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 the geometrical properties of the detector. Theoretical values of the angular correlation function are obtained for DPI in xenon and these are shown to be in good agreement with the experimental results given by Kämmerling and Schmidt.
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…
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 dir…
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 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 the shape of a right circular cylinder. The different factors in the efficiency operator are discussed in detail keeping in mind the fundamental epistemological question of the role of the observer (or his equipment) in such experiments.
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.
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 perform numerical simulations for photoionization of the argon atom when exposed to a combined field of an infrared laser (abbreviated IR) and its 13th harmonic (H13) by solving the Time-Dependent Schrödinger Equation (TDSE)], noting that the associated energy spectrum displays a harmonic peak dressed by the IR and other peaks called side-bands SB+-n corresponds to the absorption (+n) and the emission (-n) of the n-infrared photons above the ionization threshold. In two-color H13+IR photoionization of argon, the analysis of the angular distribution of the ejected electron in the continuum, …
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…
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…
Studying magnetic circular vortex dichroism effect for photoionization of Rydberg atoms with vortex photons
State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University（华南师范大学量子物质研究所核物理与技术国家重点实验室）；Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science（广东省核科学省级重点实验室物质结构与基本相互作用卓越基础研究广东中心）
We calculated ab initio the three-fold differential cross section of a double single-photon Helium photoionization at equal energy sharing, and obtained from one the Gaussian width parameter, describing the angular interelectron correlations, for the total electrons energies range E from 0.1 eV to 100 eV. The results are in excellent agreement with experimental data but indicate that the Wannier threshold law for angular distribition is not correct at energies attainable in modern experiments. It is shown that the Gaussian width parameter dependence on energy is much better described by the mo…
We demonstrate that the angular distribution of electrons knocked out from an atom by a fast charge particle is determined not only by dipole but also by quadrupole transitions, the contribution of which can be considerably enhanced as compared to the case of photoionization. To obtain these matrix elements one has to study the angular distribution of electrons emitted by the atom in its collision with a fast charged particle. The distribution has to be measured relative to the momentum q transferred from the projectile to the target atom. The situation is similar, but not identical to the pho…
Intense laser ionization expands Einstein's photoelectric effect rules giving a wealth of phenomena widely studied over the last decades. In all cases, so far, photons were assumed to carry one unit of angular momentum. However it is now clear that photons can possess extra angular momentum, the orbital angular momentum (OAM), related to their spatial profile. We show a complete description of photoionization by OAM photons, including new selection rules involving more than one unit of angular momentum. We explore theoretically the interaction of a single electron atom located at the center of…
The photoionization cross section $σ$, spin-polarization parameters $P$ and $Q$, and the angular-distribution asymmetry parameter $β$ are calculated for the $7s$ state of francium for photon energies below 10 eV. Two distinct calculations are presented, one based on many-body perturbation theory and another based on the model potential method. Although predictions of the two calculations are similar, the detailed energy dependence of the photoionization parameters from the two calculations differ. From the theoretical p-wave phase shifts, we infer quantum defects for $p_{1/2}$ and $p_{3/2}$ Ry…
The nondipole parameters that characterize the angular disribution of the photoelectrons from the 3d subshell of Cs are found to be altered qualitatively by the inclusion of correlation in the form of interchannel coupling between the $3d_{3/2}$ and $3d_{5/2}$ photoionization channels. A prominent characteristic maximum is predicted only in the parameters for $3d_{5/2}$ photoionization, while the effect for $3d_{3/2}$ is rather weak. The results are obtained within the framework of the Generalized Random Phase Approximation with Exchange (GRPAE), which in addition to the RPAE effects takes int…
It is demonstrated for the first time that in spite of well known big similarities between atomic ionization by photons and fast electrons, a qualitative difference exists in angular anisotropy parameters of electrons knocked out in these processes. The difference is disclosed here and attributed to distinction between normal (transverse) and virtual (longitudinal) photons. Formulas are derived for dipole and non-dipole angular anisotropy parameters in fast electronatom scattering. The ratio of quadrupole-to-dipole matrix elements is determined by the parameter ωR/v << 1 where ωis the transfer…
Orbital-angular-momentum partition in hydrogen photoionization by a monochromatic vortex beam
Peking University（北京大学）；Wuhan Institute of Technology（武汉工程大学）；Huazhong University of Science and Technology（华中科技大学）；Guangdong Technion - Israel Institute of Technology（广东以色列理工学院）；Technion – Israel Institute of Technology（以色列理工学院）
Within the framework of a model representing the potential of a graphene sheet U(z) as an electro-neutral layer formed by smeared carbon atoms, the effect of this potential on spectral characteristics of atoms adsorbed on a graphene sheet has been studied. Since the distance between the adsorbed atom nucleus and sheet surface significantly exceeds the radii of inner atomic shells the potential U(z) makes influence on the continuum wave functions only. Their behavior in the upper semi-space (z>0) and in the lower one (z<0) where the adsorbed atom is located is defined by a jump of the logarithm…
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 …
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…
We present the angular distribution of electrons knocked out from an atom in a fast charge particle collision at small momentum transfer. It is determined not only by dipole but also by quadrupole transitions, the contribution of which can be considerably enhanced as compared to the case of photoionization. There the non-dipole parameters are suppressed as compared to the dipole ones by the parameter ωR/c << 1, where is the photon energy, R is the ionized shell radius and c is the speed of light. This suppression in fast electron-atom collisions can be considerably reduced: the corresponding e…
We examine the angular distributions of all three electrons ionized from Li by a single photon near the triple ionization threshold using a fully quantum-mechanical treatment. We find strong evidence for a {\bf T}-shape break-up pattern at 5 eV excess energy as previously predicted by quasi-classical simulations [A. Emmanouilidou and J. M. Rost, \jpb {\bf 39}, 4037 (2006); A. Emmanouilidou, P. Wang, and J. M. Rost, \prl {\bf 100}, 063002 (2008)]. This finding is in conflict with the expected Wannier break-up dynamics of three electrons moving at mutual angles of 120$^{\circ}$, which is expecte…
We demonstrate rather interesting manifestations of co-existence of resonance features in characteristics of the photoionization of 3d-electrons in Xe@C60. It is shown that the reflection of photoelectrons produced by the 3d Xe photoionization affects greatly partial photoionization cross-sections of and levels and respective angular anisotropy parameters, both dipole and non-dipole adding to all of them additional maximums and minimums. The calculations are performed treating the 3/2 and 5/2 electrons as electrons of different kinds with their spins "up" and "down". The effect of C60 shell is…
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…
The application of a matrix-based reconstruction protocol for obtaining Molecular Frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is explored. Similarly to other recent works on the topic of MF reconstruction, this protocol makes use of time-resolved LF measurements, in which a rotational wavepacket is prepared and probed via photoionization, followed by a numerical reconstruction routine; however, in contrast to other methodologies, the protocol developed herein does not require determination of photoionization matrix elements, and cons…
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 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…
Extracting single photoionization time delays associated with atomic (or molecular) species from attosecond time scale two-photon experiments usually relies on the theoretical description of continuum-continuum transitions. The available models for those processes predict a universal phase contribution, independent of the angular quantum numbers of final states. However, a recent experimental-theoretical study [Fuchs, \emph{et al.} Optica 7, 154 (2020)] determined a sizable time delay dependence on the angular momentum of near-threshold photoelectrons. In this study, we present an analytical m…
We present R-Matrix with time dependence (RMT) calculations for the photoionization of helium irradiated by an EUV laser pulse and an overlapping IR pulse with an emphasis on the anisotropy parameters of the sidebands generated by the dressing laser field. We investigate how these parameters depend on the amount of atomic structure included in the theoretical model for two-photon ionization. To verify the accuracy of the RMT approach, our theoretical results are compared with experiment.
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…
We present the results of calculations of outer shell non-dipole angular anisotropy parameters for semi-filled shell atoms in the Hartree-Fock (HF) one-electron approximation and with account of inter-electron correlations in the frame of the Spin Polarized Random Phase Approximation with Exchange (SP RPAE). We demonstrate for the first time that this characteristic of photoionization process is essentially sensitive to the fact whether the photoelectron has the same or opposite spin orientation to that of the semi-filled shell.
We study the double electronic emission by photon impact from He in the center of a spherical fullerene, which is modeled by a square-well shell. This system exhibits a manifold of avoided crossings as a function of the well depth, and present mirror colapses. However, this symmetry is broken in the triple differential cross section due to the delocalization of the He electrons in the initial state. Moreover, the fullerene potential involves higher angular momenta partial waves to be included in the process, which modifies the well-known two-lobe cross section from isolated He.
We demonstrate rather interesting manifestations of co-existence of resonance features in characteristics of the photoionization of 3d-electrons in Xe, Cs and Ba endohedral atoms. It is shown that for all of the considered atoms the reflection by the fullerene shell of photoelectrons produced by the 3d subshell photoionization affects greatly partial photoionization cross-sections of 3d5/2 and 3d3/2 levels and respective angular anisotropy parameters, both dipole and non-dipole adding to all of them additional maximums and minimums. The results obtained demonstrate distinctive differences betw…
Powerful hybridization of the Cd 4$d$ state with the $d$-angular momentum state of C$_{60}$ $π$ symmetry is found in the local density approximation (LDA) structure of Cd@C$_{60}$ ground state. The photoionization of the resulting symmetric and antisymmetric levels are computed using the time dependent LDA method to include electron correlations. Cross sections exhibit effects of the C$_{60}$ plasmonic motion coherently coupled to the diffraction-type cavity oscillations induced by local emissions from C$_{60}$. The Cd@C$_{60}$ results exhibit a substantial difference from our previous results…
Focused laser fields with textured polarization on a sub-wavelength scale allow extracting information on electronic processes which are not directly accessible by homogeneous fields. Here, we consider photoionization in radially and azimuthally polarized laser fields and show that, due to the local polarizations of the transversal and the longitudinal laser electric field components, the detected photoelectron spectra depend on the atom position from which the electron originates. The calculation results reported here show the angular dependence of the photoionization amplitude, the quantum p…
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…
We calculate the double differential distributions and distributions in recoil momenta for the high energy non-relativistic double photoionization of helium. We show that the results of recent experiments is the pioneering experimental manifestation of the quasifree mechanism for the double photoionization, predicted long ago in our papers. This mechanism provides a surplus in distribution over the recoil momenta at small values of the latter, corresponding to nearly "back-to-back" emission of the electrons. Also in agreement with previous analysis the surplus is due to the quadrupole terms of…
The photoionization of a two-shell endohedral A@CN1@CN2 is considered. Formulas are presented for cross-sections and angular anisotropy parameters, both dipole and non-dipole. The effect of the fullerenes shell upon photoelectron from atom A is taken into account substituting the action of the fullerene by two zero-thickness "bubble potential". The fullerenes shells polarization is included assuming that the radius of the outer shell R2 is much bigger than the inner R1 and both much exceeds the atomic radius r. This permits to express the effect via CN1,N2 polarizabilities, which are connected…
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 investigate the angular distribution of electrons that are emitted in the ionization of hydrogen-like ions by twisted photons. Analysis is performed based on the first-order perturbation theory and the non-relativistic Schrödinger equation. Special attention is paid to the dependence of the electron emission pattern on the impact parameter b of the ion with respect to the centre of the twisted wave front. In order to explore such a dependence, detailed calculations were carried out for the photoionization of the 1s ground and 2 py excited states of neutral hydrogen atoms. Based on these cal…
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…
The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target (atoms) with regard to the beam …
We develop a formalism for photoionization (PI) and potential energy curves (PECs) of Rydberg atoms in ponderomotive optical lattices and apply it to examples covering several regimes of the optical-lattice depth. The effect of lattice-induced PI on Rydberg-atom lifetime ranges from noticeable to highly dominant when compared with natural decay. The PI behavior is governed by the generally rapid decrease of the PI cross sections as a function of angular-momentum ($\ell$), and by lattice-induced $\ell$-mixing across the optical-lattice PECs. In GHz-deep lattices, $\ell$-mixing leads to a rich P…
We show that the combination of two achiral components - atomic or molecular target plus a circularly polarized photon - can yield chirally structured photoelectron angular distributions. For photoionization of CO, the angular distribution of carbon K-shell photoelectrons is chiral when the molecular axis is neither perpendicular nor (anti-)parallel to the light propagation axis. In photo-double-ionization of He, the distribution of one electron is chiral, if the other electron is oriented like the molecular axis in the former case and if the electrons are distinguishable by their energy. In b…
We present a new extension of the UKRmol electron-molecule scattering code suite, which allows one to compute ab initio photoionization and photorecombination amplitudes for complex molecules, resolved both on the molecular alignment (orientation) and the emission angle and energy of the photoelectron. We illustrate our approach using CO$_2$ as an example, and analyze the importance of multi-channel effects by performing our calculations at different, increasing levels of complexity. We benchmark our method by comparing the results of our calculations with experimental data and with theoretica…
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 …
We present numerical simulations of ultrafast multiphoton ionization dynamics in a two-dimensional atomic model driven by co- and counterrotating circularly polarized single-color and bichromatic carrier envelope phase (CEP) stable ultrashort laser pulse sequences. Taking into account phase variations due to CEP fluctuations and the Gouy phase, our results accurately reproduce recently measured photoelectron momentum distributions [Pengel et al., Phys. Rev. Lett. 118, 053003 (2017), Phys. Rev. A 96, 043426 (2017); Kerbstadt et al., Nat. Comm. 10, 685 (2019), Adv. Phys. X 4, 1672583 (2019)]. Th…
Most large molecules are chiral in their structure: they exist as two enantiomers, which are mirror images of each other. Whereas the rovibronic sublevels of two enantiomers are almost identical, it turns out that the photoelectric effect is sensitive to the absolute configuration of the ionized enantiomer - an effect termed Photoelectron Circular Dichroism (PECD). Our comprehensive study demonstrates that the origin of PECD can be found in the molecular frame electron emission pattern connecting PECD to other fundamental photophysical effects as the circular dichroism in angular distributions…
We theoretically study the photoelectron angular distributions (PADs) from two-color two-photon near-threshold ionization of hydrogen and noble gas (He, Ne, and Ar) atoms by a combined action of femtosecond extreme ultraviolet (EUV) and near-infrared (IR) laser pulses. Using the second-order time-dependent perturbation theory, we clarify how the two-photon ionization process depends on EUV-IR pulse delay and how it is connected to the interplay between resonant and nonresonant ionization paths. Furthermore, by solving the time-dependent Schrödinger equation, we calculate the anisotropy paramet…
Double ionization of an atom by single-photon absorption in the presence of a neighbouring atom is studied. The latter is, first, resonantly photoexcited and, afterwards, transfers the excitation energy radiationlessly to the other atom, leading to its double ionization. The process relies on the combined effect of interatomic and intraatomic electron correlations. It can dominate over the direct double photoionization by several orders of magnitude at interatomic distances up to few nanometers. The relative position of the neighbouring atom is shown to exert a characteristic influence on the …
Elliptical dichroism is known in atomic photoionization as the difference in the photoelectron angular distributions produced in nonlinear ionization of atoms by left- and right-handed elliptically polarized light. We theoretically demonstrate that the maximum dichroism |Δ_{ED}|=1 always appears in two-photon ionization of any atom if the photon energy is tuned in so that the electron emission is dominantly determined by two intermediate resonances. We propose the two-photon ionization of atomic helium in order to demonstrate this remarkable phenomenon. The maximum elliptical dichroism could b…
