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 harmonics and nuclear reactions with single atoms feasible.
During the ionization of atoms irradiated by linearly polarized intense laser fields, we find for the first time that the transverse momentum distribution of photoelectrons can be well fitted by a squared zeroth-order Bessel function because of the quantum interference effect of Glory rescattering. The characteristic of the Bessel function is determined by the common angular momentum of a bunch of semiclassical paths termed as Glory trajectories, which are launched with different nonzero initial transverse momenta distributed on a specific circle in the momentum plane and finally deflected to …
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.
Strong field ionization provides a unique mean to address complex dynamics of an electron in competing Coulomb and laser fields. Recent streak camera experiment (Kübel, et al., Phys. Rev. Lett. 119, 183201) analyzed asymmetries in the low-energy region of ejected electron momenta distribution and associated them with multiple rescattering of the electron on the parent ion. In this work we directly confirm the multiple rescattering nature of the asymmetry in the low-energy region. Such electron-ion collisions cannot be described within one-dimensional simulations even taking into account focal-…
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…
The nonperturbative role of multiple forward scattering for Coulomb focusing in mid-infrared laser fields and its dependence on a laser intensity and wavelength are investigated for low-energy photoelectrons at above-threshold ionization. We show that high-order rescattering events can have comparable contributions to the Coulomb focusing and the effective number of rescattering depends weakly on laser parameters in the classical regime. However, the relative contribution of the forward scattering to the Coulomb focusing and the Coulomb focusing in total decrease with the rise of the laser int…
Vortex photoelectron holography in strong-field tunneling ionization
School of Physics and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology（华中科技大学物理科学与技术学院与武汉光电国家研究中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Advanced Science, The University of Electro-Communications（电波大学高级科学研究所）；Hubei Fundamental Research Center for Physics（湖北物理基础研究中心）
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.
Few-cycle pulses of intense 800 nm light are used to probe ionization and dissociation of carbon disulfide in the intensity and temporal regime where rescattering is expected to dominate the laser-molecule interaction. The wavepacket of the rescattered electron destructively interferes with the anti-bonding $π$-orbital of CS$_2^+$ such that rescattering is effectively "switched off". Direct signature of enhanced ionization being "switched off" in the ultrashort domain is also obtained. Consequently, dissociation becomes an almost non-existent channel when few-cycle pulses are used, with only l…
We investigate the ionization dynamics of atoms irradiated by an intense laser field using a semiclassical model that includes magnetic Lorentz force in the rescattering process. We find that, the electrons tunneled with different initial transverse momenta (i.e., perpendicular to the instantaneous electric field direction) distributed on a specific circle in the momentum plane can finally converge to the same transverse momentum after experiencing Coulomb forward scattering. These electron trajectories lead to a bright spot structure in the 2D transverse momentum distribution, and particularl…
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 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…
In this paper, we have investigated the correlated electron emission of the nonsequence double ionization (NSDI) in an intense linearly polarized field. The theoretical model we employed is the semiclassical rescattering model, the model atom we used is the helium. We find a significant correlation between magnitude and direction of the momentum of two emission electrons, and give a good explanation for this striking phenomenon by observing the classical collisional trajectories. We argue that this correlation phenomenon is universal in NSDI process, as revealed by the recent experiment on the…
We report on the observation of discrete structures in the electron energy distribution for strong field double ionization of Argon at 394 nm. The experimental conditions were chosen in order to ensure a non-sequential ejection of both electrons with an intermediate rescattering step. We have found discrete ATI (above-threshold ionization) like peaks in the sum energy of both electrons, as predicted by all quantum mechanical calculations. More surprisingly however is the observation of two ATI combs in the energy distribution of the individual electrons.
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.
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 …
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…
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 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…
We describe first-principles in-plane calculations of non-sequential triple ionization (NSTI) of atoms in a linearly polarized intense laser pulse. In a fully classically correlated description, all three electrons respond dynamically to the nuclear attraction, the pairwise e-e repulsions and the laser force throughout the duration of a 780nm laser pulse. Nonsequential ejection is shown to occur in a multi-electron, possibly multi-cycle and multi-dimensional, rescattering sequence that is coordinated by a number of sharp transverse recollimation impacts.
We have probed the fragmentation dynamics in a bent triatomic molecule, water, a non-planar molecule, methanol, and a planar ring-structured molecule, benzene, using 100 fs duration pulses of linearly and circularly polarized, infrared, intensity-selected laser light. At laser intensities larger than 10$^{15}$ W cm$^{-2}$, the yield of singly and multiply charged atomic fragments from these molecules is suppressed when the light is circularly polarized. At lower intensities, the fragment ion yield is not significantly polarization dependent. This hitherto-unobserved intensity dependent effect …
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…
We study ab initio computations of the interaction of Lithium with a strong laser field. Numerical solutions of the time-dependent fully-correlated three-particle Schroedinger equation restricted to the one-dimensional soft-core approximation are presented. Our results show a clear transition from non-sequential to sequential double ionization for increasing intensities. Non sequential double ionization is found to be sensitive to the spin configuration of the ionized pair. This asymmetry, also found in experiments of photoionization of Li with synchrotron radiation, shows the evidence of the …
The full three-dimensional photoelectron momentum distributions of argon are measured in intense near-circularly polarized laser fields. We observed that the transverse momentum distribution of ejected electrons by 410-nm near-circularly polarized field is unexpectedly narrowed with increasing laser intensity, which is contrary to the conventional rules predicted by adiabatic theory. By analyzing the momentum-resolved angular momentum distribution measured experimentally and the corresponding trajectories of ejected electrons semiclassically, the narrowing can be attributed to a temporary trap…
It is well-known from numerical and experimental results that the fraction of Rydberg states (excited neutral atoms) created by tunnel ionization declines dramatically with increasing ellipticity of laser light. We present a method to analyze this dependence on ellipticity, deriving a probability distribution of Rydberg states that agrees closely with recent experimental [1] and numerical results. In particular, contradicting the existing proposed mechanism [1] and general expectations, our results indicate that the dependence of Rydberg yield on laser ellipticity is not caused by a rescatteri…
We study double ionization (DI) dynamics of vibrating HeH$^+$ versus its isotopic variant HeT$^+$ in strong laser fields numerically. Our simulations show that for both cases, these two electrons in DI prefer to release together along the H(T) side. At the same time, however, the single ionization (SI) is preferred when the first electron escapes along the He side. This potential mechanism is attributed to the interplay of the rescattering of the first electron and the Coulomb induced large ionization time lag. On the other hand, the nuclear motion increases the contributions of these two elec…
We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the classical cutoff is found to be vastly different from that below the cutoff. A V-shape structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analy…
We analyzed the two-dimensional (2D) electron momentum distributions of high-energy photoelectrons of atoms in an intense laser field using the second-order strong field approximation (SFA2). The SFA2 accounts for the rescattering of the returning electron with the target ion to first order and its validity is established by comparing with results obtained by solving the time-dependent Schrödinger equation (TDSE) for short pulses. By analyzing the SFA2 theory, we confirmed that the yield along the back rescattered ridge (BRR) in the 2D momentum spectra can be interpreted as due to the elastic …
A general method for solving numerically the time-dependent Schrödinger equation, that is based on the Suzuki-Trotter scheme with the split-step Fourier approach, is introduced. The method relies on a Hamiltonian decomposition, where except of the components depending exclusively on the momentum or on the position operators, there are also terms depending on both momentum and position operators in particular configurations. We demonstrate that, for as long as the latter does not depend on noncommuting coordinates of the momentum and position operators, nondipole effects in laser-matter interac…
We report on tunnel ionization of Xe by 2-cycle, intense, infrared laser pulses and its dependence on carrier-envelope-phase (CEP). At low values of optical field ($E$), the ionization yield is maximum for cos-like pulses with the dependence becoming stronger for higher charge states. At higher $E$-values, the CEP dependence either washes out or flips. A simple phenomenological model is developed that predicts and confirms the observed results. CEP effects are seen to persist for 8-cycle pulses. Unexpectedly, electron rescattering plays an unimportant role in the observed CEP dependence. Our r…
We show that electrons recolliding with the ionic core upon tunnel ionization of noble gas atoms driven by a strong circularly polarized laser field in combination with a counter-rotating second harmonic are spin polarized and that their degree of polarization depends strongly on the recollision time. Spin polarization arises as a consequence of (1) entanglement between the recolliding electron and the ion, and (2) sensitivity of ionization to the sense of electron rotation in the initial state. We demonstrate that one can engineer the degree of spin polarization as a function of time by tunin…
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…
We study the influence of the pulse duration on high harmonic generation (HHG) with exploring a wide laser-parameter region theoretically. Previous studies have showed that for high laser intensities near to the saturation ionization intensity, the HHG inversion efficiency is higher for shorter pulses since the ground-state depletion is weaker in the latter. Surprisingly, our simulations show this high efficiency also appears even for a moderate laser intensity at which the ionization is not strong. A classical effect relating to shorter travel distances of the rescattering electron in shorter…
We present a joint experimental and theoretical study of non-sequential double ionization (NSDI) in argon driven by a 3100-nm laser source. The correlated photoelectron momentum distribution (PMD) shows a strong dependence on the pulse duration, and the evolution of the PMD can be explained by an envelope-induced intensity effect. Determined by the time difference between tunneling and rescattering, the laser vector potential at the ionization time of the bound electron will be influenced by the pulse duration, leading to different drift momenta. Such a mechanism is extracted through a classic…
We analyze how bound-state excitation, electron exchange and the residual binding potential influence above-threshold ionization (ATI) in Helium prepared in an excited $p$ state, oriented parallel and perpendicular to a linearly polarized mid-IR field. Using ab initio B-spline Algebraic Diagrammatic Construction (ADC), and several one-electron methods with effective potentials, including the Schrödinger solver Qprop, modified versions of the Strong-Field Approximation and the Coulomb-Quantum Orbit Strong-Field Approximation (CQSFA), we find that these specific physical mechanisms leave signifi…
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 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 present an ab initio analytic theory to account for both the very low energy structure (VLES) [C. Y. Wu et al., Phys. Rev. Lett. 109, 043001 (2012); W. Quan et al., Phys. Rev. Lett. 103, 093001 (2009)], and the low energy structure (LES) [W. Quan et al. Phys. Rev. Lett. 103, 093001 (2009); C.I. Blaga et al., Nat. Phys. 5, 335 2009)] of above threshold ionization. The origin of both VLES and LES lies in a forward scattering mechanism by the Coulomb potential. We parameterize the S matrix in terms of ?, which is the displacement of the the classical motion of an electron in the laser field. W…
We analyzed the energy and momentum distributions of laser-induced high-energy photoelectrons of alkali and rare gas atoms. For the plateau electrons with energies above $4U_p$, ($U_p$ is the ponderomotive energy), in the tunneling ionization regime, we showed that they originate from the backscattering of laser-induced returning electrons. Using the differential elastic scattering cross sections between the target ion with \emph{free} electrons, we explain experimental observations of whether the plateau electron spectra is flat or steeply descending, and their dependence on species and laser…
We propose a new type of gauge-invariant expansion of the ionization probability amplitudes of atoms by short pulses of electromagnetic radiation. Contrary to previous gauge-invariant approaches to this problem it does not require different partitions of the total Hamiltonian depending on the choice of gauge. In a natural way the atomic potential is treated as perturbation acting on an electron interacting with strong pulse. Whereas this is a standard assumption of strong field approximation (SFA), we show that grouping consequently together \textit{all} terms of the same order in the atomic p…
The requirement of high space-time resolution and brightness is a great challenge for imaging atomic motion and making molecular movies. Important breakthroughs in ultrabright tabletop laser, x-ray and electron sources have enabled the direct imaging of evolving molecular structures in chemical processes. And recent experimental advances in preparing ultrafast laser and electron pulses equipped molecular imaging with femtosecond time resolution. This Perspectives present an overview of versatile imaging methods of molecular dynamics. High-order harmonic generation imaging and photoelectron dif…
A theoretical study of the interference pattern imprinted on the doubly differential momentum distribution of the photoelectron due to atomic ionization induced by a short laser pulse is developed from a semiclassical standpoint. We use the semiclassical two-step model of Shvetsov-Shilovski et al. (Phys. Rev. A 94, 013415) to elucidate the nature of the holographic structure. Three different types of trajectories are characterized during the ionization process by a single cycle pulse with three different types of interferences. We show that the holographic interference arises from the ionizati…
We study the generation of terahertz radiation from atoms and molecules driven by an ultrashort fundamental laser and its second harmonic field by solving time-dependent Schrödinger equation (TDSE). The comparisons between one-, two-, and three- dimensional TDSE numerical simulations show that initial ionized wave-packet and its subsequent acceleration in the laser field and rescattering with long-range Coulomb potential play key roles. We also present the dependence of the optimum phase delay and yield of terahertz radiation on the laser intensity, wavelength, duration, and the ratio of two-c…
RMT is a program which solves the time-dependent Schrodinger equation for general, multielectron atoms, ions and molecules interacting with laser light. As such it can be used to model ionization (single-photon, multi-photon and strong-field), recollision (high-harmonic generation, strong-field rescattering), and more generally absorption or scattering processes with a full account of the multielectron correlation effects in a time-dependent manner. Calculations can be performed for targets interacting with ultrashort, intense laser pulses of long-wavelength and arbitrary polarization. Calcula…
Carrier envelope phase (CEP) stabilized pulses of intense 800 nm light of 5 fs duration are used to probe the dissociation dynamics of dications of isotopically-substituted water, HOD. HOD$^{2+}$ dissociates into either H$^+$ + OD$^+$ or D$^+$ + OH$^+$. The branching ratio for these two channels is CEP-dependent; the OD$^+$/OH$^+$ ratio (relative to that measured with CEP-unstabilized pulses) varies from 150% to over 300% at different CEP values, opening prospects of isotope-dependent control over molecular bond breakage. The kinetic energy released as HOD$^{2+}$ Coulomb explodes is also CEP-d…
The coherent control of electron beams and ultrafast electron wave packets dynamics have attracted significant attention in electron microscopy as well as in atomic physics. In order to unify the conceptual pictures developed in both fields, we demonstrate the generation and manipulation of tailored electron orbital angular momentum (OAM) superposition states either by employing customized holographic diffraction masks in a transmission electron microscope or by atomic multiphoton ionization utilizing pulse-shaper generated carrier-envelope phase stable bichromatic ultrashort laser pulses. Bot…
