A three-dimensional semiclassical model is used to study double ionization of Ar when driven by a near-infrared and near-single-cycle laser pulse for intensities ranging from 0.85$\times$10$^{14}$ W/cm$^{2}$ to 5$\times$10$^{14}$ W/cm$^{2}$. Asymmetry parameters, distributions of the sum of the two electron momentum components along the direction of the polarization of the laser field and correlated momenta are computed as a function of intensity and of the carrier envelope phase. A very good agreement is found with recently obtained results in kinematically complete experiments employing near-single-cycle laser pulses. Moreover, the contribution of the direct and delayed pathways of double ionization is investigated for the above observables. Finally, an experimentally obtained anti-correlation momentum pattern at higher intensities is reproduced with the three-dimensional semiclassical model and shown to be due to a transition from strong to soft recollisions with increasing intensity.
This is a Reply on the proceeding comment on our paper titled "Classical Simulations Including Electron Correlations for Sequential Double Ionization".
Non-adiabatic photo-ionization is difficult to control as it relies on the derivatives of the envelope and not on phase-details of the short ionizing pulse. Here, we introduce a catalyzing state, whose presence render non-adiabatic ionization sensitive to phase-details of tailored pulses. Since a catalyzing state is in general easy to create, this opens a perspective for coherent control of ultra-fast ionization.
Experiments have shown that the microwave ionization probability of a highly excited almost monodimensional hydrogen atom subjected to a microwave pulse sometimes grows in steps when the peak electric field of the pulse is increased. Classical pulsed simulations display the same steps, which have been traced to phase-space metamorphoses. Quantum numerical calculations again exhibit the same ionization steps. I show that the time-sequence of two level interactions, responsible for the observed steps in the quantum picture, is strictly related to the classical phase space structures generated by…
Multielectron double ionization with elliptically polarized light is examined theoretically using a classical ensemble method going beyond the single-active-electron approximation. A knee structure in the ion signal is found. Our analysis provides an explanation for newly observed SDI phenomena.
Ionization by relativistically intense laser pulses of finite duration is considered in the framework of strong-field quantum electrodynamics. Our main focus is on the formation of ionization supercontinua. More specifically, when studying the energy distributions of photoelectrons ionized by circularly polarized pulses, we observe the appearance of broad structures lacking the interference patterns. These supercontinua extend over hundreds of driving photon energies, thus corresponding to high-order nonlinear processes. The corresponding polar-angle distributions show asymmetries which are at…
We study the field-ionization threshold behavior when a Rydberg atom is ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are considered. The required threshold field amplitude is found to scale \emph{inversely} with the binding energy when the pulse duration becomes shorter than the classical Rydberg period, and, thus, more weakly bound electrons require larger fields for ionization. This threshold scaling behavior is confirmed by both 3D classical trajectory Monte Carlo simulations and numerically solving the time-dependent Schrödinger equation. More surprisingly, t…
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 obs…
We predict new end-of-pulse behavior in high-field atomic double ionization. Calculations of atomic electron trajectories in short intense laser pulses confirm our analysis of elliptical polarization. We exhibit a four-band structure in ion momentum distributions under various ellipticities, and predict that sequential and non-sequential double ionization can be cleanly distinguished under elliptical polarization.
Above 54.4 eV, two-photon double ionization of helium is dominated by a sequential absorption process, producing characteristic behavior in the single and triple differential cross sections. We show that the signature of this process is visible in the nuclear recoil cross section, integrated over all energy sharings of the ejected electrons, even below the threshold for the sequential process. Since nuclear recoil momentum imaging does not require coincident photoelectron measurement, the predicted images present a viable target for future experiments with new short-pulse VUV and soft X-ray so…
We join the tribute to Professor N.B. Delone in this memorial issue by presenting the results of new calculations on the effects of ellipticity on double ionization by short and strong near-optical laser pulses.
We review the semiclassical two-step model for strong-field ionization. The semiclassical two-step model describes quantum interference and accounts for the ionic potential beyond the semiclassical perturbation theory. We discuss formulation and implementation of this model, its further developments, as well as some of the applications. The reviewed applications of the model include strong-field holography with photoelectrons, multielectron polarization effects in ionization by an intense laser pulse, and strong-field ionization of the hydrogen molecule.
We introduce a unified and simplified theory of atomic double ionization. Our results show that at high laser intensities ($I \ge 10^{14}$ watts/cm$^2$) purely classical correlation is strong enough to account for all of the main features observed in experiments to date.
In a previous publication, procedures were proposed for unambiguously extracting amplitudes for single and double ionization from a time-dependent wavepacket by effectively propagating for an infinite time following a radiation pulse. Here we demonstrate the accuracy and utility of those methods for describing two-photon single and one-photon double ionization of helium. In particular it is shown how narrow features corresponding to autoionizing states are easily resolved with these methods.
Ionization with ultrashort pulses in the extreme ultraviolet (XUV) regime can be used to prepare an ion in a superposition of spin--orbit substates. In this work, we study the coherence properties of such a superposition, created by ionizing xenon atoms using two phase-locked XUV pulses at different frequencies. In general, if the duration of the driving pulse exceeds the quantum beat period, dephasing will occur. If however, the frequency difference of the two pulses matches the spin--orbit splitting, the coherence can be efficiently increased and dephasing does not occur.
How fast can a laser pulse ionize an atom? We address this question by considering pulses that carry a fixed time-integrated energy per-area, and finding those that achieve the double requirement of maximizing the ionization that they induce, while having the shortest duration. We formulate this double-objective quantum optimal control problem by making use of the Pareto approach to multi-objetive optimization, and the differential evolution genetic algorithm. The goal is to find out how much a precise time-profiling of ultra-fast, large-bandwidth pulses may speed up the ionization process wit…
Double electron ionisation process occurs when an intense laser pulse interacts with atoms or molecules. Exact {\it ab initio} numerical simulation of such a situation is extremely computer resources demanding, thus often one is forced to apply reduced dimensionality models to get insight into the physics of the process. The performance of several algorithms for simulating double electron ionization by strong femtosecond laser pulses are studied. The obtained ionization yields and the momentum distributions of the released electrons are compared, and the effects of the model dimensionality on …
Multiphoton ionization of sodium by laser pulses of 800 nm wavelength and 57 fs duration is studied in the range of laser peak intensities belonging to over-the-barrier ionization regime. Photoelectron momentum distributions (PMD) and the energy spectra are determined numerically by solving the time dependent Schrödinger equation. The calculated spectra agree well with the spectra obtained experimentally by Hart et al. [Phys. Rev. A 93, 063426 (2016)]. The contributions of photoelectrons with different values of the orbital quantum number in the PMD are determined by expanding the photoelectro…
A simple model for sequential multiphoton ionization by ultra-intense x-rays is presented. The derived scaling of the ion yield with pulse energy quantitatively reproduces the experimental data, which shows that the ion yield increases according to the "power law" behavior typical of multiphoton ionization, followed by saturation at high pulse energies. The calculated average time interval between ionizations for producing ions at a certain charge state is found to be proportional to the pulse duration and independent of all other x-ray pulse parameters. This agrees with previous studies where…
We consider atomic strong-field ionization in the long-pulse limit for linearly polarized infrared laser fields. We show how nondipole effects in the plane formed by the propagation and polarization directions lead to (i) a shift of the origin of the rings describing the energetically allowed final electron momenta for individual above-threshold ionization channels and (ii) a redistribution in the continuum population on each ring.
We investigate the strong-field ionization of atomic hydrogen in a few-cycle elliptically polarized infrared pulse by solving the time-dependent Schrödinger equation. The dependence of the photoelectron momentum distribution on the pulse intensity, ellipticity, length, envelope, and carrier envelope phase is analyzed. In particular, we explain the variation of the electron offset angle with asymptotic electron energy through the combined action of the field and the Coulomb potential, and demonstrate that low-ellipticity pulses make it possible to access the electron release time.
The multiphoton ionization and photoelectron spectra of magnesium were studied at laser intensities of up to 6x10^{13} Wcm^{-2} using 150 fs laser pulses of a wavelength of 400 nm. The results indicated that a variety of different ionization mechanisms played a role in both types of spectra. A theoretical model describing the processes is presented and the routes to ionization are identified. The work demonstrates the significance of the two-electron nature of the atom in interpreting the experimental results.
In conditions where the interaction betweeen an atom and a short high-frequency extreme ultraviolet laser pulse is a perturbation, we show that a simple theoretical approach, based on Coulomb-Volkov-type states, can make reliable predictions for ionization. To avoid any additional approximation, we consider here a standard case : the ionization of hydrogen atoms initially in their ground state. For any field parameter, we show that the method provides accurate energy spectra of ejected electrons, including many above threshold ionization peaks, as long as the two following conditions are simul…
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 take advantage of the information provided by use of elliptical polarization in a recent two-electron release time experiment [A.N. Pfeiffer et al., Nature Physics 7, 428 (2011)]. This allows a comparative test of the currently dominant conjectures regarding independent-electron tunneling theory vs. fully electron-correlated classical release theory to describe electron release in strong-field double ionization.
With a classical ensemble model that including electron correlations during the whole ionization process, we investigated strong-field sequential double ionization of Ar by elliptically polarized pulses at the quantitative level. The experimentally observed intensity-dependent three-band or four-band structures in the ion momentum distributions are well reproduced with this classical model. More importantly, the experimentally measured ionization time of the second electrons [A. N. Pfeiffer et al., Nature Phys. 7, 428 (2011)], which can not be predicted by the standard independent-electron mod…
We theoretically study the pulse-width dependence of the photoelectron angular distribution (PAD) from the resonance-enhanced two-photon single ionization of He by femtosecond ($\lesssim 20$ fs) extreme-ultraviolet pulses, based on the time-dependent perturbation theory and simulations with the full time-dependent Schrödinger equation. In particular, we focus on the competition between resonant and nonresonant ionization paths, which leads to the relative phase $δ$ between the $S$ and $D$ wave packets distinct from the corresponding scattering phase shift difference. When the spectrally broade…
This paper concerns the theory of non-recollisional ionization or detachment of atoms or ions by intense few-cycle pulses. It is shown that in certain conditions of pulse duration, peak intensity and carrier-envelope phase, the ionization probability integrated over ejection angle varies almost periodically with energy, with a period roughly equal to the photon energy for slow enough outgoing electrons. This modulation is found both in calculations based on the strong field approximation (SFA) and in ab initio time-dependent calculations. It is explained as resulting from the interference betw…
The interaction of a short, few-cycle light pulse and an atom which is prepared initially in a superposition of two stationary states is shown to exhibit strong signatures of atomic coherence. For a given waveform of the laser pulse, appropriate quantum mechanical relative phase between the constituents of the initial superposition can increase the ionization probability by a factor of three. A similarly strong effect can be observed when the waveform of the ionizing pulse is changed. These results allow for intuitive explanations, which are in agreement with the numerical integration of the t…
We theoretically study the photoelectron angular distributions (PADs) from two-color two-photon near-threshold ionization of hydrogen and noble gas (He, Ne, and Ar) atoms by a combined action of femtosecond extreme ultraviolet (EUV) and near-infrared (IR) laser pulses. Using the second-order time-dependent perturbation theory, we clarify how the two-photon ionization process depends on EUV-IR pulse delay and how it is connected to the interplay between resonant and nonresonant ionization paths. Furthermore, by solving the time-dependent Schrödinger equation, we calculate the anisotropy paramet…
We report full-dimensionality quantum and classical calculations for double ionization of laser-driven helium at 390 nm. Good qualitative agreement is observed. We show that the classical double ionization trajectories can be divided into two distinct pathways: direct and delayed. The direct pathway, with an almost simultaneous ejection of both electrons, emerges from small laser intensities. With increasing intensity its relative importance, compared to the delayed ionization pathway, increases until it becomes the predominant pathway for total electron escape energy below around 5.25 $U_{p}$…
Owing to its numerical simplicity, a two-dimensional two-electron model atom, with each electron moving in one direction, is an ideal system to study non-perturbatively a fully correlated atom exposed to a laser field. Frequently made assumptions, such as the ``single active electron''- approach and calculational approximations, e.g. time dependent density functional theory or (semi-) classical techniques, can be tested. In this paper we examine the multiphoton short pulse-regime. We observe ``non-sequential'' ionization, i.e.\ double ionization at lower field strengths as expected from a sequ…
The experimental observations of sequential double ionization (SDI) of Ar [A. N. Pfeiffer {\it et al.}, Nature Phys. {\bf 7}, 428 (2011)], such as the four-peak momentum distribution and the ionization time of the first and second electrons, are investigated and reproduced with a quantum model by including and excluding the $e$-$e$ correlation effect. Based on the comparison of experiment and simulation, the role of $e$-$e$ correlation in SDI is discussed. It is shown that the inclusion of $e$-$e$ correlation is necessary to reproduce the momentum distribution of electrons.
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 theoretically study multiphoton ionization through the triplet states of Mg by linearly polarized (LP) and circularly polarized (CP) fs laser pulses. After the construction of the atomic basis using the frozen-core Hartree-Fock potential (FCHFP) as well as the model potential (MP) approaches for both singlet and triplet series which show rather good agreements with the existing data in terms of state energies and dipole matrix elements, we solve time-dependent Schrödinger equations with $3s3p$ $^{3}P_{1}$ as an initial state, and calculate the total ionization yield and photoelectron energy…
We consider the ionization of neon induced by a femtosecond laser pulse composed of overlapping, linearly polarized bichromatic extreme ultraviolet and infrared fields. In particular, we study the effects of the infrared light on a two-pathway ionization scheme for which Ne 2s22p53s1P is used as intermediate state. Using time-dependent calculations, supported by a theoretical approach based on the strong-field approximation, we analyze the ionization probability and the photoelectron angular distributions associated with the different sidebands of the ionization spectrum. Complex oscillations …
We investigate the laser-assisted single XUV photon double ionization of ground state helium. By solving full six-dimensional time-dependent schr{ö}dinger equation, we study the correlation and angular distribution. The discussion in joint energy and angular distributions reveals the competition in odd and even parity double ionization processes in the presence of weak laser field. The emission angle between two photoelectrons can be adjusted by the laser parameters. We depicts how the laser field enhance and/or enable the back-to-back and side-by-side emission of double ionization.
We provide theoretical investigations of the response of the Ar and H atoms to an intense elliptically polarized few-cycle laser pulse, as a function of light ellipticity. The time-dependent Schr{ö}dinger equation describing the least-bound electron is solved numerically, and differential quantities such as the momentum distribution, the electron density in the continuum, and the above-threshold ionization spectra are computed. These quantities provide insight into the ionization dynamics and the electron rescattering process as a function of light ellipticity, and reveal great similarities be…
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.
We consider the process of atomic ionization driven by a laser pulse with varying ellipticity. We study distribution of the momenta of the photoelectrons, ionized by a strong laser field, emitted in the direction perpendicular to the polarization plane (transverse distribution). We show, that with changing laser pulse ellipticity, the transverse distribution evolves from the singular cusp-like distribution for the close to linear polarization to the smooth gaussian-like structure for the close to circular polarization. In the latter case, when the ellipticity parameter $ε\to 1$ the strong-fiel…
Breakdown of sequential tunnel ionization in ultrashort electromagnetic pulses
National Research Nuclear University MEPhI（国立研究核大学）；P.N. Lebedev Physical Institute of the Russian Academy of Sciences（俄罗斯科学院列别捷夫物理研究所）；Prokhorov General Physics Institute of the Russian Academy of Sciences（俄罗斯科学院普罗霍罗夫普通物理研究所）
We present an {\it ab initio} and non-perturbative time-dependent approach to the problem of double ionization of a general atom driven by intense XUV laser pulses. After using a highly flexible $B$-Spline $R$-matrix method to generate field-free Hamiltonian and electric dipole matrices, the initial state is propagated in time using an efficient Arnoldi-Lanczos scheme. Test calculations for double ionization of He by a single laser pulse yield good agreement with benchmark results obtained with other methods. The method is then applied to two-color pump-probe processes, for which momentum and …
Strong-field ionization with few-cycle, mid-infrared laser pulses induces a localized ionization followed by long-lasting charge migration in halogenated organic molecules
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 a theoretical study of the ionization dynamics of a hydrogen atom exposed to attosecond laser pulses in the extreme ultra violet region at very high intensities. The pulses are such that the electron is expected to reach relativistic velocities, thus necessitating a fully relativistic treatment. We solve the time dependent Dirac equation and compare its predictions with those of the corresponding non-relativistic Schr{ö}dinger equation. We find that as the electron is expected to reach about 20% of the speed of light, relativistic corrections introduces a finite yet small decrease i…
We report on non-sequential double ionization of Ar by a laser pulse consisting of two counter rotating circularly polarized fields (390 nm and 780 nm). The double ionization probability depends strongly on the relative intensity of the two fields and shows a "knee"-like structure as function of intensity. We conclude that double ionization is driven by a beam of nearly monoenergetic recolliding electrons, which can be controlled in intensity and energy by the field parameters. The electron momentum distributions show the recolliding electron as well as a second electron which escapes from an …
We examine correlated electron and doubly charged ion momentum spectra from strong field double ionization of Neon employing intense elliptically polarized laser pulses. An ellipticity-dependent asymmetry of correlated electron and ion momentum distributions has been observed. Using a 3D semiclassical model, we demonstrate that our observations reflect the sub-cycle dynamics of the recollision process. Our work reveals a general physical picture for recollision-impact double ionization with elliptical polarization, and demonstrates the possibility of ultrafast control of the recollision dynami…
We have investigated the ionization of the H atom by intense few-cycle laser pulses, in particular the intra-pulse interference effects, and their dependence on the carrier-envelope phase (CEP) of the laser pulse. In the final momentum distribution of the continuum electrons the imprint of two types of intra-pulse interference effects can be observed, namely the temporal and spatial interference. During the spatial interference electronic wave packets emitted at the same time, but following different paths interfere leading to an interference pattern measurable in the electron spectra. This ca…
The interaction of relativistically strong tailored laser pulses with an atomic system is considered. Due to a special tailoring of the laser pulse, the suppression of the relativistic drift of the ionized electron and a dramatic enhancement of the rescattering probability is shown to be achievable. The high harmonic generation rate in the relativistic regime is calculated and shown to be increased by several orders of magnitude compared to the case of conventional laser pulses. The energies of the revisiting electron at the atomic core can approach the MeV domain, thus rendering hard x-ray ha…
Multiphoton ionization of sodium by femtosecond laser pulses of 800 nm wavelength in the range of laser peak intensities entering over-the-barrier ionization domain is studied. Photoelectron momentum distributions and the energy spectra are determined numerically by solving the time dependent Schroedinger equation for three values of the laser intensity from this domain. The calculated spectra agree well with the spectra obtained experimentally by Hart et al (Phys. Rev. A 2016 93 063426). A partial wave analysis of the spectral peaks related to Freeman resonances has shown that each peak is a …
We present a theoretical framework to describe state-resolved ionization dynamics of neon atoms driven by ultraintense x-ray free-electron-laser pulses. In general, x-ray multiphoton ionization dynamics of atoms have been described by time-dependent populations of the electronic configurations visited during the ionization dynamics, neglecting individual state-to-state transition rates and energies. Combining a state-resolved electronic-structure calculation, based on first-order many-body perturbation theory, with a Monte Carlo rate-equation method, enables us to study state-resolved dynamics…
We consider the final stage of double ionization of $\rm O_2$ molecules by short linearly polarized laser pulses. The saddles of the effective adiabatic potential energy close to which simultaneous escape of electrons from a molecule takes place are identified. The analysis of the saddles and numerical simulations of the ionization indicate that to observe clear signatures of simultaneous electron escape in double ionization of $\rm O_2$ molecules stronger and much shorter laser pulses than those used in the recent experiment [E. Eremina, {\it et al}, Phys. Rev. Lett. {\bf 92}, 173001 (2004)] …
We investigate differential electron distributions in nonsequential double ionization (NSDI) with linearly polarized, few-cycle pulses, using a classical model based on a laser-assisted inelastic $(e^-,2e^-)$ rescattering mechanism. We show that these yields, as functions of the momentum components parallel to the laser polarization, are highly asymmetric, and strongly influenced by the absolute phase, i.e., the phase difference between the carrier oscillation of a few-cycle laser pulse and its envelope. Indeed, around a critical phase, such distributions change their sign in a radical fashion…
Double ionization in intense laser fields can comprise electron correlations, which manifest in the non-independent emission of two electrons from an atom or molecule. However, experimental methods that directly access the electron emission times have been scarce. Here, we explore the application of an all-optical streaking technique to strong-field double ionization both theoretically and experimentally. We show that both sequential and non-sequential double ionization processes lead to streaking delays that are distinct from each other and single ionization. Moreover, coincidence detection o…
We have constructed deep neural networks, which can map fluctuating photo-electron spectra obtained from noisy pulses to spectra from noise-free pulses. The network is trained on spectra from noisy pulses in combination with random Hamilton matrices, representing systems which could exist but do not necessarily exist. In [Giri et al., Phys. Rev. Lett. 124,113201 (2020)] we performed a purification of fluctuating spectra, that is mapping them to those from Fourier-limited Gaussian pulses. Here, we investigate the performance of such neural-network-based maps for predicting spectra of double pul…
At intensities below-the-recollision threshold, we show that re-collision-induced excitation with one electron escaping fast after re-collision and the other electron escaping with a time delay via a Coulomb slingshot motion is one of the most important mechanisms of non-sequential double ionization, for strongly-driven He at 400 nm. Slingshot-NSDI is a general mechanism present for a wide range of low intensities and pulse durations. Anti-correlated two-electron escape is its striking hallmark. This mechanism offers an alternative explanation of anti-correlated two-electron escape obtained in…
