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Resonances leave prominent signatures in atomic and molecular ionization triggered by the absorption of single or multiple photons. These signatures reveal various aspects of the ionization process, characterizing both the initial and final states of the target. Resonant spectral features are typically associated with sharp variations in the photoionization phase, providing an opportunity for laser-assisted interferometric techniques to measure this phase and convert it into a photoemission time delay. This time delay offers a precise characterization of the timing of the photoemission process. In this review, a unified approach to resonant photoionization is presented by examining the analytic properties of ionization amplitude in the complex photoelectron energy plane. This approach establishes a connection between the resonant photoemission time delay and the corresponding photoionization cross-section. Numerical illustrations of this method include: (i) giant or shape resonances, where the photoelectron is spatially confined within a potential barrier, (ii) Fano resonances, where bound states are embedded in the continuum, (iii) Cooper minima (anti-resonances) arising from kinematic nodes in the dipole transition matrix elements, and (iv) confinement resonances in atoms encapsulated within a fullerene cage. The second part of this review focuses on two-photon resonant ionization processes, where the photon energies can be tuned to a resonance in either the intermediate or final state of the atomic target. Our examples include one- or two-electron discrete excitations both below and above the ionization threshold. These resonant states are probed using laser-assisted interferometric techniques. Additionally, we employ laser-assisted photoemission to measure the lifetimes of several atomic autoionizing states., Comment: 33 pages, 18 figures

Two-photon atomic ionization driven by time-locked XUV and IR pulses allows to study dynamics of Fano resonances in time and energy domains. Different time evolution of the two interfering pathways leading to a Fano resonance can be exploited to turn the Fano profile of the two-photon XUV/IR ionization into a symmetric Gaussian once the directly ejected photoelectron leaves the parent ion and cannot any longer absorb an IR photon. This line shape transformation allows for the direct determination of the resonant lifetime from the spectroscopic measurements without need for an extremely fine energy resolution. Ubiquitous nature of Fano resonances makes this determination a universal tool in diverse quantum systems ranging from nuclei to nano-fabricated solids., Comment: 5 pages, 3 figures

We study formation and evolution of the electron wave-packets in the process of strong field ionization of various atomic targets. Our study is based on reformulating the problem in terms of conditional amplitudes, i.e., the amplitudes describing outcomes of measurements of different observables provided that the electron is found in the ionized state after the end of the pulse. By choosing the electron coordinate as such an observable, we were able to define unambiguously the notion of the ionized wave-packets and to study their formation and spread. We show that the evolution of the ionized wave packets obtained in this way follows closely the classical trajectories at the initial stages of evolution providing an {\it ab initio} quantum-mechanical confirmation of the basic premises of the Classical Monte Carlo Calculations approach. At the later stages of evolution the picture becomes more complicated due to the wave packets' spread and due to interference of wave packets originating from different field maxima. Our approach also allowed us to obtain information about the coordinate and velocity electron distributions at the tunnel exit.

The mutual angle formed by the non-collinear polarization axes of two laser pulses is used to control two-photon XUV+IR ionization of noble gas atoms in the process of reconstruction of attosecond bursts by beating of two-photon transitions (RABBITT). The magnitude and the phase of this beating can be controlled very efficiently by the mutual polarization angle. The mechanism of this control can be understood within the lowest order perturbation theory and the soft photon approximation. We offer a very sensitive test on the polarization control of the angular dependent RABBITT process which validates our numerical simulations. We apply this test to the recent theoretical and experimental results of polarization controlled RABBITT on hydrogen and helium by Boll et al., Phys. Rev. A 107, 043113 (2023) and heavier noble gases by Jiang et~al., Nature Comms. 13, 5072 (2022)., Comment: 15 pages, 7 figures

Determination and interpretation of Wigner-like photoionisation delays is one of the most active fields of attosecond science. Previous results have suggested that large photoionisation delays are associated with structured continua, but a quantitative relation between photoionisation cross sections and time delays has been missing. Here, we derive a Kramers-Kronig-like relation between these quantities and demonstrate its validity for (anti)resonances. This new concept defines a topological analysis, which rationalises the sign of photoionisation delays and thereby sheds new light on a long-standing controversy regarding the sign of the photoionisation delay near the Ar 3s Cooper minimum. Our work bridges traditional photoionisation spectroscopy with attosecond chronoscopy and offers new methods for analysing and interpreting photoionisation delays.

Shape resonances in photoionization of atoms and molecules arise from a particular geometry of the ionic potential which traps the receding photoelectron in a quasi-bound state in a particular partial wave. This mechanism allows us to connect the photoionization cross section in the resonant region with the photoelectron scattering phase in this partial wave by a simple formula $\sigma \propto \sin^2\delta_\ell$. Due to this relation, the phase $\delta_\ell$ can be extracted from an experimentally known cross section and then converted to the photoelectron group delay (Wigner time delay) $\tau_{\rm W} = \partial \delta_\ell/\partial E$ which is measurable by recently developed laser interferometric techniques. Such a direct connection of the photoionization cross section and the time delay is a fundamental property of shape resonances which provides a comprehensive test of novel measurements against a large body of older synchrotron data., Comment: 6 pages, 4 figures

We study orientation and two-center interference effects in attosecond time-resolved photoionization of the H$_2$ molecule. Time resolution of XUV ionization of H$_2$ is gained through the phase retrieval capability of attosecond angular streaking demonstrated earlier by Kheifets {\em et al} [arXiv:2202.06147 (2022)]. Once applied to H$_2$, this technique delivers an anisotropic phase and time delay which both depend sensitively on the molecular axis orientation. In addition, the photoelectron momentum distribution displays a very clear two-center interference pattern. When the interference formula due to Walter and Briggs [J. Phys. B {\bf 32} 2487 (1999)] is applied, an effective photoelectron momentum appears to be greater than the asymptotic momentum at the detector. This effect is explained by a molecular potential well surrounding the photoemission center., Comment: 8 pages, 7 figures. arXiv admin note: text overlap with arXiv:2202.06147

We demonstrate an accurate phase retrieval of XUV atomic ionization by streaking the photoelectron in a circularly polarized IR laser field. The streaking phase can then be converted to the atomic time delay containing the Wigner and continuum-continuum components. Our demonstration is based on a numerical solution of the time-dependent Schr\"odinger equation. We test this technique using the hydrogen atom ionized by an isolated attosecond XUV pulse across a wide range of photon energies. In parallel, we run a series of RABBITT simulations and demonstrate equivalence of the phase and timing information provided by the two methods. This validates the proposed technique and makes it a useful tool that can be applied to a broad range of atomic and molecular targets exposed to XUV radiation from novel free-electron laser sources., Comment: 7 pages, 5 figures

Photon exchange due to nuclear bremsstrahlung during nuclear collisions can cause Coulomb excitation in the projectile and the target nuclei. The corresponding process originated in nuclear timescales can also be observed in atomic phenomenon experimentally if it delayed by at least with an attosecond or longer timescales. We have found that this happens due to a mechanism involving the Eisenbud-Wigner-Smith time delay process. We have estimated photoionization time delays in atomic collisions utilizing the nonrelativistic version of random phase approximation with exchange and Hartree-Fock methods. We present three representative processes in which we can observe the phenomena in attosecond timescales even though they originate from excitations in the zeptosecond timescales. Thus the work represents an investigation of parallels between two neighboring areas of physics. Furthermore the present work suggests new possibilities for atomic physics research near the Coulomb barrier energy, where the laser is replaced by nuclear bremsstrahlung., Comment: 6 pages, 4 figures

We study propagation effects due to the finite speed of light in ionization of extended systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light propagation effects are encoded in the non-dipole terms of the time-dependent Shr\"odinger equation and display themselves in the photoelectron momentum distribution projected on the molecular axis. Our numerical modeling for the \Hp molecular ion and the \Ne dimer shows that the finite light propagation time from one atomic center to another can be accurately determined in a table top laser experiment which is much more readily affordable than an earlier synchrotron measurement by Grundmann {\em et al} [Science 370, 339 (2020)]

The process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) can become resonant with a discrete atomic level either in the intermediate or the final continuous states. Experimental observations of the former [Phys. Rev. Lett. 104, 103003 (2010)] or latter [Nat. Commun. 7, 10566 (2016)] cases revealed modification of only those parts of the photoelectron spectrum that overlapped directly with the resonance. In the lithium atom and other members of the alkali metal family, the valence shell $ns\to np$ transition to the intermediate RABBITT state affects the whole photoelectron spectrum in the final state. The strong additional resonant channel modifies entirely the ionization dynamics and opens direct access to the resonant phase of the two-photon transitions which is common for various single and multiple electron ionization processes. Elucidation of this phase has wider implications for strongly resonant laser-matter interaction., Comment: 5 pages, 5 figures

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., Comment: 7 pages, 4 figures

Attosecond angular streaking, also known as the "attoclock", employs a short elliptically polarized laser pulse to tunnel ionize an electron from an atom or a molecule and to put a time stamp on this process by deflecting the photoelectron in the angular spatial direction. This deflection can be used to evaluate the time the tunneling electron spends under the classically inaccessible barrier and to determine whether this time is finite. In this review, we examine the latest experimental and theoretical findings and present a comprehensive set of evidence supporting the zero tunneling time scenario., Comment: 24 pages, 11 figures

We consider the process of high-order harmonics generation (HHG) in the xenon atom enhanced by the inter-shell correlation between the valence 5p and inner 4d shells. We derive the HHG spectrum from a numerical solution of the one-electron time-dependent Schr\"odinger equation multiplied by the enhancement factor taken as the photoionization cross-sections ratio calculated with and without the inter-shell correlation. Such a simplified approach is adequate to describe the experimental HHG spectrum reported by Shiner et al [Nat. Phys. 7, 464 (2011)] generated by a single color IR laser. Similarly, we find good agreement when applied to the two-color driven HHG spectra reported by Facciala et al [Phys. Rev. Lett. 117, 093902 (2016)].

Numerical attoclock is a theoretical model of attosecond angular streaking driven by a very short, nearly a single oscillation, circularly polarized laser pulse. The reading of such an attoclock is readily obtained from a numerical solution of the time-dependent Schr\"odinger equation as well as a semi-classical trajectory simulation. By making comparison of the two approaches, we highlight the essential physics behind the attoclock measurements. In addition, we analyze the predictions of the Keldysh-Rutherford model of the attoclock [Phys. Rev. Lett. 121, 123201 (2018)]. In molecular hydrogen, we highlight a strong dependence of the width of the attoclock angular peak on the molecular orientation and attribute it to the two-center electron interference. This effect is further exemplified in the weakly bound neon dimer., Comment: 8 pages, 7 figures

We demonstrate a clear similarity between attoclock offset angles and Rutherford scattering angles taking the Keldysh tunnelling width as the impact parameter and the vector potential of the driving pulse as the asymptotic velocity. This simple model is tested against the solution of the time-dependent Schr\"odinger equation using hydrogenic and screened (Yukawa) potentials of equal binding energy. We observe a smooth transition from a hydrogenic to 'hard-zero' intensity dependence of the offset angle with variation of the Yukawa screening parameter. Additionally we make comparison with the attoclock offset angles for various noble gases obtained with the classical-trajectory Monte Carlo method. In all cases we find a close correspondence between the model predictions and numerical calculations. This suggests a largely Coulombic origin of the attoclock offset angle and casts further doubt on its interpretation in terms of a finite tunnelling time.

We report on a kinematically complete measurement of double ionization of helium by a single 1100 eV circularly polarized photon. By exploiting dipole selection rules in the two-electron continuum state, we observed the angular emission pattern of electrons originating from a pure quadrupole transition. Our fully differential experimental data and companion ab initio nonperturbative theory show the separation of dipole and quadrupole contributions to photo-double-ionization and provide new insight into the nature of the quasifree mechanism., Comment: 5 Pages, 3 Figures

We simulate angular resolved RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) measurements on valence shells of noble gas atoms (Ne, Ar, Kr, and Xe). Our non-perturbative numerical simulation is based on solution of the time-dependent Schr\"odinger equation for a target atom driven by an ionizing XUV and dressing IR fields. From these simulations we extract the angular dependent magnitude and phase of the RABBITT oscillations and deduce the corresponding angular anisotropy {\beta} parameter and Wigner time delay ${\tau}_W$ for the single XUV photon absorption which initiates the RABBITT process. Said {\beta} and ${\tau}_W$ parameters are compared with calculations in the random phase approximation with exchange (RPAE) which includes inter-shell correlation. This comparison is used to test various effective potentials employed in the one-electron TDSE. In lighter atoms (Ne and Ar), several effective potentials are found to provide accurate simulation of RABBITT measurements for a wide range of photon energies up to 100 eV above the valence shell threshold. In heavier atoms (Kr and Xe), the onset of strong correlation with the d-shell restricts the validity of the single active electron approximation to several tens of eV above the valence shell threshold.

The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the constituents is decisive and the spatial and the momentum distribution of one electron depends on those of the other electrons and the nuclei. Such correlations have escaped direct observation by imaging techniques so far. Here, we implement an imaging scheme which visualizes correlations between electrons by coincident detection of the reaction fragments after high energy photofragmentation. With this technique, we examine the H2 two-electron wave function in which electron-electron correlation beyond the mean-field level is prominent. We visualize the dependence of the wave function on the internuclear distance. High energy photoelectrons are shown to be a powerful tool for molecular imaging. Our study paves the way for future time resolved correlation imaging at FELs and laser based X-ray sources., Comment: 10 pages, 5 figures

We solve the time-dependent Schr\"odinger equation describing a water molecule driven by a superposition of the XUV and IR pulses typical for a RABBITT experiment. This solution is obtained by a combination of the time-dependent coordinate scaling and the density functional theory with self-interaction correction. Results of this solution are used to determine the time delay in photoionization of the water and hydrogen molecules., Comment: 6 pages, 3 figures. arXiv admin note: text overlap with arXiv:1604.04938

Single photon laser enabled Auger decay (spLEAD) has been redicted theoretically [Phys. Rev. Lett. 111, 083004 (2013)] and here we report its first experimental observation in neon. Using coherent, bichromatic free-electron laser pulses, we have detected the process and coherently controlled the angular distribution of the emitted electrons by varying the phase difference between the two laser fields. Since spLEAD is highly sensitive to electron correlation, this is a promising method for probing both correlation and ultrafast hole migration in more complex systems., Comment: 5 pages, 3 figures

Angular dependence of photoemission time delay for the valence $np_{3/2}$ and $np_{1/2}$ subshells of Ar, Kr and Xe is studied in the dipole relativistic random phase approximation. Strong angular anisotropy of the time delay is reproduced near respective Cooper minima while the spin-orbit splitting affects the time delay near threshold.

We investigate an angular dependence of the photoemission time delay in helium as measured by the RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) technique. The measured time delay $ \tau_a=\tau_W+\tau_{cc} $ contains two distinct components: the Wigner time delay $\tau_W$ and the continuum-continuum CC) correction $\tau_{cc}$. In the case of helium with only one $1s\to Ep$ photoemission channel, the Wigner time delay $\tau_W$ does not depend on the photoelectron detection angle relative to the polarization vector. However, the CC correction $\tau_{cc}$ shows a noticeable angular dependence. We illustrate these findings by performing two sets of calculations. In the first set, we solve the time-dependent Schr\"odinger equation for the helium atom ionized by an attosecond pulse train and probed by an IR pulse. In the second approach, we employ the lowest order perturbation theory which describes absorption of the XUV and IR photons. Both calculations produce close results in a fair agreement with experiment.

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 Schr\"odinger 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., Comment: 18 pages, 8 figures

This work describes the first observations of the ionisation of neon in a metastable atomic state utilising a strong-field, few-cycle light pulse. We compare the observations to theoretical predictions based on the Ammosov-Delone-Krainov (ADK) theory and a solution to the time-dependent Schrodinger equation (TDSE). The TDSE provides better agreement with the experimental data than the ADK theory. We optically pump the target atomic species and demonstrate that the ionisation rate depends on the spin state of the target atoms and provide physically transparent interpretation of such a spin dependence in the frameworks of the spin-polarised Hartree-Fock and random-phase approximations., Comment: 12 pages, 6 figures

We present accurate measurements of carrier-envelope phase effects on ionisation of the noble gases with few-cycle laser pulses. The experimental apparatus is calibrated by using atomic hydrogen data to remove any systematic offsets and thereby obtain accurate CEP data on other generally used noble gases such as Ar, Kr and Xe. Experimental results for H are well supported by exact TDSE theoretical simulations however significant differences are observed in case of noble gases., Comment: 4 pages, 5 figures, submitted to PRL (manuscript number LH15031)

Time delays of electrons emitted from an isotropic initial state and leaving behind an isotropic ion are assumed to be angle-independent. Using an interferometric method involving XUV attosecond pulse trains and an IR probe field in combination with a detection scheme, which allows for full 3D momentum resolution, we show that measured time delays between electrons liberated from the $1s^2$ spherically symmetric ground state of helium depend on the emission direction of the electrons relative to the linear polarization axis of the ionizing XUV light. Such time-delay anisotropy, for which we measure values as large as 60 attoseconds, is caused by the interplay between final quantum states with different symmetry and arises naturally whenever the photoionization process involves the exchange of more than one photon in the field of the parent-ion. With the support of accurate theoretical models, the angular dependence of the time delay is attributed to small phase differences that are induced in the laser-driven continuum transitions to the final states. Since most measurement techniques tracing attosecond electron dynamics involve the exchange of at least two photons, this is a general, significant, and initially unexpected effect that must be taken into account in all such photoionization measurements., Comment: 17 pages, 4 figures

We study transverse electron momentum distribution (TEMD) in strong field atomic ionization driven by laser pulses with varying ellipticity. We show, both experimentally and theoretically, that the TEMD in the tunneling and over the barrier ionization regimes evolves in a qualitatively different way when the ellipticity parameter describing polarization state of the driving laser pulse increases., Comment: 5 pages, 6 figures

The initial insight into time delay in Mn photoionization in the region of the $3p \to 3d$ giant autoionization resonance is gained in the framework of the "spin-polarized" random phase approximation with exchange. The dramatic effect of the giant autoionization resonance on time delay of photoemission from the $3d$ and $4s$ valence subshells of the Mn atom is unraveled. Strong sensitivity of the time delay of the $4s$ photoemission to the final-state term of the ion-remainder [${\rm Mn^{+}}(4s^{1},$$^{5}S)$ vs.~${\rm Mn^{+}}(4s^{1},$$^{7}S)$] is discovered. It is shown that photoionization time delay in the autoionizing resonance region is explicitly associated with the resonance lifetime, which can, thus, be directly measured in attosecond time delay experiments. Similar features are expected to emerge in photoionization time delays of other transition-metal and rare-earth atoms with half-filed subshells that possess giant autoionization resonances as well., Comment: 8 pages, 4 figures, 49 references

We analyze a transfer ionization (TI) reaction in the fast proton-helium collision $\rm H^+ + He \to H^0 + He^{2+} + e^-$ by solving a time-dependent Schr\"odinger equation (TDSE) under the classical projectile motion approximation in one-dimensional kinematics. In addition, we construct various time independent analogues of our model using lowest order perturbation theory in the form of the Born series. By comparing various aspects of the TDSE and the Born series calculations, we conclude that the recent discrepancies of experimental and theoretical data may be attributed to deficiency of the Born models used by other authors. We demonstrate that the correct Born series for TI should include the momentum space overlap between the double ionization amplitude and the wave function of the transferred electron., Comment: 10 pages, 6 figures

We study strong-field atomic ionization driven by an XUV pulse with a non\-zero displacement, the quantity defined as the integral of the pulse vector potential taken over the pulse duration. We demonstrate that the use of such pulses may lead to an extreme sensitivity of the ionization process to subtle changes of the parameters of a driving XUV pulse, in particular, the ramp-on/off profile and the carrier envelope phase. We illustrate this sensitivity for atomic hydrogen and lithium driven by few-femto\-second XUV pulses with intensity in the $\rm 10^{14}~W/cm^2$ range. We argue that the observed effect is general and should modify strong-field ionization of any atom, provided the ionization rate is sufficiently high., Comment: 5 pages, 7 figures

The effects of confinement resonances on photoelectron group delay (Wigner time delay) following ionization of an atom encapsulated inside a C$_{60}$ cage have been studied theoretically using both relativistic and non-relativistic random phase approximations. The results indicate clearly the resonant character of the confinement oscillations in time delay of the $4d$ shell of Xe@C$_{60}$ and present a most direct manifestation of Wigner time delay. These oscillations were missed in a previous theoretical investigation of Ar@C$_{60}$ [PRL 111, 203003 (2013)]

We propose a novel mechanism of electron localization and molecular symmetry breaking in dissociative photoionization of the H$_2$ molecule. The Coulomb field of the ejected electron can induce transition of the remaining H$_2^+$ ion from the gerade $^2\Sigma_g^1(1s\sigma_g)$ to the ungerade $^2\Sigma_u^1(2p\sigma_u)$ electronic state when the nuclei in a bound vibrational state are near the outer turning point. The superposition of this process with a direct transition to vibrational continuum should produce a non-gerade ionic state which results in observed asymmetry in the $p$-H ejection relative to the electron ejection direction at a small kinetic energy release., Comment: 5 pages, 5 figures

We perform time-dependent calculations of strong-field ionization of He by elliptically polarized light in configuration of recent attoclock measurements of Boge {\em et al} [PRL {\bf 111}, 103003 (2013)]. By solving a 3D time-dependent Schr\"odinger equation, we obtain the angular offset $\theta_m$ of the maximum in the photoelectron momentum distribution in the polarization plane relative to the position predicted by the strong field approximation. This offset is used in attoclock measurements to extract the tunneling time. Our calculations clearly support the set of experimental angular offset values obtained with the use of non-adiabatic calibration of the {\em in situ} field intensity, and disagree with an alternative set calibrated adiabatically. These findings are in contrast with the conclusions of Boge {\em et al} who found a qualitative agreement of their semiclassical calculations with the adiabatic set of experimental data. This controversy may complicate interpretation of the recent atto-clock measurements., Comment: 5 pages, 5 figures

We use the soft photon approximation to extract the Wigner time delay from atomic two-color photoionization experiments. Unlike the strong field approximation, the present method does not require introduction of the Coulomb-laser coupling corrections and enables one to extract the Wigner time delay directly from attosecond time delay measurements.

We use the non-relativistic random phase approximation with exchange to perform calculations of valence shell photoionization of Ne, Ar, Kr and Xe from their respective thresholds to photon energy of 200 eV. The energy derivative of the complex phase of the photoionization matrix elements is converted to the photoelectron group delay that can be measured in attosecond streaking or two-photon transitions interference experiments. Comparison with reported time delay measurements in Ne and Ar at a few selected photon energies is made. Systematic mapping of time delay across a wide range of photon energies in several atomic targets allows to highlight important aspects of fundamental atomic physics that can be probed by attosecond time delay measurements.

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 measurement is established using the recently developed asymptotic approximation for the complex transition amplitudes of laser-assisted photoionization. We compare and discuss the theoretical and experimental results especially in the region where strong intershell correlations in the 3s to kp channel lead to an induced "Cooper" minimum in the 3s ionization cross-section., Comment: submitted to PRA

We predict a significant delay of two-electron photoemission from the helium atom after absorption of an attosecond XUV pulse. We establish this delay by solving the time dependent Schr\"odinger equation and by subsequent tracing the field-free evolution of the two-electron wave packet. This delay can also be related to the energy derivative of the phase of the complex double photoionization (DPI) amplitude which we evaluate by the convergent close-coupling method. Our observations prompt future attosecond streaking experiments on DPI of He which can elucidate various mechanisms of this strongly correlated ionization process.

We analyze the time delay between emission of photoelectrons from the outer valence $ns$ and $np$ sub-shells in noble gas atoms following absorption of an attosecond XUV pulse. By solving the time dependent Schr\"odinger equation and carefully examining the time evolution of the photoelectron wave packet, we establish the apparent "time zero" when the photoelectron leaves the atom. Various processes such as elastic scattering of the photoelectron on the parent ion and many-electron correlation affect the quantum phase of the dipole transition matrix element, the energy dependence of which defines the emission timing. This qualitatively explains the time delay between photoemission from the $2s$ and $2p$ sub-shells of Ne as determined experimentally by attosecond streaking [{\em Science} {\bf 328}, 1658 (2010)]. However, with our extensive numerical modeling, we were only able to account for less than a half of the measured time delay of $21\pm5$ as. We argue that the XUV pulse alone cannot produce such a large time delay and it is the streaking IR field that is most likely responsible for this effect., Comment: 5 pages, 2 figures

Increase of the cut-off value in the high order harmonics generation process is demonstrated for a special case of the driving field composed of several harmonics of a given frequency. It is shown that a moderate, of the order of 20%, increase in the cut-off value can be achieved. This result possibly constitutes an upper limit for the increase in the cut-off value, attainable for a class of the waveforms considered in the paper.

We report the total integrated cross-section (TICS) of two-photon double ionization of helium in the photon energy range from 42 to 50 eV. Our computational procedure relies on a numerical solution of the time-dependent Schr\"odinger equation on a square-integrable basis and subsequent projection of this solution on a set of final states describing two electrons in continuum. Close to the threshold, we reproduce results previously known from the literature. The region 47-50 eV seems to have been previously unexplored. Our results suggest that TICS, as a function of the photon energy, grows monotonously in the region 42-50 eV. We also present fully resolved triple differential cross sections for selected photon energies., Comment: 12 pages, 3 figures

The quadrupole channel of two-photon double ionization of He exhibits two distinctly different modes of correlated motion of the photoelectron pair. The mode associated with the center-of-mass motion favors a large total momentum which is maximazed at a parallel emission. However, the mode associated with the relative motion favors an antiparallel emission. This difference is manifested in a profoundly different width of the angular correlation functions corresponding to the center-of-mass and relative motion modes., Comment: 4 pages, 3 figures

We apply the convergent close-coupling (CCC) formalism to the problem of two-photon double ionization of helium. The electron-photon interaction is treated perturbatively whereas the electron-electron interaction is included in full. The integrated two-photon double ionization cross-section is substantially below non-perturbative literature results. However, the pattern of the angular correlation in the two-electron continuum is remarkably close to the non-perturbative time-dependent close-coupling calculation of Hu {\em et al} [J. Phys. {\bf B38}, L35 (2005)], Comment: 15 pages, 6 figures

We employ the Kramers-Henneberger Hamiltonian for time-independent calculations of multi-photon ionization of atoms with one and two electrons. As compared to the electromagnetic interaction in the length and velocity gauges, the presently employed Kramers-Henneberger gauge has an advantage of the dipole matrix elements for the free-free electron transitions being finite and well-defined quantities. This circumstance simplifies considerably the computations and allows to obtain accurate results for the two-photon ionization of realistic atomic systems., Comment: 16 pages, 1 figure