This is a sequel to an earlier article on the theory of angular correlation for double photoionization. Here we consider the two-step double photoionization of a rare gas atom under the influence of a polarized photon beam described by appropriate Stokes parameters. Cylindrical mirror analysers (CMA) are used to detect the outgoing electrons. Theoretical values of the correlation functions are obtained for linearly polarized light. Two different situations is handled. Once, the value of the correlation function is obtained keeping the photo-electron in a fixed direction. The other case the direction of the Auger electron is kept fixed. Comparison with experiments on xenon shows excellent agreement for the case of (4d_{5/2}) photoionization followed by a subsequent (N_{5}-O_{23}O_{23} ^{1}S_{0}) Auger decay for a polarized incident photon of energy (94.5eV) {[}J. Phys.B,
The photon-ion merged-beams technique has been employed at the new Photon-Ion spectrometer at PETRA III (PIPE) for measuring multiple photoionization of Xe$^{q+}$ (q=1-5) ions. Total ionization cross sections have been obtained on an absolute scale for the dominant ionization reactions of the type hν+ Xe$^{q+}$ $\to$ Xe$^{r+}$ + (q-r) e$^-$ with product charge states q+2 $\le$ r $\le$ q+5. Prominent ionization features are observed in the photon-energy range 650-750 eV, which are associated with excitation or ionization of an inner-shell 3d electron. Single-configuration Dirac-Fock calculation…
The photon-ion merged-beams technique for the photoionization of mass/charge selected ionized atoms, molecules and clusters by x-rays from synchrotron radiation sources is introduced. Examples for photoionization of atomic ions are discussed by going from outer-shell ionization of simple few-electron systems to inner-shell ionization of complex many-electron ions. Fundamental ionization mechanisms are elucidated and the importance of the results for applications in astrophysics and plasma physics is pointed out. Finally, the unique capabilities of the photon-ion merged-beams technique for the …
Photoelectron angular distributions (PADs) obtained from ionization of potassium atoms using moderately intense femtosecond IR fields ($\sim$10$^{12}$Wcm$^{-2}$) of various polarization states are shown to provide a route to "complete" photoionization experiments. Ionization occurs by a net 3-photon absorption process, driven via the $4s\rightarrow4p$ resonance at the 1-photon level. A theoretical treatment incorporating the intra-pulse electronic dynamics allows for a full set of ionization matrix elements to be extracted from 2D imaging data. 3D PADs generated from the extracted matrix eleme…
A two-step photoionization strategy of an ultracold rubidium beam for application in a focused ion beam instrument is analyzed and implemented. In this strategy the atomic beam is partly selected with an aperture after which the transmitted atoms are ionized in the overlap of a tightly cylindrically focused excitation laser beam and an ionization laser beam whose power is enhanced in a build-up cavity. The advantage of this strategy, as compared to without the use of a build-up cavity, is that higher ionization degrees can be reached at higher currents. Optical Bloch equations including the ph…
We have considered the processes of excitation and ionization of light multicharged ions by impact of high-energy particles, which proceed with participation of the $ns$ electrons. The screening corrections to the energy levels and photoionization cross sections are evaluated analytically within the framework of the non-relativistic perturbation theory with respect to the electron-electron interaction. The universal scalings for the excitation and ionization cross sections are studied for arbitrary principal quantum numbers $n$.
In this paper we have tried to establish a theory for angular correlation between the photo- and Auger electrons in the two-step double photoionization of a rare gas atom. The basic finding of this paper is that a general theoretical expression for the angular correlation function is established in the problem of double photoionization of atoms in the presence of linearly polarized monochromatic light. We consider the case of a xenon atom and the incident light is of (94.5 eV) with arbitrary linear polarization. The theoretical results are compared with the experiments done by K(\ddot{a} )mmer…
In the semiclassical picture of photoionization process in intense laser fields, the ionization rate solely depends on the amplitude of the electric field and the final photoelectron momentum corresponds to the instant of ionization of the photoelectron, however, this picture has never been checked rigorously. Recently an attosecond angular streaking technique based on this semiclassical perspective has been widely applied to temporal measurement of the atomic and molecular dynamics in intense laser fields. We use a Wigner-distribution-like function to calculate the time-emission angle distrib…
The photoionization cross-sections of two even-parity excited states, $5d6d ^3D_1$ and $6s7d ^3D_{2}$, of atomic Ba at the ionization-laser wavelength of 556.6 nm were measured. We found that the total cross-section depends on the relative polarization of the atoms and the ionization-laser light. With density-matrix algebra, we show that, in general, there are at most three parameters in the photoionization cross-section. Some of these parameters are determined in this work. We also present the measurement of the radiative lifetime of five even-parity excited states of barium.
We give examples showing that two well-known versions of the S-matrix theory, which describes a nonresonant multiphoton ionization of atoms and ions in intense laser fields, lead to qualitatively different results. The latter refer not only to total ionization rates, but also to energy distributions of photoelectrons, for instance in a polarization plane of the laser field. It should be possible to make an experiment testing predictions of both theories in the near future.
We consider the process of double photoionization (DPI) in a rare gas atom as a two-step process, namely (i) photoionization in an inner shell followed by (ii) the emission of an Auger electron from an outer shell. An angular correlation function for the two emitted electrons is defined by analogy with the theory of angular correlation in nuclear physics. An expression is obtained for this angular correlation function by a statistical method which makes use of the density and efficiency operators. The latter takes care of the attenuation of the probability of detection of an electrons due to t…
Nonlinear relativistic ionization phenomena induced by a strong linearly polarized laser field are considered. The starting point is the classical relativistic action for a free electron moving in the electromagnetic field created by a strong laser beam. This action has been used to calculate semiclassical transition rates. Simple analytical expressions for the ionization rate, the photoelectron emission velocity and for the drift momentum distribution of the photoelectron have been found. The analytical formulas apply to nonrelativistic bound systems as well as to initial states with an energ…
We discuss the problem of the universal scalings in the double ionization of atomic K-shell electrons caused by absorption of a single photon. In particular, we envisage the following questions: Under which conditions and up to which accuracy the universal scalings are realized? Does it make sense to talk about different physical mechanisms in the double-ionization process? Finally, we present also the theoretical analysis of recent experimental measurements performed on neutral atoms. As a testing ground, QED perturbation theory is employed.
Photoionization of a cold atomic sample offers intriguing possibilities to observe collective effects at extremely low temperatures. Irradiation of a rubidium condensate and of cold rubidium atoms within a magneto-optical trap with laser pulses ionizing through 1-photon and 2-photon absorption processes has been performed. Losses and modifications in the density profile of the remaining trapped cold cloud or the remaining condensate sample have been examined as function of the ionizing laser parameters. Ionization cross-sections were measured for atoms in a MOT, while in magnetic traps losses …
Many applications are in need of accurate photoionization cross-sections, especially in the case of complex atoms. Configuration-interaction relativistic many-body perturbation theory (CI-RMBPT) that has been successful in predicting atomic energies, matrix elements between discrete states, and other properties is quite promising, but it has not been applied to photo-ionization problems owing to extra complications arising from continuum states. In this paper a method that will allow the conversion of discrete CI-(R)MPBT oscillator strengths (OS) to photo-ionization cross sections with minimal…
Photoionization of an atom $A$ by a strong laser field in the presence of a spatially well-separated neighboring atom $B$ is considered. The laser field frequency is assumed to lie below the ionization potential of atom $A$ and be resonant with a dipole-allowed transition in atom $B$. In this situation, the ionization may occur either directly by multiphoton absorption from the laser field at the first atomic center. Or via an indirect pathway involving two-center electron-electron correlations, where the neighbor atom $B$ is first photoexcited and, afterwards, transfers its energy upon deexci…
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.
Photoionization of an atom in the presence of a neighboring atom of different species is studied. The latter first undergoes resonant photoexcitation, leading to an autoionizing state of the diatomic system. Afterwards, the excitation energy is transferred radiationlessly via a two-center Auger process to the other atom, causing its ionization. Assuming a fixed internuclear distance, it has been predicted theoretically that this indirect ionization pathway can strongly dominate over the direct photoionization. Here, we extend the theory of resonant two-center photoionization by including the n…
At the free-electron laser FLASH, multiple ionization of neon atoms was quantitatively investigated at 93.0 eV and 90.5 eV photon energy. For ion charge states up to 6+, we compare the respective absolute photoionization yields with results from a minimal model and an elaborate description. Both approaches are based on rate equations and take into acccout a Gaussian spatial intensity distribution of the laser beam. From the comparison we conclude, that photoionization up to a charge of 5+ can be described by the minimal model. For higher charges, the experimental ionization yields systematical…
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…
Ionization of atoms and molecules by absorption of a light pulse results in electron wavepackets carrying information on the atomic or molecular structure as well as on the dynamics of the ionization process. These wavepackets can be described as a coherent sum of waves of given angular momentum, called partial waves, each characterized by an amplitude and a phase. The complete characterization of the individual angular momentum components is experimentally challenging, requiring the analysis of the interference between partial waves both in energy and angle. Using a two-photon interferometry …
The present tutorial provides an overview of the time-dependent configuration interaction singles (\acs{TDCIS}) scheme applied to nonlinear ionization over a broad photon-energy range. The efficient propagation of the wave function and the calculation of photoelectron spectra within this approach are described and demonstrated in various applications. Above-threshold ionization of argon and xenon in the extreme ultraviolet energy range is investigated as an example. A particular focus is put on the xenon $4d$ giant dipole resonance and the information that nonlinear ionization can provide abou…
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…
We suggest an explanation of the recently observed discrepancy between the experimental and theoretical results on ionization of atoms, encapsulated into the fullerenes by photons with the energies of about 80-190eV. On the ground of previous theoretical considerations we conclude that the photoionization of the caged atom without excitation of the fullerene shell has low probability.
Using $He@C_{60}$ as an example, we demonstrate that static potential of the fullerene core essentially alters the cross section of the two-electron ionization differential in one-electron energy $dσ^{++}(ω)/dε$. We found that at high photon energy prominent oscillations appear in it due to reflection of the second, slow electron wave on the $% C_{60}$ shell, which "dies out" at relatively high $ε$ values, of about 2$÷$3 two-electron ionization potentials. The results were presented for ratios $R_{C_{60}}(ω,ε)\equiv dσ^{++}(ω,ε)/dσ^{a++}(ω,ε)$, where $dσ^{a++}(ω,ε)/dε$ is the two-electron diff…
Two efficient and isotope-selective resonant two-photon ionization techniques for loading barium ions into radio-frequency (RF)-traps are demonstrated. The scheme of using a strong dipole-allowed transition at λ=553 nm as a first step towards ionization is compared to the established technique of using a weak intercombination line (λ=413 nm). An increase of two orders of magnitude in the ionization efficiency is found favoring the transition at 553 nm. This technique can be implemented using commercial all-solid-state laser systems and is expected to be advantageous compared to other narrowban…
The effect of noise on the nonlinear photoionization of an atom due to a femtosecond pulse is investigated in the framework of the stochastic Schrödinger equation. A modest amount of white noise results in an enhancement of the net ionization yield by several orders of magnitude, giving rise to a form of quantum stochastic resonance. We demonstrate that this effect is preserved if the white noise is replaced by broadband chaotic light.
A review of some recently developed methods of calculating multiple differential cross-sections of photoionization and electron impactionization of atoms and molecules having two active electrons is presented. The methods imply original approaches to calculating three-particle Coulomb wave functions. The external complex scaling method and the formalism of the Schroedinger equation with a source in the right-hand side are considered. Efficiency of the time-dependent approaches to the scattering problem, such as the paraxial approximation and the time-dependent scaling, is demonstrated. An orig…
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…
We experimentally investigate the effects of the linear photon momentum on the momentum distributions of photoions and photoelectrons generated in one-photon ionization in an energy range of 300 eV $\leq~E_γ~\leq$ 40 keV. Our results show that for each ionization event the photon momentum is imparted onto the photoion, which is essentially the system's center of mass. Nevertheless, the mean value of the ion momentum distribution along the light propagation direction is backward-directed by $-3/5$ times the photon momentum. These results experimentally confirm a 90 year old prediction.
Nonlinear relativistic ionization phenomena induced by a strong laser radiation with elliptically polarization are considered. The starting point is the classical relativistic action for a free electron moving in the electromagnetic field created by a strong laser beam. The application of the relativistic action to the classical barrier-suppression ionization is briefly discussed. Further the relativistic version of the Landau-Dykhne formula is employed to consider the semiclassical sub-barrier ionization. Simple analytical expressions have been found for: (i) the rates of the strong-field non…
Photoionization of an atom $A$, in the presence of a neighboring atom $B$, can proceed via resonant excitation of $B$ with subsequent energy transfer to $A$ through two-center electron-electron correlation. We demonstrate that this two-center mechanism can strongly outperform direct photoionization at nanometer internuclear distances and possesses characteristic features in its time development and the spectrum of emitted electrons.
Formulating a quasiclassical approach we determine the cross section for the complete four-body break-up of the lithium ground state following single photon absorption from threshold up to 220 eV excess energy. In addition, we develop a new classification scheme for three-electron ionizing trajectories in terms of electron-electron collisions, thereby identifying two main ionization paths which the three electrons in the ground state of lithium follow to escape to the continuum. The dominant escape paths manifest themselves in a characteristic ``T-shape'' break-up pattern of the three electron…
We continue our studies of the high energy nonrelativistic asymptotics for the photoionization cross section of the systems bound by a central field $V(r)$. We consider the bound states with the orbital momentum $\ell=1$. We show, that as well as for the $s$ states the asymptotics can be obtained without solving of the wave equations for the bound and outgoing electrons. The asymptotics of the cross sections is expressed in terms of the asymptotics of the Fourier transform $V(p)$ of the field and its derivative $V'(p)$ by employing the Lippmann--Schwinger equation. The shape of the energy depe…
Resonant two-photon ionization in a system consisting of two spatially well-separated atoms is studied. Due to two-center electron-electron correlations, the ionization may also proceed through photo-excitation of both atoms with subsequent interatomic Coulombic decay. We show that this channel may dominate the photoionization process and qualitatively change its dependence on the field intensity and the spectra of emitted electrons.
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…
Two-photon ionization of Rubidium atoms in a magneto-optical trap and a Bose-Einstein condensate (BEC) is experimentally investigated. Using 100 ns laser pulses, we detect single ions photoionized from the condenstate with a 35(10)% efficiency. The measurements are performed using a quartz cell with external electrodes, allowing large optical access for BECs and optical lattices.
Measuring and controlling the ionization dynamics by intense laser fields has recently led to important breakthroughs, from the investigation of tunneling time delays to attosecond molecular imaging by electron holography. In these experiments, extracting the subtle influence of the ionic potential on the departing electrons is of capital importance, and often challenging. Here we show that molecular chirality naturally provides a solution to this issue by breaking the symmetry of the photoionization process along the laser propagation direction. Using counter-rotating bicircular bichromatic l…
It is demonstrated that recent experiments on ionization of 3p and 3s electrons in Ni film and solid body cannot be described in the frames of Hartree-Fock or the random phase approximation with exchange. The deviation is so big that from the theoretical side it requires inclusion of huge and yet not entirely understood effects. Perhaps, it requires also experimental efforts in order to clarify the prominent difference obtained for films and crystal samples.
Ultrafast processes in matter, such as the electron emission following light absorption, can now be studied using ultrashort light pulses of attosecond duration ($10^{-18}$s) in the extreme ultraviolet spectral range. The lack of spectral resolution due to the use of short light pulses may raise serious issues in the interpretation of the experimental results and the comparison with detailed theoretical calculations. Here, we determine photoionization time delays in neon atoms over a 40 eV energy range with an interferometric technique combining high temporal and spectral resolution. We spectr…
The influence has been studied of the ionization laser polarization on the effective temperature of an ultracold electron source, which is based on near-threshold photoionization. This source is capable of producing both high-intensity and high-coherence electron pulses, with applications in for example electron diffraction experiments. For both nanosecond and femtosecond photoionization, a sinusoidal dependence of the temperature on polarization angle has been found. For most experimental conditions, the temperature is minimal when the polarization coincides with the direction of acceleration…
This tutorial presents an introduction to the interaction of light and matter on the attosecond timescale. Our aim is to detail the theoretical description of ultra-short time-delays, and to relate these to the phase of extreme ultraviolet (XUV) light pulses and to the asymptotic phase-shifts of photoelectron wave packets. Special emphasis is laid on time-delay experiments, where attosecond XUV pulses are used to photoionize target atoms at well-defined times, followed by a probing process in real time by a phase-locked, infrared laser field. In this way, the laser field serves as a "clock" to…
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…
We develop a novel technique for modeling of atomic and molecular ionization in superposition of XUV and IR fields with characteristics typical for attosecond streaking and RABBITT experiments. The method is based on solving the time-dependent Schrödinger equation in the coordinate frame expanding along with the photoelectron wave packet. The efficiency of the method is demonstrated by calculating angular anisotropy of photoemission time delay of the H$_2^+$ ion in a field configuration of recent RABBITT experiments.
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…
An additional channel opens for photoionization of atom $A$ by an electromagnetic field if it traverses a gas of atoms $B$ resonantly coupled to this field. We show that this channel, in which $A$ is ionized via resonant photoexcitation of $B$ with subsequent energy transfer to $A$ through two-center electron correlations and which is very efficient when $A$ and $B$ constitute a bound system, can strongly dominate the ionization of $A$ also in collisions where the average distance between $A$ and $B$ exceeds the typical size of a bound system by orders of magnitude.
Single, double, and triple ionization of the C+ ion by a single photon have been investigated in the energy range 286 to 326 eV around the K-shell single-ionization threshold at an unprecedented level of detail. At energy resolutions as low as 12 meV, corresponding to a resolving power of 24000, natural linewidths of the most prominent resonances could be determined. From the measurement of absolute cross sections, oscillator strengths, Einstein coefficients, multi-electron Auger decay rates and other transition parameters of the main K-shell excitation and decay processes are derived. The cro…
The newly developed method of time-of-flight (ToF) momentum microscopy was used to analyse the cold electron emission from a Cs 3D magneto-optical trap (MOT). Three-step resonant photoionization was implemented via two intermediate states (6P3/2 pumped with 852 nm laser and 7S1/2 with 1470 nm) and a tuneable femtosecond Ti:sapphire laser for the final ionization step. The magnetic field of the MOT is switched off during the photoionization step. The natural bandwidth of the fs-laser is reduced to 4 meV using optical spectral filters. Precise tuning of the photon energy makes it possible to obs…
Photoionization of an atom via interatomic correlations to N neighboring atoms may be strongly enhanced due to constructive interference of quantum pathways. The ionization proceeds via resonant photoexcitation of a neighbor atom and subsequent interatomic Coulombic decay. The enhancement can scale with N^2, leading to "super-enhanced photoionization".
We study laser-assisted photoionization by attosecond pulses using a time-independent formalism based on diagrammatic many-body perturbation theory. Our aim is to provide an ab inito route to the "delays" for this above-threshold ionization process, which is essential for a quantitative understanding of attosecond metrology. We present correction curves for characterization schemes of attosecond pulses, such as "streaking", that account for the delayed atomic response in ionization from neon and argon. We also verify that photoelectron delays from many-electron atoms can be measured using simi…
The problem of angular correlation in the double photoionization (DPI) of rare gas atoms is considered in some depth. We refer particularly to the efficiency operator for the detection of an electron by a detector having cylindrical symmetry. The different factors in the efficiency operator are discussed in detail keeping in mind the fundamental epistemological question of the role of the detection process in such experiments.
The calculation of partial two-photon ionization cross sections in the above-threshold energy region is discussed in the framework of exterior complex scaling. It is shown that with a minor modification of the usual procedure, which is based on the calculation of the outgoing partial waves of the second-order scattering wave function, reliable partial ionization amplitudes can be obtained. The modified procedure relies on a few-term least-squares fit of radial functions pertaining to different partial waves. To test the procedure, partial and total two-photon ionization cross sections of the h…
We report on kinematically complete measurements and ab initio non-perturbative calculations of double ionization of He and H2 by a single 800 eV circularly polarized photon. We confirm the quasifree mechanism of photoionization for H2 and show how it originates from the two-electron cusp in the ground state of a two-electron target. Our approach establishes a new method for mapping electrons relative to each other and provides valuable insight into photoionization beyond the electric-dipole approximation.
