Sequential Two-photon Double Ionization Research Articles

Electron Correlations in Sequential Two-Photon Double Ionization of an Ar Atom

Sequential two-photon ionization is a process that is experimentally accessible due to the use of new free-electron laser sources for excitation. For the prototypical rare Ar gas atoms, a photoelectron spectrum (PES) corresponding to the second step of the sequential two-photon double ionization (2PDIII) at a photon excitation energy of 65.3 eV was studied theoretically with a focus on the consequences of electron correlations in the considered process. The calculation predicts many intense lines at low photoelectron energies, which cannot be explained on the basis of a one-electron approximation. The processes that lead to the appearance of these lines include many-electron correlations, either in the first or second step of photoionization. A significant fraction of the intensity of the low-energy part of PES is associated with the Auger decay of the excited states formed at the second step of 2PDI. The shape of the low-energy part of the 2PDIII PES is expected to be dependent on both the energy of photon excitations and the flux of the exciting beam.

Non-dipole effects on angular distribution of photoelectrons in sequential two-photon double ionization of Ar atom and K<sup>+</sup> ion

Owing to the development of XUV and X ray of the free-electron lasers, the photoelectron angular distribution in the sequential two-photon double ionization has received increasing attention of theorists and experimentalists, because it provides the valuable information about the electronic structure of atom or molecule systems and allows the obtaining of additional information about mechanisms and pathways of the two-photon double ionization. In this paper, the expression of the sequential two-photon double ionization process of the photoelectron angular distributions, including the non-dipole effects, is obtained based on the multi-configuration Dirac-Fock method and the density matrix theory, and the corresponding calculation code is also developed. Based on the code, the sequential two-photon double ionization process of the 3p and 2p shells of Ar atom and K<sup>+</sup> ion are studied, in which, the dipole and the non-dipole parameters of photoelectron angular distribution are investigated systematically. It is found that the angular distributions of the first- and second-step electrons in sequential two-photon double ionization are similar and the two photoionization processes affect each other. Near the ionization threshold, the photoionization cross-sections and anisotropy parameters for the 3p shell and the 2p shell show a large difference. While away from the threshold, the cross-section and angular anisotropy parameters of the 3p and 2p shells show similar behaviors. At the position of Cooper minimum of the photoionization cross section, the contribution of the electric dipole is suppressed, and the non-dipole effect is obvious. The non-dipole effect leads to a forward-backward asymmetric distribution of photoelectrons relative to the direction of incident light. The results of this paper will be helpful in studying the nonlinear processes of photon and matter interaction in the XUV range.

Photoelectron spectra and angular distribution in sequential two-photon double ionization in the region of autoionizing resonances of ArII and KrII

Autoionizing hole states with electron configuration nsnp5 mp are studied in Ar+ and Kr+. Total and partial photoionization cross sections, photoelectron spectra and photoelectron angular distributions in the region of the resonances are obtained theoretically in extensive R-matrix calculations. The states of Ar+ are observed by means of excitation by a free-electron laser operating in the vacuum- and extreme-ultraviolet wavelength regime combined with angle-resolved photoelectron spectroscopy. Fine tuning of the photon energy allows scanning of the resonances and the observation of the shape of the partial cross section ratio, as well as the asymmetry parameter of the angular distribution of the photoelectrons. The calculations are in good agreement with the experimental data.

Radial and Angular Electron Ejection Patterns of Two-Electron Quantum Dots in THz Fields

In this work, we develop and apply an ab-initio method to calculate the joint radial- and- angular electron distributions following the interaction of two-electron spherical quantum dots (QD) with intense terahertz pulses of subpicosecond duration. By applying the method to two QDs of different size, we could investigate two particular ionization mechanisms: the direct and the sequential two-photon double ionization. According to our results, the two ionization mechanisms show some similarity in the angular distribution patterns, whereas the corresponding radial distributions are distinctly different, associated with their joint kinetic energy spectrum. We also discuss the time-evolution of the ionization process in the context of the different nature of the interaction of the QD with the external radiation and the electron–electron correlation interactions.

Two- and three-photon double ionization of helium by soft x-ray free-electron laser pulses

The multiphoton double ionization of He was investigated using a soft x-ray free-electron laser (SX-FEL), in the perturbative intensity regime (<1013 W cm−2). The photon energy was tuned to the transition between the 1s and 2p levels of He+ ions. At this resonance energy of 40.8 eV, both sequential three-photon double ionization (S3PDI) and two-photon double ionization (2PDI) were measured by electron spectroscopy and by ion time-of-flight mass spectroscopy. We distinguished S3PDI from 2PDI by electron spectroscopy. Based on these experimental data, SX-FEL pulse-energy dependences of electron and ion yields for both S3PDI and 2PDI were discussed. The angular distribution of 2p photoelectrons emitted from He+(2p) ions in the S3PDI process was examined as an example of the simplest photoemission dynamics.

Polarization tagging of two-photon double ionization by elliptically polarized XUV pulses

We explore the influence of elliptical polarization on the (non)sequential two-photon double ionization of atomic helium with ultrashort extreme ultraviolet (XUV) light fields using time-dependent full ab-initio simulations. The energy and angular distributions of photoelectrons are found to be strongly dependent on the ellipticity. The correlation minimum in the joint angular distribution becomes more prominently visible with increasing ellipticity. In a pump-probe sequence of two subsequent XUV pulses with varying ellipticities, polarization tagging allows to discriminate between sequential and nonsequential photoionization. This clear separation demonstrates the potential of elliptically polarized XUV fields for improved control of electronic emission processes.

Direct and Sequential Two-Photon Double Ionization of Two-Electron Quantum Dots.

In this work we study the double ionization yields and kinetic energy spectra of a two-electron spherical quantum dot (QD) exposed in laser fields. The theoretical description is based on an ab initio nonperturbative configuration interaction theory capable of describing the two-electron QD dynamics in THz and mid-IR ultrashort laser fields. The QD's confinement potential is approximated to have a Gaussian-like spatial dependence. We have found that significant variations of the two-electron kinetic energy patterns and two-photon double ionization yields occur as we vary the QD's size. For a given laser pulse, the double ionization yield increases by orders of magnitude when the dot size is reduced. The size of the QD determines the sequential or direct character of the two-photon double ionization process. Provided that it is energetically allowed, the sequential two-photon double ionization process, requiring minimal interelectronic correlations, becomes dominant over the direct one. In the sequential regime, the corresponding two-electron kinetic energy spectrum changes from a broadened single-peaked to a doubly peaked one. Moreover, we also have identified features in the spectrum that are distinctively different than those in its atomic counterpart.

Virtual Sequential Picture for Nonsequential Two-Photon Double Ionization of Helium.

By using a model based on the second-order time-dependent perturbation theory, we show that the nonsequential two-photon double ionization of He can be understood in a virtual sequential picture: to excite the final double continuum state |k_{1},k_{2}⟩ by absorbing two photons from the ground state |1s^{2},^{1}S_{0}⟩, the single continuum states |1s,k_{1}⟩ and |1s,k_{2}⟩ serve as the dominant intermediate states. This virtual sequential picture is verified by the perfect agreement of the total ionization cross section, respectively, calculated by this model and by the sophisticated numerical solution to the full-dimensional time-dependent Schrödinger equation. This model, without the consideration of the electron correlation in the final double continuum state, works well for a wide range of laser parameters extending from the nonsequential to the sequential regime. The present Letter demonstrates that the electron correlation in the final double continuum state is not important in evaluating the total cross section, while it is indispensable for an accurate computation of a triply differential cross section. In addition, the virtual sequential picture bridges the sequential and nonsequential two-photon double ionization and reveals connections and distinctions between them.

Similarity between the angular distributions of the first- and second-step electrons in sequential two-photon atomic double ionization

Angular distributions of electrons produced in sequential two-photon atomic double ionization are considered theoretically by comparing the results obtained for the first and the second electron. It is shown analytically that the angular distributions of the two emitted electrons in many cases are similar for ionization from a closed-shell atom. Numerical examples of this counter-intuitive similarity are presented. In addition, examples are given demonstrating the difference between the angular distributions of the first photoelectron in sequential two-photon double ionization and in conventional one-photon single ionization.

Electron angular distributions of noble gases in sequential two-photon double ionization

We present an angle resolved study of photoelectrons emitted from ions of the noble gases neon, argon and krypton by means of time-of-flight spectroscopy. The ionic targets are generated in a sequential two-photon process induced by the free-electron laser FLASH. Values of the anisotropy parameters and are derived from electron angular distribution measurements in the photon energy range from 38 to 91 eV and compared with recent theoretical calculations.

Two-color above-threshold and two-photon sequential double ionization beyond the dipole approximation

Two nonlinear atomic photoprocesses are theoretically considered with the emphasis on the photoelectron angular distributions and their modifications due to violation of the dipole approximation: sequential two-photon double ionization and two-color above threshold ionization. These reactions are now accessible with X-ray free electron lasers. Both processes are exemplified by the ionization of krypton: from the 4p shell in the sequential two-photon double ionization and from the 2s shell in the two-color above-threshold ionization, which are compared to the Ar(3p) and Ne(1s) ionization, respectively. Noticeable nondipole effects are predicted.

Sequential two-photon double ionization of noble gases by circularly polarized XUV radiation

Photoelectron angular distributions (PADs) and angular correlations between two emitted electrons in sequential two-photon double ionization (2PDI) of atoms by circularly polarized radiation are studied theoretically. In particular, the sequential 2PDI of the valence shell in noble gas atoms (neon, argon, krypton) is analyzed, accounting for the first-order corrections to the dipole approximation. Due to different selection rules in ionization transitions, the circular polarization of photons causes some new features of the cross sections, PADs and angular correlation functions in comparison with the case of linearly polarized photons.

Double ionization of He by time-delayed attosecond pulses

As He is exposed to double attosecond pulses with a time delay, double ionization can proceed in several different pathways. Through ab initio simulations by the fully dimensional time-dependent Schrödinger equation, we find that interferences among different pathways in the sequential two-photon double ionization can lead to interesting grid-like patterns in the joint energy spectra of the two electrons. We show that not only these interference patterns, but also the total double ionization probability critically depends on the relative carrier–envelope phase (CEP) between the two attosecond pulses. Our findings are successfully explained by a model based on second-order time-dependent perturbation theory. The present study demonstrates the feasibility of CEP control of double ionization, and provides an alternative way to characterize the relative CEP of attosecond pulses.

Non-dipole effects in the angular distribution of photoelectrons in sequential two-photon double ionization: argon and neon

As an extension to recent developments in the theory of non-dipole effects in nonlinear photoprocesses in the XUV/x-ray wavelength regime, the sequential two-photon double ionization of the 3p shell in atomic argon is studied theoretically and compared to similar processes in the 2p shell of neon. The calculations predict distinct non-dipole effects in the region of the Cooper minimum in argon at photon energies around 50 eV, where they are of similar importance as at photon energies of more than 500 eV. The non-dipole effects should therefore be clearly observable in experiments performed at the present x-ray free electron lasers.

Nonlinear phenomena in atoms when interacting with VUV and soft X-ray radiation

Theoretical description of photoelectron angular distributions in the simplest nonlinear atomic processes in X-ray and VUV is extended beyond the dipole approximation. On the example of sequential two-photon double ionization of neon it is shown that the contribution of the electric quadrupole transitions can be observed in already operating X-ray free electron lasers.

Angular correlations in the sequential two-photon double ionisation of atomic xenon

The sequential two-photon double ionization has been analyzed for the 4d electrons of atomic xenon in the region of the giant resonance and beyond (70–200 eV), for which intense FEL radiation is available at the free electron laser FLASH. The 4d vacancies in xenon couple strongly to the autoionization continuum with lifetimes of only a few fs, and their Auger decay thus competes with the subsequent (second-and higher-step) photoionization in typical FEL pulses.

Non-dipole effects in the angular distribution of photoelectrons in sequential two-photon atomic double ionization

Motivated by the recent achievements of experiments using x-ray free electron lasers, we have developed a theory for the angular distributions of photoelectrons in sequential two-photon double ionization (2PDI) of atoms beyond the dipole approximation. Expressions for the angular distributions are obtained taking into account the full multipole expansion of radiation in electric and magnetic moments. The formalism is further specified for the first-order corrections to the dipole approximation. As an illustrative example, the sequential 2PDI of the 2p shell in atomic neon is studied. The numerical calculations predict distinct non-dipole effects observable in experiments at present x-ray free electron lasers.

Sequential two-photon double ionization of the 4d shell in xenon

The sequential two-photon double ionization of 4d electrons of xenon in intense free-electron laser (FEL) radiation is theoretically investigated for photon energies of 70–200 eV. At these energies, which are available at the free-electron laser FLASH, the 4d photoionization dominates over the ionization of the valence shells, showing a giant resonance. The 4d vacancy produced by the first photon strongly couples to the (Auger) autoionization continuum with a lifetime of only ∼6 fs and thus the Auger decay competes with the second photoionization in a typical FEL pulse. The photoelectron angular distributions and angular correlation between emitted electrons are investigated as associated with the peculiar 4d character of the photoionization and Auger decay.

Universal features in sequential and nonsequential two-photon double ionization of helium

We analyze two-photon double ionization of helium in both the nonsequential ($\ensuremath{\hbar}\ensuremath{\omega}&lt;{I}_{2}\ensuremath{\approx}54.4 \mathrm{eV}$) and sequential ($\ensuremath{\hbar}\ensuremath{\omega}&gt;{I}_{2}$) regime. We show that the energy spacing $\ensuremath{\Delta}E={E}_{1}\ensuremath{-}{E}_{2}$ between the two emitted electrons provides the key parameter that controls both the energy and the angular distribution and reveals the universal features present in both the nonsequential and sequential regime. This universality, i.e., independence of $\ensuremath{\hbar}\ensuremath{\omega}$, is a manifestation of the continuity across the threshold for sequential double ionization. For all photon energies considered, the energy distribution can be described by a universal shape function that contains only the spectral and temporal information entering second-order time-dependent perturbation theory. Angular correlations and distributions are found to be more sensitive to the value of $\ensuremath{\hbar}\ensuremath{\omega}$. In particular, shake-up interferences have a large effect on the angular distribution. Energy spectra, angular distributions parametrized by the anisotropy parameters ${\ensuremath{\beta}}_{j}$, and total cross sections presented in this paper are obtained by fully correlated time-dependent ab initio calculations.

Angular correlations between two electrons emitted in the sequential two-photon double ionization of atoms

Angular correlations between two emitted photoelectrons in the sequential two-photon double ionization (TPDI) of atoms are theoretically considered. The general expression for the angular correlation function is analysed and some particular geometries of possible experiments are discussed. The concept of true angular correlations is introduced in contrast to the angular dependence of the two-electron emission from two uncorrelated ionization events. The case of a pure LS coupling description of the TPDI is considered in detail and compared with the general case. As an example, calculations of the angular correlation functions are performed and discussed for sequential TPDI from the 4p valence shell of krypton.