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Metastable states are important actors in the ionisation of atoms and molecules. Sub-femtosecond extreme ultraviolet pulses can coherently populate several transiently bound states at once, thus starting the attosecond clocks which are required to monitor and control ultrafast electronic evolution above the ionisation threshold. Here we illustrate, from a theoretical point of view, the effects coherent superpositions of 1 P o doubly excited states in the helium atom have on channel-resolved photoelectron spectra as well as on the transient absorption spectrum of the atom in the extreme ultraviolet region, when they are created by a single-attosecond pulse in the presence of a strong few-cycle near-infrared/visible pulse which acts as a probe. Interference fringes varying rapidly with the pump-probe time delay are visible in both photoelectron and transient absorption spectra. From such fringes, the wave packet itself can conceivably be reconstructed. Conversely, all observables are modulated by the characteristic beating periods of the wave packet, so that control of partial ionisation yields, branching ratios, and light absorption or amplification can be achieved ; The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No 290853, the European COST Actions CM0702 and CM1204, the ERA-Chemistry project No PIM2010EEC-00751, the Marie Curie ITN CORINF, and the MICINN projects No.s FIS2010-15127 and CSD 2007-00010 (Spain)

We present a B-spline K-matrix method for three-active-electron atoms in the presence of a polarizable core, with which it is possible to compute multichannel single-ionization scattering states with good accuracy. We illustrate the capabilities of the method by computing the parameters of several autoionizing states of the boron atom, with 2Se, 2Pe,o, and 2De symmetry, up to at least the 2p2 (1S) excitation threshold of the B II parent ion, as well as selected portions of the photoionization cross section from the ground state. Our results exhibit remarkable gauge consistency, they significantly extend the existing sparse record of data for the boron atom, and they are in good agreement with the few experimental and theoretical data available in the literature. These results open the way to extend to three-active-electron systems the spectral analysis of correlated wave packets in terms of accurate scattering states that has already been demonstrated for two-electron atoms in Argenti and Lindroth ; L.A. acknowledges support from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant XCHEM 290853, the MINECO project no. FIS2013-42002-R, the ERA-Chemistry Project PIM2010EEC-00751, the European grant MC-ITN CORINF and the European COST Action XLIC CM1204.

As a first step towards meeting the recent demand for new computational tools capable of reproducing molecular-ionization continua in a wide energy range, we introduce a hybrid Gaussian-B-spline basis (GABS) that combines short-range Gaussian functions, compatible with standard quantum-chemistry computational codes, with B splines, a basis appropriate to represent electronic continua. We illustrate the performance of the GABS hybrid basis for the hydrogen atom by solving both the time-independent and the time-dependent Schrödinger equation for a few representative cases. The results are in excellent agreement with those obtained with a purely B-spline basis, with analytical results, when available, and with recent above-threshold ionization spectra from the literature. In the latter case, we report fully differential photoelectron distributions which offer further insight into the process of above-threshold ionization at different wavelengths ; Work supported by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 290853, European COST Action No. CM1204 XLIC, and MICINN Project No. FIS2010-15127

We present a theoretical study of the photoelectron attosecond beating due to interference of two-photon transitions in the presence of autoionizing states. We show that, as a harmonic traverses a resonance, both the phase shift and frequency of the sideband beating significantly vary with photon energy. Furthermore, the beating between two resonant paths persists even when the pump and the probe pulses do not overlap, thus providing a nonholographic interferometric means to reconstruct coherent metastable wave packets. We characterize these phenomena by means of a general analytical model that accounts for the effect of both intermediate and final resonances on two-photon processes. The model predictions are in excellent agreement with those of accurate ab initio calculations for the helium atom in the region of the N=2 doubly excited states ; We acknowledge computer time from the CCCUAM and Marenostrum Supercomputer Centers and financial support from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 290853 XCHEM, the MINECO Project No. FIS2013-42002-R, the ERA-Chemistry Project No. PIM2010EEC-00751, and the European COST Action XLIC CM1204

We present an analytical model capable of describing two-photon ionization of atoms with attosecond pulses in the presence of intermediate and final isolated autoionizing states. The model is based on the finite-pulse formulation of second-order time-dependent perturbation theory. It approximates the intermediate and final states with Fano's theory for resonant continua, and it depends on a small set of atomic parameters that can either be obtained from separate ab initio calculations or be extracted from a few selected experiments. We use the model to compute the two-photon resonant photoelectron spectrum of helium below the N=2 threshold for the RABITT (reconstruction of attosecond beating by interference of two-photon transitions) pump-probe scheme, in which an XUV attosecond pulse train is used in association with a weak IR probe, obtaining results in quantitative agreement with those from accurate ab initio simulations. In particular, we show that (i) the use of finite pulses results in a homogeneous redshift of the RABITT beating frequency, as well as a resonant modulation of the beating frequency in proximity to intermediate autoionizing states; (ii) the phase of resonant two-photon amplitudes generally experiences a continuous excursion as a function of the intermediate detuning, with either zero or 2π overall variation ; We acknowledge support from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant No. XCHEM 290853, the MINECO Project No. FIS2013-42002-R, the ERA-Chemistry Project No. PIM2010EEC-00751, the European grant MC-ITN CORINF, and the European COST Action XLIC CM1204.

We use the soft-photon approximation, formulated for finite pulses, to investigate the effects of the dressing pulse duration and intensity on simulated attosecond pump–probe experiments employing trains of attosecond extremeultraviolet pulses in conjunction with an IR probe pulse.We illustrate the validity of the approximation by comparing the modelled photoelectron distributions for the helium atom, in the photon energy region close to the N = 2 threshold, to the results from the direct solution of the time-dependent Schr¨odinger equation for two active electrons. Even in the presence of autoionizing states, the model accurately reproduces most of the background features of the ab initio photoelectron spectrum in the 1s channel. A splitting of the photoelectron harmonic signal along the polarization axis, in particular, is attributed to the finite duration of the probe pulse. Furthermore, we study the dependence of the sideband integrated signal on the pump–probe time delay for increasing IR field strengths. Starting at IR intensities of the order of 1TWcm−2, overtones in the sideband oscillations due to the exchange of three or more IR photons start to appear. We derive an analytical expression in the frequency-comb limit of the soft-photon model for the amplitude of all the sideband frequency components and show that these amplitudes oscillate as a function of the intensity of the IR field. In particular, we predict that the amplitude of the fundamental component with frequency 2!IR, on which the rabitt optical reconstruction technique is based, changes sign periodically ; We thank Mare Nostrum BSC and CCC-UAM (Centro de Computación Científica, Universidad Autónoma de Madrid) for allocation of computer time. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 290853, the European COST Actions CM0702 and CM1204, the ERA-Chemistry project number PIM2010EEC-00751, the Marie Curie ITN CORINF and the MICINN projects numbers FIS2010-15127 and CSD 2007-00010 (Spain)

We present an analytical model that characterizes two-photon transitions in the presence of autoionising states. We applied this model to interpret resonant RABITT spectra, and show that, as a harmonic traverses a resonance, the phase of the sideband beating significantly varies with photon energy. This phase variation is generally very different from the π jump observed in previous works, in which the direct path contribution was negligible. We illustrate the possible phase profiles arising in resonant two-photon transitions with an intuitive geometrical representation ; Financial support from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) /ERC grant agreement 290853 XCHEM, the MINECO project FIS2013-42002-R, the ERA-Chemistry Project PIM2010EEC-00751, the European COST Action XLIC CM1204, the Marie Curie ITN CORINF, and the CAM project NANOFRONTMAG

This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in The Journal of Physical Chemistry Letters, copyright © 2018 American Chemical Society after peer review. To access the final edited and published work see https://pubs.acs.org/doi/10.1021/acs.jpclett.7b03220 ; Direct measurement of autoionization lifetimes by using time-resolved experimental techniques is a promising approach when energy-resolved spectroscopic methods do not work. Attosecond time-resolved experiments have recently provided the first quantitative determination of autoionization lifetimes of the lowest members of the well-known Hopfield series of resonances in N2. In this work, we have used the recently developed XCHEM approach to study photoionization of the N2molecule in the vicinity of these resonances. The XCHEM approach allows us to describe electron correlation in the molecular electronic continuum at a level similar to that provided by multireference configuration interaction methods in bound state calculations, a necessary condition to accurately describe autoionization, shakeup, and interchannel couplings occurring in this range of photon energies. Our results show that electron correlation leading to interchannel mixing is the main factor that determines the magnitude and shape of the N2photoionization cross sections, as well as the lifetimes of the Hopfield resonances. At variance with recent speculations, nonadiabatic effects do not seem to play a significant role. These conclusions are supported by the very good agreement between the calculated cross sections and those determined in synchrotron radiation and attosecond experiments ; This work has been supported by the ERC advanced grant 290853 - XCHEM - within the seventh framework programme of the European Union, the ERC proof-of-concept grant 780284 - Imaging-XChem - within the Horizon2020 Framework Programme, and the MINECO projects FIS2013-42002-R and FIS2016-77889-R (AEI/FEDER, UE). We also acknowledge computer time from CCC-UAM and Marenostrum Supercomputer Centers. L.A. acknowledges support from the TAMOP NSF Grant No. 1607588, as well as UCF funding

We present an in-depth theoretical study of N2 photoionization in the region between the second (2Πu) and third (2Σu+) ionization thresholds. In this region, the electronic continuum includes the Hopfield series of autoionizing states, corresponding to excitations to nsσd, ndσd, and ndπg molecular orbitals. Calculations have been performed by using the xchem code, which makes use of a Gaussian and B-spline hybrid basis in the framework of a close-coupling approach. We provide total and partial photoionization cross sections for all open channels, energy positions, and widths for the five lowest resonances of each series and, when resonances are well isolated from each other, Fano and Starace parameters. We also discuss how the coupling between the two series of overlapping resonances, nsσd and ndσd, affects their energies and autoionization widths. These results show the potential of the xchem method to describe resonant photoionization in molecules ; This work has been supported by the ERC Advanced Grant No. 290853 – XCHEM – within the Seventh Framework Program of the European Union, the ERC Proof-of-Concept Grant No. 780284 – Imaging-XChem – within the Horizon 2020 Framework Programme, and MINECO Project No. FIS2016-77889-R (AEI/FEDER, UE). L.A. acknowledges support from the TAMOP NSF through Grant No. 1607588, as well as UCF funding

Strong-field manipulation of autoionizing states is a crucial aspect of electronic quantum control. Recent measurements of the attosecond transient absorption spectrum (ATAS) of helium dressed by a few-cycle visible pulse [C. Ott, Nature (London) 516, 374 (2014)] provide evidence of the inversion of Fano profiles. With the support of accurate ab initio calculations that reproduce the results of the latter experiment, here we investigate the new physics that arise from ATAS when the laser intensity is increased. In particular, we show that (i) previously unnoticed signatures of the dark 2p2 1S doubly excited state are observed in the experimental spectrum, (ii) inversion of Fano profiles is predicted to be periodic in the laser intensity, and (iii) the ac Stark shift of the higher terms in the sp2,n+ autoionizing series exceeds the ponderomotive energy, which is the result of a genuine two-electron contribution to the polarization of the excited atom ; We acknowledge computer time from the CCC-UAM and Marenostrum Supercomputer Centers and financial support from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 290853 XCHEM, the MINECO project FIS2013-42002-R, the ERAChemistry Project PIM2010EEC-00751, the European COST Action XLIC CM1204, the Marie Curie ITN CORINF, and the CAM project NANOFRONTMAG. C.O. and T.P. acknowledge financial support by the Max-Planck Research Group Program of the Max-Planck Gesellschaft (MPG) and the European Research Council (ERC, Grant No. X-MuSiC-616783)

The XCHEM approach interfaces well established quantum chemistry packages with scattering numerical methods in order to describe single-ionization processes in atoms and molecules. This should allow one to describe electron correlation in the continuum at the same level of accuracy as quantum chemistry methods do for bound states. Here we have applied this method to study multichannel photoionization of Ne in the vicinity of the autoionizing states lying between the 2s22p5 and 2s2p6 ionization thresholds. The calculated total photoionization cross sections are in very good agreement with the absolute measurement of Samson et al. [J. Electron Spectrosc. Relat. Phenom. 123, 265 (2002)], and with independent benchmark calculations performed at the same level of theory. From these cross sections, we have extracted resonance positions, total autoionization widths, Fano profile parameters, and correlation parameters for the lowest three autoionizing states. The values of these parameters are in good agreement with those reported in earlier theoretical and experimental work. We have also evaluated β asymmetry parameter and partial photoionization cross sections and, from the latter, partial autoionization widths and Starace parameters for the same resonances, not yet available in the literature. Resonant features in the calculated β parameter are in good agreement with the experimental observations. We have found that the three lowest resonances preferentially decay into the 2p-1ϵd continuum rather than into the 2p-1ϵs one [Phys. Rev. A 89, 043415 (2014)], in agreement with previous expectations, and that in the vicinity of the resonances the partial 2p-1ϵs cross section can be larger than the 2p-1ϵd one, in contrast with the accepted idea that the latter should amply dominate in the whole energy range. These results show the potential of the XCHEM approach to describe highly correlated process in the ionization continuum of many-electron systems, in particular molecules, for which the XCHEM code has been specifically designed ; We acknowledge computer time from the CCC-UAM and Marenostrum Supercomputer Centers, and financial support from the European Research Council under the European Union's Seventh Framework Programme (No. FP7/2007-2013)/ERC Grant Agreement No. 290853 XCHEM, the MINECO Projects No. FIS2013-42002-R and No. FIS2016-77889-R, and the European COST Action XLIC CM1204 and STSM CM1204-26542. L.A. acknowledges support from the TAMOP NSF Grant No. 1607588, as well as UCF fundings. E.L. and T.K. acknowledge support from the Swedish Research Council, Grant No. 2016-03789

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 wave packet resulting from the integration of the time-dependent Schrodinger equation in a finite-element discrete variable representation basis. These techniques are projection on products of hydrogenic bound and continuum states, projection onto multichannel scattering states computed in a B-spline close-coupling basis, and a technique based on exterior complex scaling implemented in the same basis used for the time propagation. These methods allow one to monitor the population of continuum states in wave packets created with ultrashort pulses in different regimes. Applications include photo cross sections and anisotropy parameters in the spectral region of doubly excited resonances, time-resolved photoexcitation of autoionizing resonances in an attosecond pump-probe setting, and the energy and angular distribution of correlated wave packets for two-photon double ionization ; This work was supported by the G¨oran Gustafsson Foundation, the Swedish Science Research Council (VR), the European COST Action CM0702, the FWF-Austria, Grants No. P21141-N16 and No. P23359-N16, the SFB ViCoM, SFB NextLite, and in part by the National Science Foundation through XSEDE resources provided by NICS and TACC under Grant No. TG-PHY090031. L.A. acknowledges support from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 290853, and the MICINN Project No. FIS2010-15127. J.F. acknowledges support from the NSF through a grant to ITAMP and by the European Research Council under Grant No. 290981 (PLASMONANOQUANTA). R.P. acknowledges support by the TU Vienna Doctoral Program Functional Matter. M.L. acknowledges funding by the Vienna Science and Technology Fund (WWTF) through Project No. MA09-030

We have determined spectral phases of Ne autoionizing states from extreme ultraviolet and midinfrared attosecond interferometric measurements and ab initio full-electron time-dependent theoretical calculations in an energy interval where several of these states are coherently populated. The retrieved phases exhibit a complex behavior as a function of photon energy, which is the consequence of the interference between paths involving various resonances. In spite of this complexity, we show that phases for individual resonances can still be obtained from experiment by using an extension of the Fano model of atomic resonances. As simultaneous excitation of several resonances is a common scenario in many-electron systems, the present work paves the way to reconstruct electron wave packets coherently generated by attosecond pulses in systems larger than helium ; Work supported by the ERC proof-of-concept Grant No. 780284-Imaging-XChem within the seventh framework program of the European Union, the MINECO Project No. FIS2013-42002-R, the EU-H2020- LASERLABEUROPE-654148, the ANR Projects No. ANR-15-CE30-0001-CIMBAAD, No. ANR-11- EQPX0005-ATTOLAB, and No. ANR-10-LABX-0039- PALM, the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award no. DEGF02-04ER15614, and the NSF Grant No. PHY-1607588. Calculations were performed at CCC-UAM and Marenostrum Supercomputer Center. F. M. acknowledges support from the "Severo Ochoa" Programme for Centres of Excellence in R&D (MINECO, Grant No. SEV-2016- 0686) and the "María de Maeztu" Programme for Units of Excellence in R&D (Grant No. MDM-2014-0377)

Time delays of electrons emitted from an isotropic initial state with the absorption of a single photon and leaving behind an isotropic ion are 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 three-dimensional momentum resolution, we show that measured time delays between electrons liberated from the 1s2 spherically symmetric ground state of helium depend on the emission direction of the electrons relative to the common linear polarization axis of the ionizing XUV light and the IR-probing field. Such time delay anisotropy, for which we measure values as large as 60 as, 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. 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 and significant effect that must be taken into account in all measurements of time delays involving photoionization processes ; S.H, C.C, L.G., and U.K. acknowledge support by the ERC advanced Grant No. ERC-2012-ADG_20120216 within the seventh framework program of the European Union and by the NCCR MUST, funded by the Swiss National Science Foundation. M.L. acknowledges support from the ETH Zurich Postdoctoral Fellowship Program. A.J.G., L.A., and F.M. acknowledge the support from the European Research Council under the ERC Grant No. 290853 XCHEM, from the European COST Action No. CM1204 XLIC, the MINECO Project No. FIS2013-42002-R, the ERA-Chemistry Project No. PIM2010EEC- 00751, and the European Grant No. MC-ITN CORINF. Calculations were performed at the Centro de Computacion Científica of the Universidad Autónoma de Madrid (CC-UAM) and the Barcelona Supercomputing Center (BSC). I.I. and A.S.K. acknowledge support of the Australian Research Council (Grant No. DP120101805) and the use of the National Computational Infrastructure Facility. J.M.D. acknowledges support from the Swedish Research Grants No. 2013-344 and No. 2014-3724. E.L. acknowledges support from the Swedish Research Council, Grant No. 2012-3668. Moreover, this research was supported in part by the Kavli Institute for Theoretical Physics (National Science Foundation under Grant No. NSF PHY11-25915) and by NORDITA, the Nordic Institute for Theoretical Physics