Tunneling ionization of an atom in ultrashort laser pulses is considered. When the driving laser pulse is switched-on and -off with a steep slope, the photoelectron momentum distribution (PMD) shows an edge-effect because of the photoelectron diffraction by the time-slit of the pulse. The trivial diffraction pattern of the edge effect consisting of fast oscillations in the PMD disguises in the deep nonadiabatic regime the physically more interesting features in the spectrum which originate from the photoelectron dynamics. We point out the precise conditions how to avoid this scenario experimentally and if unavoidable in theory we put forward an efficient method to remove the edge-effect in the PMD. This allows to highlight the nonadiabatic dynamical features of the PMD, which is indispensable for their further investigation in complex computationally demanding scenarios. The method is firstly demonstrated on a one-dimensional problem, and further applied in three-dimensions for the attoclock. The method is validated by a comparison of analytical results via the strong-field approximation with numerical solutions of the time-dependent Schrödinger equation.
Classically allowed transport is shown to compete with quantum tunneling during the ionization of atoms by ultrashort and intense laser pulses, despite Keldysh parameters smaller than unity. This is done by comparing exact probability densities with the ones obtained from purely classical propagation using the Truncated Wigner Approximation. Not only is classical transport capable of moving trajectories away from the core, but it can also furnish ionization probabilities of the same order as the quantum ones for intensities currently employed in experiments. Our results have implications rangi…
We theoretically analyze the quantum vortices - the zeros of electron wave function which are formed through atom ionization by ultrashort laser pulse. In 2D space we consider the case of above-threshold ionization of hydrogen atom and in 3D space the ionization of the atom in the zero-radius-potential approximation. With the help of obtained analytical results we make the assumption that localization of quantum vortices in 3D space can be predicted by analysis of 2D model.
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.
The processes of ionization and energy transfer in a quantum system composed of two distant H atoms with an initial internuclear separation of 100 atomic units (5.29 nm) have been studied by the numerical solution of the time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation. Thereby it has been assumed that only one of the two H atoms was excited by temporally and spatially shaped laser pulses at various laser carrier frequencies. The quantum dynamics of the extended H-H system, which was taken to be initially either in an unentangled or an entangled ground state, has b…
We study the photoionization and autoionization of Helium atom subject to ultrashort laser pulses by using a Feshbach formalism in the time domain. We solve the time-dependent Schrödinger equation in terms of a configuration interaction (CI) spectral method, in which the total wavefunction is expanded with configurations defined within bound-like ($\mathcal{Q}$) and scattering-like ($\mathcal{P}$) halfspaces. The method allowsone to provide accurate descriptions of both the atomic structure (energy positions and widths) and the photodynamics. We illustrate our approach by i) calculating the ti…
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）
Phase-shift differences and amplitude ratios of the outgoing $s$ and $d$ continuum wave packets generated by two-photon ionization of helium atoms are determined from the photoelectron angular distributions obtained using velocity map imaging. Helium atoms are ionized with ultrashort extreme-ultraviolet free-electron laser pulses with a photon energy of 20.3, 21.3, 23.0, and 24.3 eV, produced by the SPring-8 Compact SASE Source test accelerator. The measured values of the phase-shift differences are distinct from scattering phase-shift differences when the photon energy is tuned to an excited …
Ionization and excitation of water molecules in intense laser pulses is studied theoretically by solving the three-dimensional time-dependent electronic Schrödinger equation within the single-active-electron approximation. The possibility to image orbital densities by measurement of the orientation-dependent ionization of H2O in few-cycle, 800nm linear-polarized laser pulses is investigated. While the highest-occupied molecular orbital 1b1 is found to dominate the overall ionization behavior, contributions from the energetically lower lying 3a1 orbital dominate the ionization yield in the noda…
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…
The ionization of atomic hydrogen in intense laser fields is studied theoretically. The calculations were performed applying both quantummechanical and classical approaches. Treating the problem quantummechanically, the time dependent Schrödinger equation (TDSE) of our system was first transformed into a pseudo-momentum space and solved in this space iteratively. While neglecting the Coulomb potential during the solution of the TDSE we got the results in the Volkov approximation, in the first order solution we taken into account the Coulomb potential as perturbation. The classical calculations…
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 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…
A quasi-classical model (QCM) of molecular dynamics in intense femtosecond laser fields has been developed, and applied to a study of the effect of an ultrashort `control' pulse on the vibrational motion of a deuterium molecular ion in its ground electronic state. A nonadiabatic treatment accounts for the initial ionization-induced vibrational population caused by an ultrashort `pump' pulse. In the QCM, the nuclei move classically on the molecular potential as it is distorted by the laser-induced Stark shift and transition dipole. The nuclei then adjust to the modified potential, non-destructi…
We study theoretically the dipole radiation of a hydrogen atom driven by an intense sub-cycle pulse. The time-dependent Schrödinger equation for the system is solved by ab initio calculation to obtain the dipole response. Remarkably, a narrowband emission lasting longer than the driving pulse appears at a frequency just above the ionization threshold. An additional calculation using the strong field approximation also recovers this emission, which suggests that it corresponds to the oscillation of nearly-bound electrons that behave similarly to Rydberg electrons. The predicted phenomenon is un…
We investigate theoretically the dissociative ionization of a H2+ molecule using two ultrashort laser (pump-probe) pulses. The pump pulse prepares a dissociating nuclear wave packet on an ungerade surface of H2+. Next, an UV (or XUV) probe pulse ionizes this dissociating state at large (R = 20 - 100 bohr) internuclear distance. We calculate the momenta distributions of protons and photoelectrons which show a (two-slit-like) interference structure. A general, simple interference formula is obtained which depends on the electron and protons momenta, as well as on the pump-probe delay on the puls…
For ultrashort VUV pulses with a pulse length comparable to the orbital time of the bound electrons they couple to we propose a simplified envelope Hamiltonian. It is based on the Kramers-Henneberger representation in connection with a Floquet expansion of the strong-field dynamics but keeps the time dependence of the pulse envelope explicit. Thereby, the envelope Hamiltonian captures the essence of the physics, -- light-induced shifts of bound states, single-photon absorption, and non-adiabatic electronic transitions. It delivers quantitatively accurate ionization dynamics and allows for phys…
We present experimental results for the ionization of aniline and benzene molecules subjected to intense ultrashort laser pulses. Measured parent molecular ions yields were obtained using a recently developed technique capable of three-dimensional imaging of ion distributions within the focus of a laser beam. By selecting ions originating from the central region of the focus, where the spatial intensity distribution is nearly uniform, volumetric-free intensity-dependent ionization yields were obtained. The measured data revealed a previously unseen resonant-like multiphoton ionization process.…
Time-resolved investigations of ultrafast electronic and molecular dynamics were not possible until recently. The typical time scale of these processes is in the picosecond to attosecond realm. The tremendous technological progress in recent years made it possible to generate ultrashort pulses, which can be used to trigger, to watch, and to control atomic and molecular motion. This tutorial focuses on experimental and theoretical advances which are used to study the dynamics of electrons and molecules in the presence of ultrashort pulses. In the first part, the rotational dynamics of molecules…
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…
It is shown that it is feasible to use ultrashort time delay between two XUV femtosecond pulses in order to control two photon resonant ionization. The proposal is demonstrated on the spectrum of Helium, in terms of nonperturbative solutions of the time dependent Schroedinger equation. Comparison with results from second order time dependent perturbation theory provides additional insight.
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…
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.
We theoretically examine neon atoms in ultrashort and intense x rays from free electron lasers and compare our results with data from experiments conducted at the Linac Coherent Light Source (LCLS). For this purpose, we treat in detail the electronic structure in all possible nonrelativistic cationic configurations using a relativistic multiconfiguration approach. The interaction with the x rays is described in rate-equation approximation. To understand the mechanisms of the interaction, a path analysis is devised which allows us to investigate what sequences of photoionization and decay proce…
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 …
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…
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…
Effects of the laser pulse wavelength and intensity on the HHG production from the \textit{ionic} and \textit{homolytic} pre-ionization transient states of the two-electron H$_{2}$ system exposed to ultrashort intense laser pulses are studied by solving time-dependent Schrödinger equation. It is found that for the populated homolytic species in each half cycle of the laser pulse having enough strength, a pair of strong and weak HHG radiations are produced simultaneously. For the populated ionic species divided into two regions, in each half cycle, one of the ionic regions has a strong radiatio…
The alignment- and internuclear-distance dependent ionization of H$_2$ exposed to intense, ultrashort laser fields is studied by solving the time-dependent two-electron Schrödinger equation. In the regime of perturbative few-photon ionization, a strong dependence of the ionization yield on the internuclear distance is found. While this finding confirms a previously reported breakdown of the fixed-nuclei approximation for parallel alignment, a simpler explanation is provided and it is demonstrated that this breakdown is not due to vibrational dynamics during the laser pulse. The persistence of …
We investigate the ionization dynamics of Argon atoms irradiated by an ultrashort intense laser of a wavelength up to 3100 nm, addressing the momentum distribution of the photoelectrons with near-zero-energy. We find a surprising accumulation in the momentum distribution corresponding to meV energy and a \textquotedblleft V"-like structure at the slightly larger transverse momenta. Semiclassical simulations indicate the crucial role of the Coulomb attraction between the escaping electron and the remaining ion at extremely large distance. Tracing back classical trajectories, we find the tunneli…
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 electron correlation effects in internuclear-distance-dependent enhanced ionization of $\mathrm{H}_2$, $\mathrm{LiH}$, and $\mathrm{HF}$ molecules by intense near-infrared laser pulses using a 3D description of the systems with the time-dependent generalized-active-space configuration-interaction method. This method systematically incorporates electron-electron correlation of the quantum many-electron system under consideration. Our correlated description of diatomic molecules shows that enhanced ionization occurs at certain critical internuclear separations and electron correla…
High-order harmonic generation is investigated for H$_2^+$ and D$_2^+$ with and without Born-Oppenheimer approximation by numerical solution of full dimensional electronic time-dependent Schrödinger equation under 4-cycle intense laser pulses of 800 nm wavelength and $I$=4, 5, 7, 10 $\times 10^{14}$ W$/$cm$^2$ intensities. For most harmonic orders, the intensity obtained for D$_2^+$ is higher than that for H$_2^+$, and the yield difference increases as the harmonic order increases. Only at some low harmonic orders, H$_2^+$ generates more intense harmonics compared to D$_2^+$. The results show …
Interaction of a strong laser pulse with matter transfers not only energy but also linear momentum of the photons. Recent experimental advances have made it possible to detect the small amount of linear momentum delivered to the photoelectrons in strong-field ionization of atoms. We present numerical simulations as well as an analytical description of the subcycle phase (or time) resolved momentum transfer to an atom accessible by an attoclock protocol. We show that the light-field-induced momentum transfer is remarkably sensitive to properties of the ultrashort laser pulse such as its carrier…
We present numerical simulations of ultrafast multiphoton ionization dynamics in a two-dimensional atomic model driven by co- and counterrotating circularly polarized single-color and bichromatic carrier envelope phase (CEP) stable ultrashort laser pulse sequences. Taking into account phase variations due to CEP fluctuations and the Gouy phase, our results accurately reproduce recently measured photoelectron momentum distributions [Pengel et al., Phys. Rev. Lett. 118, 053003 (2017), Phys. Rev. A 96, 043426 (2017); Kerbstadt et al., Nat. Comm. 10, 685 (2019), Adv. Phys. X 4, 1672583 (2019)]. Th…
The generation of high-order harmonics in bulk solids subjected to intense ultrashort laser pulses has opened up new avenues for research in extreme nonlinear optics and light-matter interaction on sub-cycle timescales. Despite significant advancement over the past decade, a complete understanding of the involved phenomena is still lacking. High-harmonic generation in solids is currently understood as arising from nonlinear intraband currents, interband recollision and ionization-related phenomena. As all of these mechanisms involve or rely upon laser-driven excitation we combine measurements …
As a fundamental property of the electron, the spin plays a decisive role in the electronic structure of matter from solids to molecules and atoms, e.g. causing magnetism. Yet, despite its importance, the spin dynamics of electrons released during the interaction of atoms with strong ultrashort laser pulses has remained unexplored. Here we report on the experimental detection of electron spin polarization by strong-field ionization of Xenon atoms and support our results by theoretical analysis. We found up to 30% spin polarization changing its sign with electron energy. This work opens the new…
We demonstrate that ultrashort pulses carry the possibility for a new regime of light-matter interaction with nonadiabatic electron processes sensitive to the envelope-derivative of the light pulse. A standard single pulse with its two peaks in the derivative separated by the width of the pulse acts in this regime like a traditional double pulse. The two ensuing nonadiabatic ionization bursts have slightly different ionization amplitudes. This difference is due to redistribution of continuum electron energy during the bursts, negligible in standard photo-ionization. A time-dependent close- cou…
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 theoretically demonstrate a one-to-one mapping between the direction of electron ionization and the phase delay between a linearly polarized VUV and a circular IR laser pulse. To achieve this, we use an ultrashort VUV pulse that defines the moment in time and space when an above threshold electron is released in the IR pulse. The electron can then be accelerated to high velocities escaping in a direction completely determined by the phase delay between the two pulses. The dipole matrix element to transition from an initial bound state of the N$_2$ molecule, considered in this work, to the c…
We apply a fundamental definition of time delay, as the difference between the time a particle spends within a finite region of a potential and the time a free particle spends in the same region, to determine results for photoionization of an electron by an extreme ultraviolet (XUV) laser field using numerical simulations on a grid. Our numerical results are in good agreement with those of the Wigner-Smith time delay, obtained as the derivative of the phase shift of the scattering wave packet with respect to its energy, for the short-range Yukawa potential. In case of the Coulomb potential we …
We show how to emulate a conventional pump-probe scheme using a single frequency-chirped ultrashort UV pulse to obtain a time-resolved image of molecular ultrafast dynamics. The chirp introduces a spectral phase in time that encodes the delay between the pump and the probe frequencies contained in the pulse. By comparing the results of full dimensional ab initio calculations for the H$^+_2$ molecule with those of a simple sequential model, we demonstrate that, by tuning the chirp parameter, two-photon energy-differential ionization probabilities directly map the wave packet dynamics generated …
We report on precise measurements of absolute nonlinear ionization probabilities obtained by exposing optically trapped ultracold rubidium atoms to the field of an ultrashort laser pulse in the intensity range of $1 \times 10^{11}$ to $4 \times 10^{13}$ W/cm$^2$. The experimental data are in perfect agreement with ab-initio theory, based on solving the time-dependent Schrödinger equation without any free parameters. Ultracold targets allow to retrieve absolute probabilities since ionized atoms become apparent as a local vacancy imprinted into the target density, which is recorded simultaneousl…
Tunnel ionization of room-temperature D$_2$ in an ultrashort (12 femtosecond) near infra-red (800 nm) pump laser pulse excites a vibrational wavepacket in the D2+ ions; a rotational wavepacket is also excited in residual D2 molecules. Both wavepacket types are collapsed a variable time later by an ultrashort probe pulse. We isolate the vibrational wavepacket and quantify its evolution dynamics through theoretical comparison. Requirements for quantum computation (initial coherence and quantum state retrieval) are studied using this well-defined (small number of initial states at room temperatur…
We investigate the possible reasons for the discrepancy between the theoretical two-photon ionization cross section, $\sim 10^{-56}$ $\text{cm}^4 \text{s}$, of Ne$^{8+}$ obtained within the perturbative nonrelativistic framework for monochromatic light [J. Phys. B {\bf 34}, 4857 (2001)] and the experimental value, $7 \times 10^{-54}$ $\text{cm}^4 \text{s}$, reported in [Phys. Rev. Lett. {\bf 106}, 083002 (2011)] at a photon energy of 1110 eV. To this end, we consider Ne$^{8+}$ exposed to deterministic and chaotic ensembles of intense x-ray pulses. The time-dependent configuration-interaction s…
In the first part of this paper, the different distinguishable pathways and regions of the single and sequential double ionization are determined and discussed. It is shown that there are two distinguishable pathways for the single ionization and four distinct pathways for the sequential double ionization. It is also shown that there are two and three different regions of space which are related to the single and double ionization respectively. In the second part of the paper, the time dependent Schrödinger and Newton equations are solved simultaneously for the electrons and the nuclei of H$_2…
We make a systematic study of high-order harmonic generation (HHG) in a He$^+$-like model ion when the initial states are prepared as a coherent superposition of the ground state and an excited state. It is found that, according to the degree of the ionization of the excited state, the laser intensity can be divided into three regimes in which HHG spectra exhibit different characteristics. The pulse-duration dependence of the HHG spectra in these regimes is studied. We also demonstrate evident advantages of using coherent superposition state to obtain high conversion efficiency. The conversion…
Ultrafast processes in matter, such as the electron emission following light absorption, can now be studied using ultrashort light pulses of attosecond duration ($10^{-18}$s) in the extreme ultraviolet spectral range. The lack of spectral resolution due to the use of short light pulses may raise serious issues in the interpretation of the experimental results and the comparison with detailed theoretical calculations. Here, we determine photoionization time delays in neon atoms over a 40 eV energy range with an interferometric technique combining high temporal and spectral resolution. We spectr…
