the photoionization spectrum of C$_{60}$ atop the dominating plasmon excitations have the quantum origin. In particular, we demonstrate that a series…
Results from large-scale theoretical cross section calculations for the total photoionization of the 4f, 5s, 5p and 6s orbitals of the neutral tungsten atom using the Dirac Coulomb R-matrix approximation (DARC: Dirac-Atomic R-matrix codes) are presented. Comparisons are made with previous theoretical methods and prior experimental measurements. In previous experiments a time-resolved dual laser approach was employed for the photo-absorption of metal vapours and photo-absorption measurements on tungsten in a solid, using synchrotron radiation. The lowest ground state level of neutral tungsten i…
Recent angle-resolved RABBITT experiments have shown that the photoionization time delay depends on the emission angle of the photoelectron. In this work we demonstrate that for photoemission from helium accompanied by shake-up (correlation satellites), the angular variation of the time delay is dramatically enhanced by the dipolar coupling between the photoelectron and the highly polarizable bound electron in the IR field. We show that the additivity rule for the time delays due to the atomic potential, the continuum-continuum (cc) coupling by the IR field, and due to this two-electron proces…
Measured photoionization time delays may exhibit large variations as a function of the emission angles, even for spherically symmetric targets, as shown in recent RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) experiments. The contributions from different pathways to the two-photon quantum channels can already explain the observed phase jumps that shape those angular distributions. Here, we propose a simple analytical model to describe angularly-resolved RABBITT spectra as a function of the relative polarization angle between the ionizing attosecond pu…
Based on the Rb$^+$-Rb hybrid trap, we investigate the effect of ion-atom elastic collisions on the number and temperature of the remaining atoms. We measured the remaining atomic number and temperature as a function of the wavelength and intensity of the ionization laser, and whether the ion trap was turned on. Fittings with a single exponential decay function plus an offset to the number and radius of the remaining atoms are found to be in good agreement. We found a difference in the exponential factor of different wavelengths of ionization laser with the ion trap on or off. We suppose that …
The time-dependent Schrödinger equation for the hydrogen atom and its interaction with coherent intense high-frequency short laser pulses is solved numerically exactly by propagating the single-electron wave packets. Thereby, the wavefunction is followed in space and time for times longer than the pulse duration. Results are explicitly shown for 3 and 10 fs pulses. Particular attention is paid to identifying the effect of dynamic interference of photoelectrons emitted with the same kinetic energy at different times during the rising and falling sides of the pulse predicted in [\emph{Ph.V. Deme…
Most astrophysical plasmas entail a balance between ionization and recombination. We present new results from the powerful R-matrix method which yields in an ab initio manner: (I) self-consistent photoionization and recombination cross sections using identical wavefunction expansions, (II) unified e-ion recombination rates at all temperatures of interest, incorporating non-resonant and resonant processes, radiative and dielectronic recombination (RR and DR), and (III) level-specific recombination rates for many excited atomic levels. RR and DR processes can not be measured or observed independ…
We present an experimental study on the photoionization dynamics of non-resonant one-color two-photon single valence ionization of neutral argon atoms. Using 9.3 eV photons produced via high harmonic generation and a 3-D momentum imaging spectrometer, we detect the photoelectrons and ions produced from non-resonant two-photon ionization in coincidence. Photoionization from the $3p$ orbital produces a photoelectron scattering wave function with $p$ and $f$ partial wave components, which interfere and result in a photoelectron angular distribution with peak amplitude perpendicular to the VUV pol…
We theoretically study orbital alignment in x-ray-ionized atoms and ions, based on improved electronic-structure calculations starting from the Hartree-Fock-Slater model. We employ first-order many-body perturbation theory to improve the Hartree-Fock-Slater calculations and show that the use of first-order-corrected energies yields significantly better transition energies than originally obtained. The improved electronic-structure calculations enable us also to compute individual state-to-state cross sections and transition rates and, thus, to investigate orbital alignment induced by linearly …
Recent developments toward the production and laboratory use of pulses of high intensity, and/or of very high frequency, and/or of ultrashort duration, make possible experiments which can produce time-resolved data on ultrafast transformations involving motions of electrons. The formulation, quantitative understanding and prediction of related new phenomena entail the possibility of computing and applying solutions of the many-electron time-dependent Schroedinger equation, for arbitrary electronic structures, including the dominant effects of Rydberg series, of multiply excited states and of t…
The acetylene-vinylidene system serves as a benchmark for investigations of ultrafast dynamical processes where the coupling of the electronic and nuclear degrees of freedom provides a fertile playground to explore the femto- and sub-femto-second physics with coherent extreme-ultraviolet (EUV) photon sources both on the table-top as well as free-electron lasers. We focus on detailed investigations of this molecular system in the photon energy range $19...40$ eV where EUV pulses can probe the dynamics effectively. We employ photoelectron-photoion coincidence (PEPICO) spectroscopy to uncover hit…
A time-dependent approach for the kinetic energy release (KER) spectrum is developed for a fragmentation of a diatomic molecule after an electronic decay process, e.g. Auger process. It allows one to simulate the time-resolved spectra and provides more insight into the molecular dynamics than the time-independent approach. Detailed analysis of the time-resolved emitted electron and KER spectra sheds light on the interrelation between wave packet dynamics and spectra.
