We describe numerically the ionization process induced by linearly and circularly polarized XUV attosecond laser pulses on an aligned atomic target, specifically, the excited state Ne$^*(1s^22s^22p^5[{}^2\text{P}^\text{o}_{1/2}]3s[^1\text{P}^o])$. We compute the excited atomic state by applying the time-dependent restricted-active-space self-consistent field (TD-RASSCF) method to fully account for the electronic correlation. We find that correlation-assisted ionization channels can dominate over channels accessible without correlation. We also observe that the rotation of the photoelectron momentum distribution by circularly polarized laser pulses compared to the case of linear polarization can be explained in terms of differences in accessible ionization channels. This study shows that it is essential to include electron correlation effects to obtain an accurate description of the photoelectron emission dynamics from aligned excited states.
We study the role of electron-electron correlation in the ground-state of Ne, as well as in photoionization dynamics induced by an attosecond XUV pulse. For a selection of central photon energies around 100 eV, we find that while the mean-field time-dependent Hartree-Fock method provides qualitatively correct results for the total ionization yield, the photoionization cross section, the photoelectron momentum distribution as well as for the time-delay in photoionization, electron-electron correlation is important for a quantitative description of these quantities.
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…
We report measurements of energy-dependent attosecond photoionization delays between the two outer-most valence shells of N$_2$O and H$_2$O. The combination of single-shot signal referencing with the use of different metal foils to filter the attosecond pulse train enables us to extract delays from congested spectra. Remarkably large delays up to 160 as are observed in N$_2$O, whereas the delays in H$_2$O are all smaller than 50 as in the photon-energy range of 20-40 eV. These results are interpreted by developing a theory of molecular photoionization delays. The long delays measured in N$_2$O…
A technique for measuring photoionization time delays with attosecond precision is combined with calculations of photoionization matrix elements to demonstrate how multi-electron dynamics affect photoionization time delays in carbon dioxide. Electron correlation is observed to affect the time delays through two mechanisms: autoionization of molecular Rydberg states and accelerated escape from a continuum shape resonance.
We study the temporal aspects of laser-assisted extreme ultraviolet (XUV) photoionization using attosecond pulses of harmonic radiation. The aim of this paper is to establish the general form of the phase of the relevant transition amplitudes and to make the connection with the time-delays that have been recently measured in experiments. We find that the overall phase contains two distinct types of contributions: one is expressed in terms of the phase-shifts of the photoelectron continuum wavefunction while the other is linked to continuum--continuum transitions induced by the infrared (IR) la…
Exchange correlation plays an important role in double-ionization of complex atoms by ultrashort laser pulse. In this work, we investigate two-photon double inner-shell electron ionization of neon induced by an attosecond extreme ultraviolent pulse in the framework of the quantum master equation. Our simulations reveal a distinct non-sequential effect via broadened double peaks, as a result of energy sharing between the two ionized electrons. When dissipation is included to show the interplay of coherence and decoherence, the two-photon double-ionization scaling law breaks down. We further stu…
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…
We present the first demonstration of two-photon double ionization of neon using an intense extreme ultraviolet (XUV) attosecond pulse train (APT) in a photon energy regime where both direct and sequential mechanisms are allowed. For an APT generated through high-order harmonic generation (HHG) in argon we achieve a total pulse energy close to 1 $μ$J, a central energy of 35 eV and a total bandwidth of $\sim30$ eV. The APT is focused by broadband optics in a neon gas target to an intensity of $3\cdot10^{12} $W$\cdot$cm$^{-2}$. By tuning the photon energy across the threshold for the sequential …
We describe in detail how attosecond delays in laser-assisted photoionization can be computed using perturbation theory based on two-photon matrix elements. Special emphasis is laid on above-threshold ionization, where the electron interacts with an infrared field after photoionization by an extreme ultraviolet field. Correlation effects are introduced using diagrammatic many-body theory to the level of the random-phase approximation with exchange (RPAE). Our aim is to provide an ab initio route to correlated multi-photon processes that are required for an accurate description of experiments o…
We theoretically study time-resolved photoemission in atoms as probed by attosecond streaking. We review recent advances in the study of the photoelectric effect in the time domain and show that the experimentally accessible time shifts can be decomposed into distinct contributions that stem from the field-free photoionization process itself and from probe-field induced corrections. We perform accurate quantum-mechanical as well as classical simulations of attosecond streaking for effective one-electron systems and determine all relevant contributions to the time delay with attosecond precisio…
We determine and analyze the quantum phases and time delays in photoionization and photorecombination of valence 3p and 3s electrons of argon using the Kohn-Sham local density functional approach. The time-dependent local density approximation (TDLDA) is used to account for the electron correlation. Resulting attosecond Wigner-Smith time delays show excellent agreements with two recent independent experiments on argon that measured the relative 3s-3p time delay in photoionization [Physical Review Letters {\bf 106}, 143002 (2011)] and the delay in 3p photorecombination [Physical Review Letters …
We investigate the angle-resolved photoelectron spectra from laser-assisted photoionization for helium and neon atoms using an \textit{ab initio} method based on time-dependent surface flux and configuration interaction singles. We find that the shape of the distributions can be interpreted using a propensity rule, an intrinsic difference in the absorption and emission processes, as well as interference effects between multiple paths to the final angular momentum state. In neon we find that the difference between absorption and emission is hidden in the first sideband due to the multiple compe…
We revisit the time-resolved photoemission in neon atoms as probed by attosecond streaking. We calculate streaking time shifts for the emission of 2p and 2s electrons and compare the relative delay as measured in a recent experiment by Schultze et al. [Science 328, 1658 (2010)]. The B-spline R-matrix method is employed to calculate accurate Eisenbud-Wigner-Smith time delays from multi- electron dipole transition matrix elements for photoionization. The additional laser field-induced time shifts in the exit channel are obtained from separate, time-dependent simulations of a full streaking proce…
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…
Attosecond photoionization delays have mostly been interpreted within the single-particle approximation of multi-electron systems. The strong electron correlation between the photoionization channels associated with the 3p and 3s orbitals of argon presents an interesting arena where this single-particle approximation breaks down. Around photon energies of 42~eV, the 3s photoionization channel of argon experiences a ``Cooper-like" minimum, which is exclusively the result of inter-electronic correlations with the 3p shell. Photoionization delays around this ``Cooper-like" minimum have been predi…
Attosecond noncollinear four wave mixing spectroscopy with one attosecond extreme ultraviolet (XUV) pulse and two few-cycle near-infrared (NIR) pulses was used to measure the autoionization decay lifetimes of inner valence electronic excitations in neon atoms. After a 43-48 eV XUV photon excites a 2s electron into the 2s2p6[np] Rydberg series, broadband NIR pulses couple the 2s2p6[3p] XUV-bright state to neighboring 2s2p6[3s] and 2s2p6[3d] XUV-dark states. Controllable delays of one or both NIR pulses with respect to the attosecond XUV pulse reveal the temporal evolution of either the dark or …
We investigate ionization of neon atoms by an isolated attosecond pump pulse in the presence of two coherent extreme ultraviolet or x-ray probe fields. The probe fields are tuned to a core-valence transition in the residual ion and induce spectral shearing of the photoelectron distributions. We show that the photoelectron-ion coincidence signal contains an interference pattern that depends on the temporal structure of the attosecond pump pulse and the stimulated core-valence transition. Many-body perturbation theory is used to compute "atomic response times" for the processes and we find strik…
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 ti…
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…
A Kohn-Sham time-dependent local-density-functional scheme is utilized to predict attosecond time delays of xenon 4d photoionization that involves the 4d giant dipole resonance and Cooper minimum. The fundamental effect of electron correlations to uniquely determine the delay at both regions is demonstrated. In particular, for the giant dipole resonance, the delay underpins strong collective effect, emulating the recent prediction at C60 giant plasmon resonance [T. Barillot et al, Phys. Rev. A 91, 033413 (2015)]. For the Cooper minimum, a qualitative similarity with a photorecombination experi…
The R-Matrix incorporating Time (RMT) method is a new method for solving the time-dependent Schroedinger equation for multi-electron atomic systems exposed to intense short-pulse laser light. We have employed the RMT method to investigate the time delay in the photoemission of an electron liberated from a 2p orbital in a neon atom with respect to one released from a 2s orbital following absorption of an attosecond XUV pulse. Time delays due to XUV pulses in the range 76-105 eV are presented. For an XUV pulse at the experimentally relevant 105.2 eV, we calculate the time delay to be 10.2 +/- 1.…
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.
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 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…
The photoionization of xenon atoms in the 70-100 eV range reveals several fascinating physical phenomena such as a giant resonance induced by the dynamic rearrangement of the electron cloud after photon absorption, an anomalous branching ratio between intermediate Xe$^+$ states separated by the spin-orbit interaction and multiple Auger decay processes. These phenomena have been studied in the past, using in particular synchrotron radiation, but without access to real-time dynamics. Here, we study the dynamics of Xe 4d photoionization on its natural time scale combining attosecond interferometr…
We study experimentally the influence of the intensity of the infrared (IR) probe field on attosecond pulse train (APT) phase measurements performed with the RABITT method (Reconstruction of Attosecond Beating by Interference in Two-Photon Transitions). We find that if a strong IR field is applied, the attosecond pulses will appear to have lower-than-actual chirp rates. We also observe the onset of the streaking regime in the breakdown of the weak-field RABITT conditions. We perform a Fourier-analysis of harmonic and sideband continuum states and show that the mutual phase relation of the harm…
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…
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 present the first numerical simulation of the time delay in the photoionization of the simplest diatomic molecule H$_2^+$ as observed by attosecond streaking. We show that the strong variation of the Eisenbud-Wigner-Smith time delay as a function of energy and emission angle becomes observable in the streaking time shift provided laser field-induced components are accounted for. The strongly enhanced photoemission time shifts are traced to destructive Cohen-Fano (or two-center) interferences. Signatures of these interferences in the streaking trace are shown to be enhanced when the ionic fr…
Using a spectrally resolved electron interferometry technique, we measure photoionization time delays between the $3s$ and $3p$ subshells of argon over a large 34-eV energy range covering the Cooper minima in both subshells. The observed strong variations of the $3s-3p$ delay difference, including a sign change, are well reproduced by theoretical calculations using the Two-Photon Two-Color Random Phase Approximation with Exchange. Strong shake-up channels lead to photoelectrons spectrally overlapping with those emitted from the $3s$ subshell. These channels need to be included in our analysis …
The creation of superpositions of hole states via single-photon ionization using attosecond extreme-ultraviolet pulses is studied with the time-dependent configuration interaction singles (TDCIS) method. Specifically, the degree of coherence between hole states in atomic xenon is investigated. We find that interchannel coupling not only affects the hole populations, it also enhances the entanglement between the photoelectron and the remaining ion, thereby reducing the coherence within the ion. As a consequence, even if the spectral bandwidth of the ionizing pulse exceeds the energy splittings …
We present a new theoretical approach to attosecond laser-assisted photo- and Compton ionization. Attosecond x-ray absorption and scattering are described by $\hat{\mathrsfs{S}}^{(1,2)}$-matrices, which are coherent superpositions of "monochromatic" $\hat{S}^{(1,2)}$-matrices in a laser-modified Furry representation. Besides refining the existing theory of the soft x-ray photoelectron attosecond streak camera and spectral phase interferometry (ASC and ASPI), we formulate a theory of hard x-ray photoelectron and Compton ASC and ASPI. The resulting scheme has a simple structure and leads to clos…
We study photoionization of various noble gas atoms by attosecond pulses produced in High Harmonic Generation (HHG). We use a pump-probe experiment to measure the time delays of electrons photoionized from Neon, Argon, and Krypton relative to those photoionized from Helium atoms. The Attosecond Pulse Train (APT) is characterized and the relative delay in photoionization of various noble gases is measured. The photoionization delay of Ne, Ar, and Kr is determined using previously calculated values for the He atomic delay and the delay associated with the probe process.
Two XUV-photon double ionization of Ne, induced by an intense few-pulse attosecond train with a ~ 4 fs envelope duration is investigated experimentally and theoretically. The experiment is performed at ELI-ALPS utilizing the recently constructed 10 Hz gas phase high-order harmonic generation SYLOS GHHG-COMPACT beamline. A total pulse energy up to ~1 μJ generated in Argon in conjunction with high reflectivity optics in the XUV region, allowed the observation of the doubly charged state of Ne induced by 40 eV central XUV photon energies. The interaction of the intense attosecond pulse train with…
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…
Attosecond interferometry (AI) is an experimental technique based on ionizing a system with an attosecond pulse train in the presence of an assisting laser. This assisting laser provides multiple pathways for the photoelectron wave packet to reach the same final state, and interference of these pathways can be used to probe properties of matter. The mechanism of AI is well-understood for isolated atoms and molecules in the gas phase, but not so much in the condensed phase, especially if the substrate under study is transparent. Then, additional pathways open up for the electron due to scatteri…
Nonsequential multiple ionization of atoms in intense laser fields is initiated by a recollision between an electron, freed by tunneling, and its parent ion. Following recollision, the initial electron shares its energy with several bound electrons. We use a classical model based on rapid electron thermalization to interpret recent experiments. For neon, good agreement with the available data is obtained with an upper bound of 460 attoseconds for the thermalization time.
The photoionization of the CO molecule from the C$-1s$ orbital does not obey the Franck-Condon approximation, as a consequence of the nuclear recoil that accompanies the direct emission and intra-molecular scattering of the photoelectron. We use an analytical model to investigate the temporal signature of the entangled nuclear and electronic motion in this process. We show that the photoelectron emission delay can be decomposed into its localization and resonant-confinement components. Finally, photoionization by a broadband soft-x-ray pulse results in a coherent vibrational ionic state with a…
We present the experimental observation of two-center interference in the ionization time delays of Kr2. Using attosecond electron-ion-coincidence spectroscopy, we simultaneously measure the photoionization delays of krypton monomer and dimer. The relative time delay is found to oscillate as a function of the electron kinetic energy, an effect that is traced back to constructive and destructive interference of the photoelectron wave packets that are emitted or scattered from the two atomic centers. Our interpretation of the experimental results is supported by solving the time-independent Schr…
We study the photoionization of argon atoms close to the 3s$^2$3p$^6$ $\rightarrow$ 3s$^1$3p$^6$4p $\leftrightarrow$ 3s$^2$3p$^5$ $\varepsilon \ell$, $\ell$=s,d Fano window resonance. An interferometric technique using an attosecond pulse train, i.e. a frequency comb in the extreme ultraviolet range, and a weak infrared probe field allows us to study both amplitude and phase of the photoionization probability amplitude as a function of photon energy. A theoretical calculation of the ionization process accounting for several continuum channels and bandwidth effects reproduces well the experimen…
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…
High-order harmonic generation by few-cycle 800 nm laser pulses in neon gas in the presence of a strong terahertz (THz) field is investigated numerically with propagation effects taken into account. Our calculations show that the combination of THz fields with up to 12 fs laser pulses can be an effective gating technique to generate single attosecond pulses. We show that in the presence of the strong THz field only a single attosecond burst can be phase matched, whereas radiation emitted during other half-cycles disappears during propagation. The cutoff is extended and a wide supercontinuum ap…
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…
Quantum mechanically, photoionization can be fully described by the complex photoionization amplitudes that describe the transition between the ground state and the continuum state. Knowledge of the value of the phase of these amplitudes has been a central interest in photoionization studies and newly developing attosecond science, since the phase can reveal important information about phenomena such as electron correlation. We present a new attosecond-precision interferometric method of angle-resolved measurement for the phase of the photoionization amplitudes, using two phase-locked Extreme …
