The dissociation dynamics of diatomic molecules interacting with (near) optical laser pulses of different duration is investigated by an elaborate discussion of the electric field of the laser and by a direct solution of the time-dependent molecular Schrödinger equation. The systematic variation of the pulse duration from the electronic time scale (attoseconds) to the nuclear time scale (femtoseconds) shows that the employed few-cycle laser pulses lead to well-known but quite different dissociation mechanisms. A comparative calculation with a model pulse and an experimentally realized attosecond pulse emphasizes that, and to what extent, a realistic modeling of the electric field is of central importance in the attosecond regime.
The kinetic energy distribution of D$^+$ ions resulting from the interaction of a femtosecond laser pulse with D$_2$ molecules is calculated based on the rescattering model. From analyzing the molecular dynamics, it is shown that the recollision time between the ionized electron and the D$_2^+$ ion can be read from the D$^+$ kinetic energy peaks to attosecond accuracy. We further suggest that more precise reading of the clock can be achieved by using shorter fs laser pulses (about 15fs).
Strong-field ionization (SFI) has been shown to prepare wave packets with few-femtosecond periods. Here, we explore whether this technique can be extended to the attosecond time scale. We introduce an intuitive model for predicting the bandwidth of ionic states that can be coherently prepared by SFI. This bandwidth is given by the Fourier-transformed sub-cycle SFI rate and decreases considerably with increasing central wavelength of the ionizing pulse. Many-body calculations based on time-dependent configuration-interaction singles (TDCIS) quantitatively support this result and reveal an addit…
We study the influence of polarization effects in streaking by combined atto- and femtosecond pulses. The polarization-induced terms alter the streaking spectrum. The normal streaking spectrum, which maps to the vector potential of the femtosecond pulse, is modified by a contribution following the field instead. We show that polarization effects may lead to an apparent temporal shift, that needs to be properly accounted for in the analysis. The effect may be isolated and studied by angle-resolved photoelectron spectroscopy from oriented polar molecules. We also show that polarization effects w…
We study the breakup of $\text{H}_2^+$ exposed to super-intense, femtosecond laser pulses with frequencies greater than that corresponding to the ionization potential. By solving the time-dependent Schrödinger equation in an extensive field parameter range, it is revealed that highly nonresonant dissociation channels can dominate over ionization. By considering field-dressed Born-Oppenheimer potential energy curves in the reference frame following a free electron in the field, we propose a simple physical model that characterizes this dissociation mechanism. The model is used to predict contro…
Extreme ultraviolet (XUV) attosecond pulses, generated by a process known as laser-induced electron recollision, are a key ingredient for attosecond metrology, providing a tool to precisely initiate and probe sub-femtosecond dynamics in the microcosms of atoms, molecules and solids[1]. However, with the current technology, extending attosecond metrology to scrutinize the dynamics of the inner-shell electrons is a challenge, that is because of the lower efficiency in generating the required soft x-ray \hbarω>300 eV attosecond bursts and the lower absorption cross-sections in this spectral range…
Studies of ultrafast dynamics along with femtosecond-pulse metrology rely on non-linear processes, induced solely by the exciting/probing pulses or the pulses to be characterized. Extension of these approaches to the extreme-ultraviolet (XUV) spectral region opens up a new, direct route to attosecond scale dynamics. Limitations in available intensities of coherent XUV continua kept this prospect barren. The present work overcomes this barrier. Reaching condition at which simultaneous ejection of two bound electrons by two-XUV-photon absorption becomes more efficient than their one-by-one remov…
Atomic motion dynamics during structural changes or chemical reactions have been visualized by picosecond and femtosecond pulsed electron beams via ultrafast electron diffraction and microscopy. Imaging the even faster dynamics of electrons in atoms, molecules and solids requires electron pulses with sub-femtosecond durations. We demonstrate here the all-optical generation of trains of attosecond free-electron pulses. The concept is based on the periodic energy modulation of a pulsed electron beam via an inelastic interaction with the ponderomotive potential of an optical travelling wave gener…
In the last decade, the development of Ultrafast Electron Diffraction (UED) and Microscopy (UEM) has enabled the imaging of atomic motion in real time and space. These pivotal table-top tools opened the door for a vast range of applications in different areas of science spanning chemistry, physics, materials science, and biology. We first discuss the basic principles and recent advancements, including some of the important applications, of both UED and UEM. Then, we discuss the recent advances in the field that have enhanced the spatial and temporal resolutions, where the latter, however, is s…
We examine the attosecond electron recollision dissociation of D2+ recently demonstrated experimentally [H. Niikura et al., Nature (London) 421, 826 (2003)] from a coherent control perspective. In this process, a strong laser field incident on D2 ionizes an electron, accelerates the electron in the laser field to eV energies, and then drives the electron to recollide with the parent ion, causing D2+ dissociation. A number of results are demonstrated. First, a full dimensional Strong Field Approximation (SFA) model is constructed and shown to be in agreement with the original experiment. This i…
Recent developments toward the production and laboratory use of pulses of high intensity, and/or of very high frequency, and/or of ultrashort duration, make possible experiments which can produce time-resolved data on ultrafast transformations involving motions of electrons. The formulation, quantitative understanding and prediction of related new phenomena entail the possibility of computing and applying solutions of the many-electron time-dependent Schroedinger equation, for arbitrary electronic structures, including the dominant effects of Rydberg series, of multiply excited states and of t…
Using extreme-ultraviolet attosecond-pulse-trains, we investigate the photoionization dynamics of a Helium atom in the presence of moderately-strong (~10^12 W/cm^2) femtosecond laser pulses. The electronic structure of a laser-dressed atom is traced in real-time through precision measurements of ion-yields and photo-electron angular distributions. Quantum interferences between photo-excitation paths are interpreted using the Floquet formalism. As the laser pulse intensity ramps on femtosecond timescales, we observe transitions between ionization channels mediated by different atomic resonances…
Attosecond pulses can be used to initiate and control electron dynamics on a sub-femtosecond time scale. The first step in this process occurs when an atom absorbs an ultraviolet photon leading to the formation of an attosecond electron wave packet (EWP). Until now, attosecond pulses have been used to create free EWPs in the continuum, where they quickly disperse. In this paper we use a train of attosecond pulses, synchronized to an infrared (IR) laser field, to create a series of EWPs that are below the ionization threshold in helium. We show that the ionization probability then becomes a fun…
Numerical simulations are presented to validate the possible use of cutting-edge attosecond time- resolved photoelectron spectroscopy to observe in real time the creation of an electronic wavepacket and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds.
Imaging the structure of molecules in transient excited states remains a challenge due to the extreme requirements for spatial and temporal resolution. Ultrafast electron diffraction from aligned molecules (UEDAM) provides atomic resolution and allows for the retrieval of structural information without the need to rely on theoretical models. Here we use UEDAM and femtosecond laser mass spectrometry (FLMS) to investigate the dynamics in carbon disulfide (CS2) following the interaction with an intense femtosecond laser pulse. We have retrieved images of ground state and excited molecules with 0.…
We present experimental results on the ionization/dissociation of methane in femtosecond pulses of radiation. Angular and intensity dependent yields of singly and doubly charged species were measured using an imaging mass spectrometer. The measured data shows that all fragments yields exhibit some degree of anisotropy as a result of them being preferably ejected parallel to the polarization direction. Additionally, an anomalous perpendicular fragmentation pattern is found for CH\-(2)\+(2+). We find evidence of multiple dissociation mechanisms including statistical decay, field assisted dissoci…
In this work we demonstrate the generation of two intense, ultrafast laser pulses that allow a controlled interferometric measurement of higher harmonic generation pulses with 12.8 attoseconds in resolution (half the atomic unit of time) and a precision as low as 680 zeptoseconds ($10^{-21}$ seconds). We create two replicas of a driving femtosecond pulse which share the same optical path except at the focus where they converge to two foci. An attosecond pulse train emerges from each focus through the process of HHG. The two attosecond pulse trains from each focus interfere in the far field pro…
The evolution of electron wavepackets determines the course of many physical and chemical phenomena and attosecond spectroscopy aims to measure and control such dynamics in real-time. Here, we investigate radial electron wavepacket motion in Helium by using an XUV attosecond pulse train to prepare a coherent superposition of excited states and a delayed femtosecond IR pulse to ionize them. Quantum beat signals observed in the high resolution photoelectron spectrogram allow us to follow the field-free evolution of the bound electron wavepacket and determine the time-dependent ionization dynamic…
The possibility of achieving highly selective excitation of low metastable states of hydrogen and helium atoms by using short laser pulses with reasonable parameters is demonstrated theoretically. Interactions of atoms with the laser field are studied by solving the close-coupling equations without discretization. The parameters of laser pulses are calculated using different kinds of optimization procedures. For the excitation durations of hundreds of femtoseconds direct optimization of the parameters of one and two laser pulses with Gaussian envelopes is used to introduce a number of simple s…
Light-induced states are commonly observed in the photoionization spectra of laser-dressed atoms. The properties of autoionizing polaritons, entangled states of light and Auger resonances, however, are largely unexplored. We employ attosecond transient-absorption spectroscopy to study the evolution of autoionizing states in argon, dressed by a tunable femtosecond laser pulse. The avoided crossings between the $3s^{-1}4p$ and several light-induced states indicates the formation of polariton multiplets. We measure a controllable stabilization of the polaritons against ionization, in excellent ag…
The basic properties of atoms, molecules and solids are governed by electron dynamics which take place on extremely short time scales. To measure and control these dynamics therefore requires ultrafast sources of radiation combined with efficient detection techniques. The generation of extreme ultraviolet (XUV) attosecond (1 as = 10-18 s) pulses has, for the first time, made direct measurements of electron dynamics possible. Nevertheless, while various applications of attosecond pulses have been demonstrated experimentally, no one has yet captured or controlled the full three dimensional motio…
Attosecond pulses, produced through high-order harmonic generation in gases, have been successfully used for observing ultrafast, sub-femtosecond electron dynamics in atoms, molecules and solid state systems. Today's typical attosecond sources, however, are often impaired by their low repetition rate and the resulting insufficient statistics, especially when the number of detectable events per shot is limited. This is the case for experiments where several reaction products must be detected in coincidence, and for surface science applications where space-charge effects compromise spectral and …
In our model the electron dynamics are described by a two-state approximation. This might appear a rough approximation since it neglects coupling through excited electronic states and ionization channels. However at high intensity (laser fields equivalent to the Coulomb force) and long wavelength (photon energy much lower than the ionization potential) the dissociation process occurs by adiabatic polarization involving the lowest electronic states. For the experiment in question, with intensities above 10x14 W cm-2 and photon energies of 1.5eV, such an approach is well justified. More contenti…
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 briefly review the pilot ideas on the generation of EM-pulses much shorter than already available sub-femtosecond pulses, and outline inroads and venues into the physics of pulses mush shorter than an attosecond (10^-18 s), in particular the so called zeptosecond (10^-21 s) and yoctosecond (10^-24 s) pulses that may allow one to operate on QED and nuclear as well as quark-gluon time plasma scales. We also very briefly outline the entire time-scale available in the existing universe, down to the ultimately short the so called Planck time ~ 10^-43 s, which is the time-scale of Big Bang, and t…
An optical coherent control scheme has been proposed and theoretically investigated where an extreme ultraviolet single attosecond pulse (SAP) propagates through a dense helium gas dressed by a time-delayed femtosecond laser pulse. The laser pulse couples the 2s2p(^1P) and 2s^2(^1S) autoionizing states when the SAP excites the 2s2p state. After going through the gas, the spectral and temporal profiles of the SAP are strongly distorted. A narrowed but enhanced spike in the spectrum shows up for specific intensities and time delays of the laser, which exemplifies the control of a broadband photo…
The release of conduction-band electrons from a metal surface by a sub-femtosecond extreme ultraviolet (XUV) pulse, and their propagation through the solid, provokes a dielectric response in the solid that acts back on the photoelectron wave packet. We calculated the (wake) potential associated with this photoelectron self-interaction in terms of bulk and surface plasmon excitations and show that it induces a considerable, XUV-frequency-dependent temporal shift in laser-streaked XUV photoemission spectra, suggesting the observation of the ultrafast solid-state dielectric response in contempora…
We report on the generation of intense extreme ultraviolet (EUV) supercontinuum with photon energies spanning from 35 eV to 50 eV (i. e., supporting an isolated attosecond pulse with a duration of ~271 as) by loosely focusing 35 fs, 11 mJ pulses from a femtosecond laser amplifier into a 10-mm long gas cell filled with krypton gas. The dramatic change of spectral and temporal properties of the driver pulses after passing through the gas cell indicates that propagation effects play a significant role in promoting the generation of the EUV supercontinuum.
Photoinduced quantum dynamics in molecules have hierarchical temporal structures with different energy scales that are associated with electron and nuclear motions. Femtosecond-to-attosecond transient absorption spectroscopy (TAS) using high-harmonic generation (HHG) with a photon energy below 300 eV has been a powerful tool to observe such electron and nuclear dynamics in a table-top manner. However, comprehensive measurements of the electronic, vibrational, and rotational molecular dynamics have not yet been achieved. Here, we demonstrate HHG-based TAS at the nitrogen K-edge (400 eV) for the…
We investigate the characteristic effects of nuclear motion on attosecond transient absorption spectra in molecules by calculating the spectrum for different model systems. Two models of the hydrogen molecular ion are considered: one where the internuclear separation is fixed, and one where the nuclei are free to vibrate. The spectra for the fixed nuclei model are similar to atomic spectra reported elsewhere, while the spectra obtained in the model including nuclear motion are very different and dominated by extremely broad absorption features. These broad absorption features are analyzed and …
Coherent nonlinear spectroscopies and imaging in the X-ray domain provide direct insight into the coupled motions of electrons and nuclei with resolution on the electronic length and time scale. The experimental realization of such techniques will strongly benefit from access to intense, coherent pairs of femtosecond X-ray pulses. We have observed phase-stable X-ray pulse pairs containing more thank 3 x 10e7 photons at 5.9 keV (2.1 Angstrom) with about 1 fs duration and 2-5 fs separation. The highly directional pulse pairs are manifested by interference fringes in the superfluorescent and seed…
High harmonic light sources make it possible to access attosecond time-scales, thus opening up the prospect of manipulating electronic wave packets for steering molecular dynamics. However, two decades after the birth of attosecond physics, the concept of attosecond chemistry has not yet been realized. This is because excitation and manipulation of molecular orbitals requires precisely controlled attosecond waveforms in the deep ultraviolet, which have not yet been synthesized. Here, we present a novel approach using attosecond vacuum ultraviolet pulse-trains to coherently excite and control t…
We propose a general technique to retrieve the information of dipole-forbidden resonances in the autoionizing region. In the simulation, a helium atom is pumped by an isolated attosecond pulse in the extreme ultraviolet (EUV) combined with a few-femtosecond laser pulse. The excited wave packet consists of the $^1S$, $^1P$, and $^1D$ states, including the background continua, near the $2s2p(^1P)$ doubly excited state. The resultant electron spectra with various laser intensities and time delays between the EUV and laser pulses are obtained by a multilevel model and an ab initio time-dependent S…
Natively, atomic and molecular processes develop in a sub-femtosecond time scale. In order to, for instance, track and capture the electron motion in that scale we need suitable `probes'. Attosecond pulses configure the most appropriate tools for such a purpose. These ultrashort bursts of light are generated when a strong laser field interacts with matter and high-order harmonics of the driving source are produced. In this work, we propose a way to twist attosecond pulse trains. In our scheme, each of the attosecond pulses in the train has a well-defined linear polarization, but with a differe…
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…
An extreme ultraviolet (EUV) single attosecond pulse passing through a laser-dressed dense gas is studied theoretically. The weak EUV pulse pumps the helium gas from the ground state to the 2s2p(1P) autoionizing state, which is coupled to the 2s2(1S) autoionizing state by a femtosecond infrared laser with the intensity in the order of 10^{12} W/cm2. The simulation shows how the transient absorption and emission of the EUV are modified by the coupling laser. A simple analytical expression for the atomic response derived for delta-function pulses reveals the strong modification of the Fano lines…
Two emerging areas of research, attosecond and nanoscale physics, have recently started to merge. Attosecond physics deals with phenomena occurring when ultrashort laser pulses, with duration on the femto- and sub-femtosecond time scales, interact with atoms, molecules or solids. The laser-induced electron dynamics occurs natively on a timescale down to a few hundred or even tens of attoseconds (1 attosecond=1 as=10$^{-18}$ s), which is of the order of the optical field cycle. For comparison, the revolution of an electron on a $1s$ orbital of a hydrogen atom is $\sim152$ as. On the other hand,…
At the core of attosecond science lies the ability to generate laser pulses of sub-femtosecond duration. In tabletop devices the process relies on high-harmonic generation, where a major challenge is to obtain high yields and high cutoff energies required for the generation of attosecond pulses. We develop a computational method that can simultaneously resolve these issues by optimizing the driving pulses using quantum optimal control theory. Our target functional, an integral over the harmonic yield over a desired energy range, leads to a remarkable cutoff extension and yield enhancement for …
Attosecond pulses are fundamental for the investigation of valence and core-electron dynamics on their natural timescale. At present the reproducible generation and characterisation of attosecond waveforms has been demonstrated only through the process of high-order harmonic generation. Several methods for the shaping of attosecond waveforms have been proposed, including metallic filters, multilayer mirrors and manipulation of the driving field. However, none of these approaches allow for the flexible manipulation of the temporal characteristics of the attosecond waveforms, and they suffer fro…
High harmonic generation driven by femtosecond lasers makes it possible to capture the fastest dynamics in molecules and materials. However, to date the shortest attosecond (as) pulses have been produced only in the extreme ultraviolet (EUV) region of the spectrum below 100 eV, which limits the range of materials and molecular systems that can be explored. Here we use advanced experiment and theory to demonstrate a remarkable convergence of physics: when mid-infrared lasers are used to drive the high harmonic generation process, the conditions for optimal bright soft X-ray generation naturally…
We describe an ab initio and non-perturbative $R$-matrix with time-dependence theory for ultrafast atomic processes in light fields of arbitrary polarization. The theory is applicable to complex, multielectron atoms and atomic ions subject to ultrashort (particularly few-femtosecond and attosecond) laser pulses with any given ellipticity, and generalizes previous time-dependent $R$-matrix techniques restricted to linearly polarized fields. We discuss both the fundamental equations, required to propagate the multielectron wavefunction in time, as well as the computational developments necessary…
Time-resolved femtosecond x-ray diffraction patterns from laser-excited molecular iodine are used to create a movie of intramolecular motion with time and space resolution of $30~$fs and $0.3$ Å. The high spatial fidelity is due to interference between the moving excitation and the static initial charge distribution. This x-ray interference has not been employed to image internal motion in molecules before. The initial state is used as the local oscillator for heterodyne amplification of the excited charge distribution to retrieve real-space movies of atomic motion on Ångstrom and femtosecond …
Recently two emerging areas of research, attosecond and nanoscale physics, have started to come together. Attosecond physics deals with phenomena occurring when ultrashort laser pulses, with duration on the femto- and sub-femtosecond time scales, interact with atoms, molecules or solids. The laser-induced electron dynamics occurs natively on a timescale down to a few hundred or even tens of attoseconds, which is comparable with the optical field. On the other hand, the second branch involves the manipulation and engineering of mesoscopic systems, such as solids, metals and dielectrics, with na…
X-ray spectroscopy is an important tool for the investigation of matter. X rays primarily interact with inner-shell electrons creating core (inner-shell) holes that will decay on the time scale of attoseconds to few femtoseconds through electron relaxations involving the emission of a photon or an electron. The advent of femtosecond x-ray pulses expands x-ray spectroscopy to the time domain and will eventually allow the control of core-hole population on timescales comparable to core-vacancy lifetimes. For both cases, a theoretical approach that accounts for the x-ray interaction while the ele…
Single-cycle optical pulses with a controlled electromagnetic waveform allow to steer the motion of low-energy electrons in atoms, molecules, nanostructures or condensed-matter on attosecond dimensions in time. However, high-energy electrons under single-cycle light control would be an enabling technology for beam-based attosecond physics with free-electron lasers or electron microscopy. Here we report the control of freely propagating keV electrons with an isolated optical cycle of mid-infrared light and create a modulated electron current with a peak-cycle-specific sub-femtosecond structure …
The ongoing development of intense high-harmonic generation (HHG) sources has recently enabled highly nonlinear ionization of atoms by the absorption of at least 10 extreme-ultraviolet (XUV) photons within a single atom [Senfftleben \textit{et al.}, arXiv1911.01375]. Here we investigate the role that reshaping of the fundamental, few-cycle, near-infrared (NIR) driving laser within the 30-cm-long HHG Xe medium plays in the generation of the intense HHG pulses. Using an incident NIR intensity that is higher than what is required for phase-matched HHG, signatures of reshaping are found by measuri…
We investigate the dynamics of molecular photoexcitation by unchirped femtosecond laser pulses using RbCs as a model system. This study is motivated by a goal of optimizing a two-color scheme of transferring vibrationally-excited ultracold molecules to their absolute ground state. In this scheme the molecules are initially produced by photoassociation or magnetoassociation in bound vibrational levels close to the first dissociation threshold. We analyze here the first step of the two-color path as a function of pulse intensity from the low-field to the high-field regime. We use two different a…
Polyatomic molecules in strong laser fields can undergo substantial nuclear motion within tens of femtoseconds. Ion imaging methods based on dissociation or Coulomb explosion therefore have difficulty faithfully recording the geometry dependence of the field ionization that initiates the dissociation process. Here we compare the strong-field double ionization and subsequent dissociation of water (both H$_2$O and D$_2$O) in 10-fs and 40-fs 800-nm laser pulses. We find that 10-fs pulses turn off before substantial internuclear motion occurs, whereas rapid internuclear motion can take place durin…
