The role of shake-off for double ionization of atoms by a single photon with finite energy has become the subject of debate. In this letter, we attempt to clarify the meaning of shake-off at low photon energies by comparing different formulations appearing in the literature and by suggesting a working definition. Moreover, we elaborate on the foundation and justification of a mixed quantum-classical ansatz for the calculation of single-photon double ionization.
We have measured the molecular frame angular distributions of photoelectrons emitted from the Carbon K shell of fixed-in-space CO molecules for the case of simultaneous excitation of the remaining molecular ion. Normal and conjugate shake up states are observed. Photo electrons belonging to normal Σ-satellite lines show an angular distribution resembling that observed for the main photoline at the same electron energy. Surprisingly a similar shape is found for conjugate shake up states with Π-symmetry. In our data we identify shake rather than electron scattering (PEVE) as the mechanism produc…
Recent angle-resolved RABBITT experiments have shown that the photoionization time delay depends on the emission angle of the photoelectron. In this work we demonstrate that for photoemission from helium accompanied by shake-up (correlation satellites), the angular variation of the time delay is dramatically enhanced by the dipolar coupling between the photoelectron and the highly polarizable bound electron in the IR field. We show that the additivity rule for the time delays due to the atomic potential, the continuum-continuum (cc) coupling by the IR field, and due to this two-electron proces…
We study excitation and ionization in the 1.5 MeV/amu O$^{8+}$-Li collision system, which was the subject of a recent reaction-microscope-type experiment [Fischer \textit{et al.}, Phys. Rev. Lett. \textbf{109}, 113202 (2012)]. Starting from an independent-electron model based on determinantal wave functions and using single-electron basis generator method and continuum distorted-wave with eikonal initial-state calculations we show that pure single ionization of a lithium $K$-shell electron is too weak a process to explain the measured single differential cross section. Rather, our analysis sug…
Shake-up and shake-off spectra in the electron capture decay of atomic $^7$Be
Universidade NOVA de Lisboa（新里斯本大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Université Paris-Saclay（巴黎萨克雷大学）；Sorbonne Université（索邦大学）；Colorado School of Mines（科罗拉多矿业学院）；STAR Cryoelectronics LLC（STAR低温电子有限责任公司）；Patrick Space Force Base（帕特里克太空军基地）；XIA LLC（XIA有限责任公司）；Université de Caen（卡昂大学）；Université de Strasbourg（斯特拉斯堡大学）
Electron-impact direct double ionization (DDI) process is studied as a sequence of two and three step processes. Contribution from ionization-ionization, ionization-excitation-ionization, and excitation-ionization-ionization processes is taken into account. The present results help to resolve the long-standing discrepancies; in particular, a good agreement with experimental measurements is obtained for double ionization cross-sections of $O^{1+}$, $O^{2+}$, $O^{3+}$, $C^{1+}$, and $Ar^{2+}$ ions. We show that distribution of the energy of scattered and ejected electrons, which participate in t…
We demonstrate kinematically complete measurements on frustrated double ionization of argon atoms in strong laser fields with a reaction microscope. We found that the electron trapping probability after strong field double ionization is much higher than that after strong field single ionization, especially in case of high laser intensity. The retrieved electron momentum distributions of frustrated double ionization show a clear transition from the nonsequential to the sequential regime, similar to those of strong field double ionization. The dependence of electron momentum width on the laser i…
Quantum calculations of a 1+1-dimensional model for double ionization in strong laser fields are used to trace the time evolution from the ground state through ionization and rescattering to the two electron escape. The subspace of symmetric escape, a prime characteristic of nonsequential double ionization, remains accessible by a judicious choice of 1-d coordinates for the electrons. The time resolved ionization fluxes show the onset of single and double ionization, the sequence of events during the pulse, and the influences of pulse duration, and reveal the relative importance of sequential …
The degree of elliptical polarization of intense short laser pulses is shown to be related to the timing of strong-field non-sequential double ionization. Higher ellipticity is predicted to force the initiation of double ionization into a narrower time window, and this "pins" the ionizing field strength in an unexpected way, leading to the first experimentally testable formula for double ionization probability as a function of ellipticity.
This is a Reply on the proceeding comment on our paper titled "Classical Simulations Including Electron Correlations for Sequential Double Ionization".
We study double ionization of Mg by electron impact through the vantage point of classical mechanics. We consider all electron-electron correlations in a Coulomb four-body problem, where three electrons belong to the atom and the fourth electron causes the impact ionization. From our model we compute the double-ionization probability of Mg for impact energies from 15, to 125 eV. Double ionization occurs through eight double-ionization mechanisms, which we classify into four categories: inner shell capture, direct, delay and ionized inner shell mechanisms. We show that delay and ionized inner s…
We analyze the dynamical processes behind delayed double ionization of atoms subjected to strong laser pulses. Using reduced models, we show that these processes are a signature of Hamiltonian chaos which results from the competition between the laser field and the Coulomb attraction to the nucleus. In particular, we exhibit the paramount role of the unstable manifold of selected periodic orbits which lead to a delay in these double ionizations. Among delayed double ionizations, we consider the case of "Recollision Excitation with Subsequent Ionization" (RESI) and, as a hallmark of this mechan…
We explore the dependence of the double ionization of the He atom on the frequency of a strong laser field while keeping the ponderomotive energy constant. As we increase the frequency we find that the remarkable "finger-like" structure for high momenta recently found for $ω=0.055$ a.u. \cite{Staudte, Rudenko} persists for higher frequencies. At the same time, at $ω=0.187$ a.u. a new X-shape structure emerges for small momenta that prevails in the correlated momenta distribution. The role of this structure as a signature of the frequency dependence of non-sequential double ionization is discus…
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.
Using a classical ensemble method, nonsequential double ionization is predicted to exist with elliptical and circular polarization. Recollision is found to be the underlying mechanism and it is only possible via elliptical trajectories.
We study the effects of spin degrees of freedom and wave function symmetries on double ionization in three-electron systems. Each electron is assigned one spatial degree of freedom. The resulting three-dimensional Schrödinger equation is integrated numerically using grid-based Fourier transforms. We reveal three-electron effects on the double ionization yield by comparing signals for different ionization channels. We explain our findings by the existence of fundamental differences between three-electronic and truly two-electronic spin-resolved ionization schemes. We find, for instance, that do…
In this paper, a quasistatic model is extended to describe the double ionization of Helium in intense linearly polarized field, yielding achieve an insight to the two-electron correlation effect in the ionization dynamics. Our numerical calculations reproduce the excessive double ionization and the photoelectron spectra observed experimentally both quantitatively and qualitatively. Moreover, it is shown that the classical collisional trajectories are the main source of the double ionization in the knee regime and responsible for the unusual angular distribution of the photoelectrons.
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…
The ionization dynamics of a two-electron atom in an attosecond XUV-infrared pump-probe experiment is simulated by solving the time-dependent two-electron Schrödinger equation. A dramatic change of the double ionization (DI) yield with variation of the pump-probe delay is reported and the governing role of electron-electron correlations is shown. The results allow for a direct control of the DI yield and of the relative strength of double and single ionization.
Double photoionization by a single photon is often discussed in terms of two contributing mechanisms, {\it knock-out} (two-step-one) and {\it shake-off} with the latter being a pure quantum effect. It is shown that a quasi-classical description of knock-out and a simple quantum calculation of shake-off provides a clear separation of the mechanisms and facilitates their calculation considerably. The relevance of each mechanism at different photon energies is quantified for helium. Photoionization ratios, integral and singly differential cross sections obtained by us are in excellent agreement w…
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 introduce a time-dependent R-matrix theory generalised to describe double ionization processes. The method is used to investigate two-photon double ionization of He by intense XUV laser radiation. We combine a detailed B-spline-based wavefunction description in a extended inner region with a single-electron outer region containing channels representing both single ionization and double ionization. A comparison of wavefunction densities for different box sizes demonstrates that the flow between the two regions is described with excellent accuracy. The obtained two-photon double ionization cr…
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 $U_{p}$…
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 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.
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.
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.
When intense laser pulses release correlated electrons, the time delay between the ionizations may last more than one laser cycle. We show that this "Recollision-Excitation with Subsequent Ionization" pathway originates from the inner electron being promoted to a sticky region by a recollision where it is trapped for a long time before ionizing. We identify the mechanism which regulates this region, and predict oscillations in the double ionization yield with laser intensity.
It is shown that recently measured cross sections for double ionization of negative ions ($H^-, O^-$, and $C^-$) possess a universal shape when plotted in suitable dimensionless units. The shape can be represented with a simple analytical function, following the same principles as it has been done in establishing a universal shape function for single ionization [Rost and Pattard 1997 Phys. Rev. A {\bf 55} R5]. Thereby, it is demonstrated that direct double ionization dominates the cross section for the targets considered.
Using a three-dimensional quasiclassical technique we explore the double ionization pathways of a diatomic molecule driven by an intense infrared (800nm) ultrashort laser pulse. For intensities corresponding to the tunneling regime, we find that the three main ionization mechanisms have distinct traces when considering the sum of the momenta parallel to the laser field as a function of the inter-electronic angle of escape. In addition, we find that the previously observed "finger-like" structure in the correlated momenta of the strongly driven He is also present for strongly driven diatomic mo…
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.
It is generally believed that the recollision mechanism of atomic nonsequential double ionization is suppressed in circularly polarized laser fields because the returning electron is unlikely to encounter the core. On the contrary, we find that recollision can and does significantly enhance double ionization, even to the extent of forming a "knee", the signature of the nonsequential process. Using a classical model, we explain two apparently contradictory experiments, the absence of a knee for helium and its presence for magnesium.
Using a three-dimensional quasiclassical technique we explore molecular double ionization by a linearly polarized, infrared (800 nm) and ultrashort (6 fs) laser pulse. We first focus on intensities corresponding to the tunneling regime and identify the main ionization mechanisms in this regime. We devise a selection of observables, such as, the correlated momenta and the sum of the momenta parallel to the laser field as a function of the inter-electronic angle of escape where all the main mechanisms have distinct traces. Secondly, we address intensities above but close to the over-the-barrier …
We examine the nature and statistical properties of electron-electron collisions in the recollision process in a strong laser field. The separation of the double ionization yield into sequential and nonsequential components leads to a bell-shaped curve for the nonsequential probability and a monotonically rising one for the sequential process. We identify key features of the nonsequential process and connect our findings in a simplified model which reproduces the knee shape for the probability of double ionization with laser intensity and associated trends.
We theoretically study frustrated double ionization (FDI) of atoms subjected to intense circularly polarized laser pulses using a three-dimensional classical model. We find a novel "knee" structure of FDI probability as a function of intensity, which is similar to the intensity dependence of nonsequential double ionization probability. The observation of FDI is more favourable when using targets with low ionization potentials and short driving laser wavelengths. This is attributed to the crucial role of recollision therein, which can be experimentally inferred from the photoelectron momentum d…
Longitudinal momentum spectra and electron drift directions are considered for several laser wavelengths in Non-Sequential Double Ionization of helium using three dimensional classical ensembles. In this model, the familiar doublet for wavelength 800 nm and intensities of order 0.5 PW/cm^2, becomes a triplet for wavelength 1314 nm, then a doublet with plateau for 2017 nm. The results are explained based on whether the post-ionization impulse from the laser results in backward drift for one or both electrons.
Double ionization of an atom by single-photon absorption in the presence of a neighbouring atom is studied. The latter is, first, resonantly photoexcited and, afterwards, transfers the excitation energy radiationlessly to the other atom, leading to its double ionization. The process relies on the combined effect of interatomic and intraatomic electron correlations. It can dominate over the direct double photoionization by several orders of magnitude at interatomic distances up to few nanometers. The relative position of the neighbouring atom is shown to exert a characteristic influence on the …
In anticipation of upcoming two-photon double ionization of atoms and particularly Helium, under strong short wavelength radiation sources (45 eV), we present quantitative signatures of direct two-photon double ejection, in the photoelectron spectrum (PES) and the peak power dependence, that can be employed in the interpretation of related data. We show that the PES provides the cleanest signature of the process. An inflection (knee) in the laser power dependence of double ionization is also discernible, within a window of intensities which depends on the pulse duration and cross sections
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 …
Using a three-dimensional quasiclassical technique we explore molecular double ionization by a linearly polarized, infrared (800~nm) 27~fs laser pulse. For intensities ranging from the tunneling to the over-the-barrier regime, we identify the double ionization pathways in a unified way as a function of total electron energy. For the tunneling regime, we discuss the differences in the interplay of double ionization (DI) pathways between strongly driven He and strongly driven $N_{2}$. For intermediate intensities in the over-the-barrier regime, we find that both the correlated momenta and the do…
We show through simulation that quantum interference in non-sequential double ionization can be used to control the recollision with subsequent ionization (RESI) mechanism. This includes the shape, localization and symmetry of RESI electron-momentum distributions, which may be shifted from a correlated to an anti-correlated distribution or vice versa, far below the direct ionization threshold intensity. As a testing ground, we reproduce recent experimental results by employing specific coherent superpositions of excitation channels. We examine two types of interference, from electron indisting…
The calculated double differential cross sections for 60eV energy, where the cross sections are also maximum, agree with the measured results of Shyn (1992) in a much better way compaired to other theories for such energies.
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 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 discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines that point towards the two-particle Stark saddle in the presence of a field. The resulting effective two dimensional model is similar to the aligned electron model, but it enables correlated escape of electrons with equal momenta, as observed experimentally. The time-dependent solution of the Schrödinger equation allows us to discuss in detail the time dynam…
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 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…
Double ionization processes triggered by intense linearly polarized laser fields have revealed the paramount role of electron-electron collisions. It has been shown that the correlated dynamics of such electronic collisions can be modeled by a two dimensional symplectic map which captures the bare essentials of the energy exchange processes occurring during a recollision between the two electrons. We investigate linear and nonlinear properties of this map and connect them to the dynamical organization of phase space and related statistical data
We report on a kinematically complete measurement of double ionization of helium by a single 1100 eV circularly polarized photon. By exploiting dipole selection rules in the two-electron continuum state, we observed the angular emission pattern of electrons originating from a pure quadrupole transition. Our fully differential experimental data and companion ab initio nonperturbative theory show the separation of dipole and quadrupole contributions to photo-double-ionization and provide new insight into the nature of the quasifree mechanism.
Using a three-dimensional semiclassical method, we theoretically investigate frustrated double ionization (FDI) of Ar atoms subjected to strong laser fields. The double-hump photoelectron momentum distribution generated from FDI observed in a recent experiment [S. Larimian et al., Phys. Rev. Research 2, 013021 (2020)] is reproduced by our simulation. We confirm that the observed spectrum is due to recollision. The laser intensity dependence of FDI is investigated. We reveal that the doubly excited states of Ar atoms and excited states of Ar+ are the dominant pathways for producing FDI at relat…
We investigate the dynamics of electron-electron recollisions in the double ionization of atoms in strong laser fields. The statistics of recollisions can be reformulated in terms of an area-preserving map from the observation that the outer electron is driven by the laser field to kick the remaining core electrons periodically. The phase portraits of this map reveals the dynamics of these recollisions in terms of their probability and efficiency.
Electron-electron correlation effects play an instrumental role in our understanding of sequential (SDI) and non-sequential double ionization (NSDI) mechanisms. Here, we present a theoretical study of NSDI driven by plasmonic-enhanced spatial inhomogeneous fields. By numerically solving the time-dependent Schrödinger equation for a linear reduced model of He and a double-electron time-evolution probability analysis, we provide evidence for the enhancement effects in NSDI showing that the double ionization yield at lower laser peak intensities is increased due to the inhomogeneity of the laser …
Using a semi-classical model, we investigate frustrated double ionization (FDI) in $\mathrm{D_3^+}$, a two-electron triatomic molecule, when driven by an intense, linearly polarized, near-infrared (800 nm) laser field. We compute the kinetic energy release of the nuclei and find a good agreement between experiment and our model. We explore the two pathways of FDI and show that, with increasing field strength, over-the-barrier ionization overtakes tunnel ionization as the underlying mechanism of FDI. Moreover, we compute the angular distribution of the ion fragments for FDI and identify a featu…
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 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 …
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 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 …
The influence of electron-electron Coulomb repulsion on nonsequential double ionization of rare-gas atoms is investigated. Several variants of the quantum-mechanical transition amplitude are evaluated that differ by the form of the inelastic electron-ion rescattering and whether or not Coulomb repulsion between the two electrons in the final state is included. For high laser intensity, an entirely classical model is formulated that simulates the rescattering scenario.
