We present accurate time-dependent ab initio calculations on fully differential and total integrated (generalized) cross sections for the nonsequential two-photon double ionization of helium at photon energies from 40 to 54 eV. Our computational method is based on the solution of the time-dependent Schroedinger equation and subsequent projection of the wave function onto Coulomb waves. We compare our results with other recent calculations and discuss the emerging similarities and differences. We investigate the role of electronic correlation in the representation of the two-electron continuum states, which are used to extract the ionization yields from the fully correlated final wave function. In addition, we study the influence of the pulse length and shape on the cross sections in time-dependent calculations and address convergence issues.
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.
The role of nucleus in strong-field nonsequential double ionization of Ar atoms is investigated using three-dimensional classical ensembles. By adjusting the nuclear Coulomb potential, we can excellently reproduce the experimental correlated electron and ion momentum spectra with laser intensities above the recollision threshold [Phys. Rev. Lett. 93, 263001 (2004)] and below the recollision threshold [Phys. Rev. Lett. 101, 053001 (2008)] quantitatively. Analysis reveals the detailed electronic dynamics when the nuclear Coulomb attraction plays a key role in the recollision process of nonsequen…
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.
Nonsequential two-photon ionization of inner-shell $np$ subshell of neutral atoms by circularly polarized light is investigated. Detection of subsequent fluorescence as a signature of the process is proposed and the dependence of fluorescence degree of polarization on incident photon beam energy is studied. It is generally expected that the degree of polarization remains approximately constant, except when the beam energy is tuned to an intermediate $n's$ resonance. However, strong unexpected change in the polarization degree is discovered for nonsequential two-photon ionization at specific in…
We develop an approximate model for the process of direct (nonsequential) two-photon double ionization of atoms. Employing the model, we calculate (generalized) total cross sections as well as energy-resolved differential cross sections of helium for photon energies ranging from 39 to 54 eV. A comparison with results of \textit{ab initio} calculations reveals that the agreement is at a quantitative level. We thus demonstrate that this complex ionization process is fully described by the simple model, providing insight into the underlying physical mechanism. Finally, we use the model to calcula…
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…
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…
We have investigated the energy correlation of the two electrons from nonsequential double ionization of helium atom in 800 nm laser fields at intensities below the recollision threshold by quantum calculations. The circular arcs structure of the correlated electron momentum spectra reveals a resonant double ionization process in which the two electrons transit from doubly excited states into continuum states by simultaneously absorbing and sharing excess energy in integer units of the photon energy. Coulomb repulsion between the two electrons in continuum states is responsible for the dominan…
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…
With quantum calculations, we have investigated the multiphoton nonsequential double ionization of helium atoms in intense laser fields at ultraviolet wavelengths. Very surprisingly, we find a so-far unobserved double-circle structure in the correlated electron momentum spectra. The double-circle structure essentially reveals multiphoton Rabi oscillations of two electrons, which are strongly supported by the oscillating population of a certain doubly excited state and by the oscillating double ionization signals. This two-electron multiphoton Rabi effect provides profound understandings of ele…
Nonsequential double ionization (NSDI) of helium in an intense few-cycle laser pulse is investigated by applying the three-dimensional semi-classical re-scattering method. It is found that the momentum distribution of He$^{2+}$ shows a single-double-single peak structure as the pulse intensity increases. According to the different mechanisms dominating the NSDI process, the laser intensity can be classified into three regimes where the momentum distribution of He$^{2+}$ exhibits different characteristics. In the relatively high intensity regime, an NSDI mechanism named the "laser-assisted coll…
We perform a systematic analysis of quantum interference in nonsequential double ionization focusing on the recollision-excitation with subsequent ionization (RESI) mechanism, employing the strong-field approximation (SFA). We find that interference has a major influence on the shape, localization and symmetry of the correlated electron momentum distributions. In particular, the fourfold symmetry with regard to the parallel momentum components observed in previous SFA studies is broken. Two types of interference are observed and thoroughly analyzed, namely that caused by electron indistinguish…
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 analyze two-photon double ionization of helium in both the nonsequential and sequential regime. We show that the energy spacing between the two emitted electrons provides the key parameter that controls both the energy and the angular distribution and reveals the universal features present in both the nonsequential and sequential regime. This universality, i.e., independence of photon energy, is a manifestation of the continuity across the threshold for sequential double ionization. For all photon energies, the energy distribution can be described by a universal shape function that contains…
We investigate laser induced nonsequential multiple ionization using a simple statistical model in which an electron recollides inelastically with its parent ion. In this collision, it thermalizes with the remaining $N-1$ bound electrons within a time interval $Δt$. Subsequently, all the $N$ electrons leave. We address the question of how the above time delays influence the individual contributions from the orbits in which the first electron, upon return, is accelerated or decelerated by the field, respectively, to the ion momentum distributions. In both cases, the time delays modify the drift…
Recently introduced time-dependent renormalized natural orbital theory (TDRNOT) is tested on non-sequential double ionization (NSDI) of a numerically exactly solvable one-dimensional model He atom subject to few-cycle, 800-nm laser pulses. NSDI of atoms in strong laser fields is a prime example of non-perturbative, highly correlated electron dynamics. As such, NSDI is an important "worst-case" benchmark for any time-dependent few and many-body technique beyond linear response. It is found that TDRNOT reproduces the celebrated NSDI "knee," i.e., a many-order-of-magnitude enhancement of the doub…
We address the influence of the orbital symmetry and of the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules, in the length and velocity gauges. We work within the strong-field approximation and assume that the second electron is dislodged by electron-impact ionization, and also consider the classical limit of this model. We show that the electron-momentum distributions exhibit interference maxima and minima due to the electron emission at spatially separated centers. The interference patterns survive the in…
Consensus has been reached that recollision, as the most important post-tunneling process, is responsible for nonsequential double ionization process in intense infrared laser field, however, its effect has been restricted to interaction between the first ionized electron and the residual univalent ion so far. Here we identify the key role of recollision between the second ionized electron and the divalent ion in the below-threshold nonsequential double ionization process by introducing a Coulomb-corrected quantum-trajectories method, which enables us to well reproduce the experimentally obser…
The collision-ionization mechanism of nonsequential double ionization (NSDI) process in IR+XUV two-color laser fields [\PRA \textbf{93}, 043417 (2016)] has been investigated by us recently. Here we extend this work to study the collision-excitation-ionization (CEI) mechanism of NSDI processes in the two-color laser fields with different laser conditions. It is found that the CEI mechanism makes a dominant contribution to the NSDI as the XUV photon energy is smaller than the ionization threshold of the He$^+$ ion, and the momentum spectrum shows complex interference patterns and symmetrical str…
We investigate the physical processes in which an electron, upon return to its parent ion, promotes a second electron to an excited state, from which it subsequently tunnels. Employing the strong-field approximation and saddle-point methods, we perform a detailed analysis of the dynamics of the two electrons, in terms of quantum orbits, and delimit constraints for their momentum components parallel to the laser-field polarization. The kinetic energy of the first electron, upon return, exhibits a cutoff slightly lower than $10U_p$, where $U_p$ is the ponderomotive energy, as in rescattered abov…
We perform a detailed analysis of the importance of causality within the strong-field approximation and the steepest descent framework for the recollision-excitation with subsequent tunneling ionization (RESI) pathway in laser-induced nonsequential double ionization (NSDI). In this time-delayed pathway, an electron returns to its parent ion, and, by recolliding with the core, gives part of its kinetic energy to excite a second electron at a time $t^{\prime}$. The second electron then reaches the continuum at a later time $t$ by tunneling ionization. We show that, if $t^{\prime}$ and $t$ are co…
We perform theoretical investigations of laser-induced nonsequential double ionization with few cycle pulses, with particular emphasis on the dependence of the electron-momentum distributions on the carrier-envelope phase. We focus on the recollision-excitation with subsequent tunneling ionization (RESI) pathway, in which a released electron, upon return to its parent ion, gives part of its kinetic energy to promote a second electron to an excited state. At a subsequent time, the second electron is freed through tunneling ionization. We show that the RESI electron-momentum distributions vary d…
We perform a detailed analysis of the recollision-excitation-tunneling (RESI) mechanism in laser-induced nonsequential double ionization (NSDI), in which the first electron, upon return, promotes a second electron to an excited state, from which it subsequently tunnels, based on the strong-field approximation. We show that the shapes of the electron momentum distributions carry information about the bound-state with which the first electron collides, the bound state to which the second electron is excited, and the type of electron-electron interaction. Furthermore, one may define a driving-fie…
We investigate laser-induced nonsequential double ionization by a polarization-gated laser pulse, constructed employing two counter-rotating circularly polarized few cycle pulses with a time delay $T_{d}$. We address the problem within a classical framework, and mimic the behavior of the quantum-mechanical electronic wave packet by means of an ensemble of classical electron trajectories. These trajectories are initially weighted with the quasi-static tunneling rate, and with suitably chosen distributions for the momentum components parallel and perpendicular to the laser-field polarization, in…
We address nonsequential double ionization induced by strong, linearly polarized laser fields of only a few cycles, considering a physical mechanism in which the second electron is dislodged by the inelastic collision of the first electron with its parent ion. The problem is treated classically, using an ensemble model, and quantum-mechanically, within the strong-field and uniform saddle-point approximations. In the latter case, the results are interpreted in terms of "quantum orbits", which can be related to the trajectories of a classical electron in an electric field. We obtain highly asymm…
We perform a systematic analysis of how nonsequential double ionization in intense, linearly polarized laser fields is influenced by the initial states in which both electrons are bound, and by the residual ionic potential. We assume that the second electron is released by electron-impact ionization of the first electron with its parent ion, using an S-Matrix approach. We work within the Strong-Field Approximation, and compute differential electron momentum distributions using saddle-point methods. Specifically, we consider electrons in $1s$, $2p$, $3p$ and localized states, which are released…
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.
For the description of nonsequential double ionization (NSDI) of rare-gas atoms by a strong linearly polarized laser field, the quantum-mechanical $S$-matrix diagram that incorporates rescattering impact ionization is evaluated in the strong-field approximation. We employ a uniform approximation, which is a generalization of the standard saddle-point approximation. We systematically analyze the manifestations of the electron-electron interaction in the momentum distributions of the ejected electrons: for the interaction, by which the returning electron frees the bound electron, we adopt either…
We address the influence of the molecular orbital geometry and of the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules for different molecular species, namely $\mathrm{N}_2$ and $\mathrm{Li}_2$. We focus on the recollision excitation with subsequent tunneling ionization (RESI) mechanism, in which the first electron, upon return, promotes the second electron to an excited state, from where it subsequently tunnels. We show that the electron-momentum distributions exhibit interference maxima and minima due to t…
In a fully classical simulation, we investigate the recollision mechanism of non-sequential double ionization (NSDI) and its manifestation in the end-of-pulse electron momentum distributions. We compare two different electron-electron potentials: a soft-core Coulombic potential and a Yukawa potential. We also implement the strong-field approximation (SFA), which is commonly made in quantum-mechanical $S$-matrix calculations, in our classical simulations and study its consequences. We find that, regardless of the form of the e-e potential, the SFA modifies the momentum distributions and recolli…
We investigate laser-induced nonsequential double ionization from aligned diatomic molecules, using the strong-field approximation in its length and velocity gauge formulations. Throughout, we consider that the first electron dislodges the second by electron-impact ionization. Employing modified saddle-point equations, we single out the contributions of different scattering scenarios to the maxima and minima observed in the differential electron momentum distributions. We show that the quantum interference between the electron orbits starting and ending at a specific center $C_{j}$%, and those…
A second plateau in the harmonic spectra of laser-driven two-electron atoms is observed both in the numerical solution of a low-dimensional model helium atom and using an extended strong field approximation. It is shown that the harmonics well beyond the usual cut-off are due to the simultaneous recombination of the two electrons, which were emitted during different, previous half-cycles. The new cut-off is explained in terms of classical trajectories. Classical predictions and the time-frequency analysis of the ab initio quantum results are in excellent agreement. The mechanism corresponds to…
The helium ground state nonrelativistic energy with 24 significant digits is presented. The calculations are based on variational expansion with randomly chosen exponents. This data can be used as a benchmark for other approaches for many electron and/or three-body systems.
Few-photon induced breakup of helium is studied using a newly developed ab initio numerical framework for solving the six-dimensional time-dependent Schroedinger equation. We present details of the method and calculate (generalized) cross sections for the process of two-photon nonsequential (direct) double ionization at photon energies ranging from 39.4 to 54.4 eV, a process that has been very much debated in recent years and is not yet fully understood. In particular, we have studied the convergence property of the total cross section in the vicinity of the upper threshold (54.4 eV), versus t…
The ionization of a one-dimensional model Helium atom in short laser pulses using time-dependent density functional theory is investigated. We calculate ionization probabilities as a function of laser intensity by approximating the correlation function of the system adiabatically with an explicit dependence on the fractional number of bound electrons. For the correlation potential we take the derivative discontinuity at integer numbers of bound electrons explicitly into account. This approach reproduces ionization probabilities from the solution of the time-dependent Schroedinger equation, in …
With the classical three-dimensional ensemble model, we have investigated the microscopic recollision dynamics in nonsequential double ionization of helium by 800 nm laser pulses at 2.0 PW/cm^2. We demonstrate that the asymmetric energy sharing between the two electrons at recollision plays a decisive role in forming the experimentally observed V-shaped structure in the correlated longitudinal electron momentum spectrum at the high laser intensity [Phys. Rev. Lett. 99, 263003 (2007)]. This asymmetric energy sharing recollision leaves footprints on the transverse electron momentum spectra, whic…
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 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…
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…
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.
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 …
We explore the influence of elliptical polarization on the (non)sequential two-photon double ionization of atomic helium with ultrashort extreme ultraviolet (XUV) light fields using time-dependent full ab-initio simulations. The energy and angular distributions of photoelectrons are found to be strongly dependent on the ellipticity. The correlation minimum in the joint angular distribution becomes more prominently visible with increasing ellipticity. In a pump-probe sequence of two subsequent XUV pulses with varying ellipticities, polarization tagging allows to discriminate between sequential …
The process of nonsequential two-photon double ionization of helium is studied by two complementary numerical approaches. First, the time-dependent Schr{ö}dinger equation is solved and the final wave function is analyzed in terms of projection onto eigenstates of the uncorrelated Hamiltonian, i.e., with no electron-electron interaction included in the final states. Then, the double ionization probability is found by means of a recently developed approach in which the concept of absorbing boundaries has been generalized to apply to systems consisting of more than one particle. This generalizati…
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…
The multiconfigurational time-dependent Hartree-Fock method (MCTDHF) is applied for simulations of the two-photon ionization of Helium. We present results for the single- and double ionization from the groundstate for photon energies in the non-sequential regime, and compare them to direct solutions of the Schrödinger equation using the time-dependent (full) Configuration Interaction method (TDCI). We find that the single-ionization is accurately reproduced by MCTDHF, whereas the double ionization results correctly capture the main trends of TDCI.
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.
Ground state ionization potential of the He^4 atom is evaluated to be 5 945 204 221 (42) MHz. Along with lower order contributions, this result includes all effects of the relative orders alpha^4, alpha^3*m_e/m_alpha and alpha^5*ln^2(alpha).
The structure of approximate two electron wavefunction is deeply investigated, both theoretically and numerically, in the strong-field driven ionization dynamics. Theoretical analyses clarify that for two electron singlet systems, the previously proposed time-dependent extended Hartree-Fock (TD-EHF) method [Phys. Rev. A 51, 3999 (1995)] is equivalent to the multiconfiguration time-dependent Hartree-Fock method with two occupied orbitals. The latter wavefunction is further transformed into the natural expansion form, enabling the direct propagation of the natural orbitals (NOs). These methods, …
Ionization of helium-like ions with simultaneous excitation of the ns-states due to photon scattering is considered. The differential and total cross sections of the process are calculated to leading order of perturbation theory with respect to the interelectron interaction. The formulas obtained are applicable in the nonrelativistic energy range far beyond the ionization threshold.
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.
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.
Attosecond pump-probe ionization process can be used to prepare atomic ions in the coherent superposition of states with opposite parity. The multiphoton shake-up ionization of Helium, in particular, generates ions with same principal quantum number and a net dipole moment that evolves on a time scale of few picoseconds, due to spin-orbit coupling. In this work we use an ab initio time-dependent close-coupling code to study how the coherence between levels of Helium ion can be controlled from the parameters of the ionizing-pulse sequence. The observed periodic revivals, on a picosecond time sc…
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…
