The attosecond ultrafast ionization dynamics of correlated two- or many-electron systems have, so far, been mainly addressed investigating atomic systems. In the case of single ionization, it is well known that electron-electron correlation modifies the ionization dynamics and observables beyond the single active electron picture, resulting in effects such as the Auger effect or shake-up/down and knock-up/down processes. Here, we extend these works by investigating the attosecond ionization of a molecular system involving correlated two-electron dynamics, as well as non-adiabatic nuclear dynamics. Employing a charge-transfer molecular model system with two differently bound electrons, a strongly and a weakly bound electron, we distinguish different pathways leading to ionization, be it direct ionization or ionization involving elastic and inelastic electron scattering processes. We find that different pathways result in a difference in the electronic population of the parent molecular ion, which, in turn, involves different subsequent (non-adiabatic) postionization dynamics on different time scales.
A universal mechanism of ultrafast two-electron orbital swap is discovered through two-photon sequential double ionization of Li. After a $1s$ electron in Li is ionized by absorbing an EUV photon, the other two bound electrons located on two different shells have either parallel or antiparallel spin orientations. In the latter case, these two electrons are in the superposition of the singlet and triplet states with different energies, forming a quantum beat and giving rise to the two-electron orbital swap with a period of several hundred attoseconds. The orbital swap mechanism can be used to m…
We develop the two-electron attosecond streak camera under realistic conditions using a quasi-classical model. We assume extreme ultra-violet (XUV) attosecond pulses with a full width at half maximum (FWHM) of 24 attoseconds, centered at 120 eV and a streaking infrared laser field of 1600 nm, and intensity of $1.8 \times 10^{12}$ W/cm$^2$. The proposed method is shown to be capable to time resolve intra-atomic collisions in double ionization.
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…
Attosecond pulses can be used to initiate and control electron dynamics on a sub-femtosecond time scale. The first step in this process occurs when an atom absorbs an ultraviolet photon leading to the formation of an attosecond electron wave packet (EWP). Until now, attosecond pulses have been used to create free EWPs in the continuum, where they quickly disperse. In this paper we use a train of attosecond pulses, synchronized to an infrared (IR) laser field, to create a series of EWPs that are below the ionization threshold in helium. We show that the ionization probability then becomes a fun…
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 show that time ordering underlying time-dependent quantum dynamics is a physical observable accessible by attosecond streaking. We demonstrate the extraction of time ordering for the prototypical case of time-resolved two-photon double ionization (TPDI) of helium by an attosecond XUV pulse. The Eisenbud-Wigner-Smith time delay for the emission of a two-electron wavepacket and the time interval between subsequent emission events can be unambiguously determined by attosecond streaking. The delay between the two emission events sensitively depends on the energy, pulse duration, and angular dis…
Strong-field ionization generally produces ions in a superposition of ionic eigenstates. This superposition is generally not fully coherent und must be described in terms of a density matrix. A recent experiment [E. Goulielmakis et al., Nature 466, 739 (2010)] employed attosecond transient absorption spectroscopy to determine the density matrix of strong-field-generated Kr+ ions. The experimentally observed degree of coherence of the strong-field-generated Kr+ ions is well reproduced by a recently developed multichannel strong-field-ionization theory. But there is significant disagreement betw…
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…
We investigate the possibility to monitor the dynamics of autoionizing states in real time and control the yields of different ionization channels in helium by simulating XUV-pump IR-probe experiments focused on the N=2 threshold. The XUV pulse creates a coherent superposition of doubly excited states which is found to decay by ejecting electrons in bursts. Prominent interference fringes in the photoelectron angular distribution of the $2s$ and $2p$ ionization channels are observed, along with sizable out-of-phase quantum beats in the yields of the corresponding parent ions.
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 mom…
Strong-field ionization (SFI) has been shown to prepare wave packets with few-femtosecond periods. Here, we explore whether this technique can be extended to the attosecond time scale. We introduce an intuitive model for predicting the bandwidth of ionic states that can be coherently prepared by SFI. This bandwidth is given by the Fourier-transformed sub-cycle SFI rate and decreases considerably with increasing central wavelength of the ionizing pulse. Many-body calculations based on time-dependent configuration-interaction singles (TDCIS) quantitatively support this result and reveal an addit…
We calculate the transient absorption of an isolated attosecond pulse by helium atoms subject to a delayed infrared (\ir) laser pulse. With the central frequency of the broad attosecond spectrum near the ionization threshold, the absorption spectrum is strongly modulated at the sub-\ir-cycle level. Given that the absorption spectrum results from a time-integrated measurement, we investigate the extent to which the delay-dependence of the absorption yields information about the attosecond dynamics of the atom-field energy exchange. We find two configurations in which this is possible. The first…
The ionization of atoms with sequences of attosecond pulses gives rise to excited ionic states that are entangled with the emitted photoelectron. Still, the ionic ensemble preserves some coherence that can be controlled through the laser parameters. In helium, control of the $2s/2p$ He$^+$ coherence is mediated by the autoionizing states below the $N=2$ threshold [Phys. Rev. Res. {\bf 3}, 023233 (2021)]. In the present work we study the role of the resonances both below and above the $N=3$ threshold on the coherence of the $N=3$ He$^+$ ion, in the attosecond pump-probe ionization of the helium…
We propose a new scenario to apply IR-pump-XUV-probe schemes to resolving strong field ionization induced and attosecond pulse driven electron-hole dynamics and coherence in real time. The coherent driving of both the infrared laser and the attoscond pulse correlates the dynamics of the core-hole and the valence-hole which leads to the otherwise forbidden absorption and emission of XUV photon. An analytical model is developed based on the strong-field approximation by taking into account of the essential multielectron configurations. The emission spectra from the core-valence transition and th…
We investigate two-photon double ionization of helium by intense ($10^{15} W/cm^2$) ultrashort ($\approx 300$ as) soft X-ray pulses (E = 91.6 eV). The time-dependent two-electron Schrödinger equation is solved using a coupled channel method. We show that for ultrashort pulses the angular distribution of ejected electrons depends on the pulse duration and provides novel insights into the role of electron correlations in the two-electron photoemission process. The angular distribution at energies near the ``independent electron'' peaks is close to dipolar while it acquires in the ``valley'' of c…
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 …
Ionization by relativistically intense short laser pulses is studied in the framework of strong-field quantum electrodynamics. Distinctive patterns are found in the energy probability distributions of photoelectrons. Except of the already observed patterns, which were studied in Phys. Rev. A {\bf 94}, 013402 (2016), we discover an additional interference-free smooth supercontinuum in the high-energy portion of the spectrum, reaching tens of kiloelectronovolts. As we show, the latter is sensitive to the driving field intensity and it can be detected in a narrow polar-angular window. Once these …
Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach due to the difficulty of combining attosecond temporal resolution with fine spectral and angular resolutions. Here, we achieve full decoding of the intricate angle-dependent dynamics of a photoemission process in helium, spectrally and anisotropically structured by twophoton transitions through intermediate bound states. Using spectrally- and angularly-resolved attosecond electron interferometry, we characterize the complex-valued transition probability amplitude towards the photo…
Recent experimental developments of high-intensity, short-pulse XUV light sources are enhancing our ability to study electron-electron correlations. We perform time-dependent calculations to investigate the so-called "sequential" regime (photon energy above 54.4 eV) in the two-photon double ionization of helium. We show that attosecond pulses allow to induce and probe angular and energy correlations of the emitted electrons. The final momentum distribution reveals regions dominated by the Wannier ridge break-up scenario and by post-collision interaction.
Light-induced states are commonly observed in the photoionization spectra of laser-dressed atoms. The properties of autoionizing polaritons, entangled states of light and Auger resonances, however, are largely unexplored. We employ attosecond transient-absorption spectroscopy to study the evolution of autoionizing states in argon, dressed by a tunable femtosecond laser pulse. The avoided crossings between the $3s^{-1}4p$ and several light-induced states indicates the formation of polariton multiplets. We measure a controllable stabilization of the polaritons against ionization, in excellent ag…
We perform a detailed analysis of how high-order harmonic generation (HHG) and above-threshold ionization (ATI) can be controlled by a time-delayed attosecond-pulse train superposed to a strong, near-infrared laser field. In particular we show that the high-harmonic and photoelectron intensities, the high-harmonic plateau structure and cutoff energies, and the ATI angular distributions can be manipulated by changing this delay. This is a direct consequence of the fact that the attosecond pulse train can be employed as a tool for constraining the instant an electronic wave packet is ejected in …
The use of semiclassical models based on the Strong Field Approximation (SFA) is ubiquitous in strong field multi-photon ionization and underlies many key developments in attosecond science, including the description of High Harmonic Generation (HHG). However, such models are notably lacking in streaking experiments, which use an attosecond pulse to initiate single-photon ionization and a lower frequency infrared pulse to provide timing information. Here, we introduce a classical Wigner propagation (CWP) method, which analogously to semiclassical models in strong field ionization, treats the i…
We study resonant two-photon ionization of helium atoms via the $1s3p$, $1s4p$ and $1s5p^1$P$_1$ states using the 15$^\mathrm{th}$ harmonic of a titanium-sapphire laser for the excitation and a weak fraction of the laser field for the ionization. The phase of the photoelectron wavepackets is measured by an attosecond interferometric technique, using the 17$^\mathrm{th}$ harmonic. We perform experiments with angular resolution using a velocity map imaging spectrometer and with high energy resolution using a magnetic bottle electron spectrometer. Our results are compared to calculations using th…
Parametric amplification of attosecond coherent pulses around 100 eV at the single-atom level is demonstrated for the first time by using the 3D time-dependent Schr{ö}dinger equation in high-harmonic generation processes from excited states of He$^+$. We present the attosecond dynamics of the amplification process far from the ionization threshold and resolve the physics behind it. The amplification of a particular central photon energy requires the seed XUV pulses to be perfectly synchronized in time with the driving laser field for stimulated recombination to the He$^+$ ground state and is o…
We present a theoretical study of the photoelectron attosecond beating at the basis of RABBIT (Reconstruction of Attosecond Beating By Interference of Two-photon transitions) in the presence of autoionizing states. We show that, as a harmonic traverses a resonance, its sidebands exhibit a peaked phase shift as well as a modulation of the beating frequency itself. Furthermore, the beating between two resonant paths persists even when the pump and the probe pulses do not overlap, thus providing a sensitive non-holographic interferometric means to reconstruct coherent metastable wave packets. We …
To measure and control the electron motion in atoms and molecules by the strong laser field on the attosecond time scale is one of the research frontiers of atomic and molecular photophysics. It involves many new phenomena and processes and raises a series of questions of concepts, theories and methods. Recent studies show that the Coulomb potential can cause the ionization time lag (about 100 attoseconds) between instants of the field maximum and the ionization-rate maximum. This lag can be understood as the response time of the electronic wave function to the strong-field-induced ionization …
We study photoionization of argon atoms excited by attosecond pulses using an interferometric measurement technique. We measure the difference in time delays between electrons emitted from the $3s^2$ and from the $3p^6$ shell, at different excitation energies ranging from 32 to 42 eV. The determination of single photoemission time delays requires to take into account the measurement process, involving the interaction with a probing infrared field. This contribution can be estimated using an universal formula and is found to account for a substantial fraction of the measured delay.
The field of attosecond nanophysics, combining the research areas of attosecond physics with nanoscale physics, has experienced a considerable rise in recent years both experimentally and theoretically. Its foundation rests on the sub-cycle manipulation and sampling of the coupled electron and near-field dynamics on the nanoscale. Attosecond nanophysics not only addresses questions of strong fundamental interest in strong-field light-matter interactions at the nanoscale, but also could eventually lead to a considerable number of applications in ultrafast, petahertz-scale electronics, and ultra…
The evolution of electron wavepackets determines the course of many physical and chemical phenomena and attosecond spectroscopy aims to measure and control such dynamics in real-time. Here, we investigate radial electron wavepacket motion in Helium by using an XUV attosecond pulse train to prepare a coherent superposition of excited states and a delayed femtosecond IR pulse to ionize them. Quantum beat signals observed in the high resolution photoelectron spectrogram allow us to follow the field-free evolution of the bound electron wavepacket and determine the time-dependent ionization dynamic…
Fullerenes have unique physical and chemical properties that are associated with their delocalized conjugated electronic structure. Among them, there is a giant ultra-broadband - and therefore ultrafast - plasmon resonance, which for C$_{60}$ is in the extreme-ultraviolet energy range. While this peculiar resonance has attracted considerable interest for the potential downscaling of nanoplasmonic applications such as sensing, drug delivery and photocatalysis at the atomic level, its electronic character has remained elusive. The ultrafast decay time of this collective excitation demands attose…
We investigate the role of electron correlation in the two-photon double ionization of helium for ultrashort XUV pulses with durations ranging from a hundred attoseconds to a few femtoseconds. We perform time-dependent ab initio calculations for pulses with mean frequencies in the so-called "sequential" regime (photon energy above 54.4 eV). Electron correlation induced by the time correlation between emission events manifests itself in the angular distribution of the ejected electrons, which strongly depends on the energy sharing between them. We show that for ultrashort pulses two-photon doub…
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 develop an analytical model of correlated two-electron ionization in strong infrared laser fields. The model includes all relevant interactions between the electrons, the laser field, and the ionic core nonperturbatively. We focus on the deeply quantum regime, where the energy of the active electron driven by the laser field is insufficient to collisionally ionize the parent ion, and the assistance of the laser field is required to create a doubly charged ion. In this regime, the electron-electron and the electron-ion interactions leave distinct footprints in the correlated two-electron spe…
We demonstrate sub-cycle control of frustrated double ionization (FDI) in the two-electron triatomic molecule D$_3^+$ when driven by two orthogonally polarized two-color laser fields. We employ a three-dimensional semi-classical model that fully accounts for the electron and nuclear motion in strong fields. We control FDI triggered by a strong near-infrared laser field with a weak mid-infrared laser field. This control as a function of the time delay between the two pulses is demonstrated when the FDI probability and the distribution of the momentum of the escaping electron along the mid-infra…
We illustrate how attosecond light pulses can be used to directly mapping out the time-dependence of the correlated motion of two excited atomic electrons, discuss how the two-electron correlations manifest themselves in realistic attosecond measurements, and propose the following for experimental exploration: (a) The single ionization signals which directly reveal bending-vibrational motion of the correlated electron pair, (b) and also its rotational motion. (c) The double ionization signals which directly reveal the two-electron density in momentum space. To facilitate the description of the…
We demonstrate fully phase matched high-order harmonic generation with emission spanning the water window spectral region important for bio- and nano-imaging and a breadth of materials and molecular dynamics studies. We also generate the broadest bright coherent bandwidth (~300eV) to date obtained from any light source, small or large. The harmonic photon flux at 0.5 keV is 10^3 higher than demonstrated previously, making it possible for the first time to demonstrate spatial coherence in the water window. The continuum emission is consistent with a single attosecond burst, that extends bright …
Attosecond x-ray pulses offer unprecedented opportunities for probing and triggering new types of ultrafast motion. At the same time, pulse characterization of x-rays presents new challenges that do not exist in the UV regime. Inner-shell ionization is the dominant ionization mechanism for x-rays and it is followed by secondary processes like fluorescence, Auger decay, and shake-up.In general, we find that inner-shell ionization and secondary processes can create additional delay-dependent modulations that will affect pulse reconstruction schemes. Our recently proposed pulse characterization m…
Ab initio simulations of a range of interferometric experiments are used to identify a strong dependence on multiphoton phase shifts in above-threshold ionization. A simple rule of thumb for interaction phase shifts is derived to explain both the conservation of photoelectron yield and its absolute CEP-dependence. For instance, it is found that interferometric above-threshold ionization experiments are shifted by $π/4$ relative to RABBIT experiments, and that there is no RABBIT-term in a laser-assisted photoionization experiment with odd and even harmonics. Thus, our work helps to resolve the …
We investigate the response of two three-body Coulomb systems when driven by attosecond half-cycle pulses: The hydrogen molecular ion and the helium atom. Using very short half-cycle pulses (HCPs) which effectively deliver ``kicks'' to the electrons, we first study how a carefully chosen sequence of HCPs can be used to control to which of one of the two fixed atomic centers the electron gets re-attached. Moving from one electron in two atomic centers to two electrons in one atomic center we then study the double ionization from the ground state of He by a sequence of attosecond time-scale HCPs…
Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, who…
We show that electrons recolliding with the ionic core upon tunnel ionization of noble gas atoms driven by a strong circularly polarized laser field in combination with a counter-rotating second harmonic are spin polarized and that their degree of polarization depends strongly on the recollision time. Spin polarization arises as a consequence of (1) entanglement between the recolliding electron and the ion, and (2) sensitivity of ionization to the sense of electron rotation in the initial state. We demonstrate that one can engineer the degree of spin polarization as a function of time by tunin…
Multi-electron dynamics in atoms and molecules very often occur on sub- to few-femtosecond timescales. The available intensities of extreme-ultraviolet (XUV) attosecond pulses have previously only allowed the time-resolved investigation of two-photon, two-electron interactions. Here we demonstrate attosecond control over double and triple ionization of argon atoms involving the absorption of up to five XUV photons. In an XUV-pump XUV-probe measurement using a pair of attosecond pulse trains (APTs), the Ar$^{2+}$ ion yield exhibits a weak delay dependence, showing that its generation predominan…
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.
Using the recently developed concept of the 2-electron streak camera (see NJP 12, 103024 (2010)), we have studied the energy-sharing between the two ionizing electrons in single-photon double ionization of He(1s2s). We find that the most symmetric and asymmetric energy sharings correspond to different ionization dynamics with the ion's Coulomb potential significantly influencing the latter. This different dynamics for the two extreme energy sharings gives rise to different patterns in asymptotic observables and different time-delays between the emission of the two electrons. We show that the 2…
