The removal of electrons located in the core shells of molecules creates transient states that live between a few femtoseconds to attoseconds. Owing to these short lifetimes, time-resolved studies of these states are challenging and complex molecular dynamics driven solely by electronic correlation are difficult to observe. Here, few-femtosecond core-excited state lifetimes of iodine monochloride are obtained by attosecond transient absorption on iodine 4d-16p transitions around 55 eV. Core-level ligand field splitting allows direct access of excited states aligned along and perpendicular to the ICl molecular axis. Lifetimes of 3.5 fs and 4.3 fs are obtained for core-hole states parallel to the bond and 6.5 fs and 6.9 fs for perpendicular states, while nuclear motion is essentially frozen on this timescale. Theory shows that the dramatic decrease of lifetime for core-vacancies parallel to the covalent bond is a manifestation of non-local interactions with the neighboring Cl atom of ICl.
Tracing ultrafast processes induced by interaction of light with matter is often very challenging. In molecular systems, the initially created electronic coherence becomes damped by the slow nuclear rearrangement on a femtosecond timescale which makes real-time observations of electron dynamics in molecules particularly difficult. In this work, we report an extension of the theory underlying the attosecond transient absorption spectroscopy (ATAS) for the case of molecules, including a full account for the coupled electron-nuclear dynamics in the initially created wave packet, and apply it to p…
A new formalism and computer code, ASTRA (AttoSecond TRAnsitions), has been developed to treat the interactions of short, intense radiation with molecules. The formalism makes extensive use of transition density matrices, computed using a state-of-the-art quantum chemistry code (LUCIA), to efficiently calculate the many-body inter-channel-coupling interactions required to simulate the highly correlated electron dynamics due to atoms and molecules exposed to attosecond laser radiation.
A time-dependent equation of motion coupled cluster singles and doubles (TD-EOM-CCSD) method is implemented, which uses a reduced basis calculated with the asymmetric band Lanczos algorithm. The approach is used to study weak-field processes in small molecules induced by ultrashort valence pump and core probe pulses. We assess the reliability of the procedure by comparing TD-EOM-CCSD absorption spectra to spectra obtained from the time-dependent coupled-cluster singles and doubles (TDCCSD) method and observe that spectral features can be reproduced for several molecules, at much lower computat…
Control over various fragmentation reactions of a series of polyatomic molecules (acetylene, ethylene, 1,3-butadiene) by the optical waveform of intense few-cycle laser pulses is demonstrated experimentally. We show both experimentally and theoretically that the responsible mechanism is inelastic ionization from inner-valence molecular orbitals by recolliding electron wavepackets, whose recollision energy in few-cycle ionizing laser pulses strongly depends on the optical waveform. Our work demonstrates an efficient and selective way of pre-determining fragmentation and isomerization reactions …
Zepto to Attosecond core-level photoemission time delays in homonuclear diatomic molecules and non-dipole effects in the framework of Multiple Scattering theory
Time-dependent quantum chemical methods coupled to Gaussian basis sets are gaining popularity in modeling the electron dynamics of atoms and molecules interacting with intense laser fields. Two approaches most widely used for this purpose, the real-time time-dependent configuration interaction singles and the real-time time-dependent density functional theory, both have their limitations, so the development of more accurate yet computationally efficient time-dependent methods is still in demand. In this work we explore the applicability of the real-time time-dependent configuration interaction…
Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry an additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences and demonstrate how it offers a novel tool to monitor non-adiabatic dynamics as it occurs in the vicinity of conical intersections and …
Attosecond charge migration is a periodic evolution of the charge density of a molecule on a time scale defined by the energy intervals between the electronic states involved. Here, we report the observation of charge migration in neutral silane (SiH$_4$) in 690~as, its decoherence within 15~fs, and its revival after 40-50~fs using X-ray attosecond transient absorption spectroscopy. The migration of charge is observed as pairs of quantum beats with a characteristic spectral phase in the transient spectrum. The decay and revival of the degree of electronic coherence is found to be a result of b…
Transient absorption is a very powerful observable in attosecond experiments on atoms, molecules and solids and is frequently used in experiments employing phase-locked few-cycle infrared and XUV laser pulses derived from high harmonic generation. We show numerically and analytically that in non-centrosymmetric systems, such as many polyatomic molecules, which-way interference enabled by the lack of parity conservation leads to new spectral absorption features, which directly reveal the laser electric field. The extension of Attosecond Transient Absorption Spectroscopy (ATAS) to such targets h…
The development of attosecond technology has enabled the real-time observation of coherent electron motion in atoms, molecules and condensed phases. Experimentally, it is now possible to generate laser pulses of durations of only a few tens of attoseconds. These durations are of the order of the revolution period of the first Bohr orbit (150 asec), opening the way to visualize and even control electron dynamics at its natural time scale. This PhD thesis constitutes a theoretical study of fundamental phenomena occurring in gas-phase molecules upon interaction with light. We have investigated ul…
The present review addresses the technical advances and the theoretical developments to realize and rationalize attosecond-science experiments that reveal a new dynamical time scale ($10^{-15}$-$10^{-18}$ s), with a particular emphasis on molecular systems and the implications of attosecond processes for chemical dynamics. After a brief outline of the theoretical framework for treating non-perturbative phenomena in Section 2, we introduce the physical mechanisms underlying high-harmonic generation and attosecond technology. The relevant technological developments and experimental schemes are c…
Chiral light-matter interactions have been investigated for two centuries, leading to the discovery of many chiroptical processes used for discrimination of enantiomers. Whereas most chiroptical effects result from a response of bound electrons, photoionization can produce much stronger chiral signals that manifest as asymmetries in the angular distribution of the photoelectrons along the light propagation axis. Here we implement a self-referenced attosecond photoelectron interferometry to measure the temporal profile of the forward and backward electron wavepackets emitted upon photoionizatio…
Charge migration is the electronic response that immediately follows localized ionization or excitation in a molecule, before the nuclei have time to move. It typically unfolds on sub-femtosecond time scales and most often corresponds to dynamics far from equilibrium, involving multi-electron interactions in a complex chemical environment. While charge migration has been documented experimentally and theoretically in multiple organic and inorganic compounds, the general mechanism that regulates it remains unsettled. In this work we use tools from nonlinear dynamics to analyze charge migration …
Electron dynamics in water are of fundamental importance for a broad range of phenomena, but their real-time study faces numerous conceptual and methodological challenges. Here, we introduce attosecond size-resolved cluster spectroscopy and build up a molecular-level understanding of the attosecond electron dynamics in water. We measure the effect that the addition of single water molecules has on the photoionization time delays of water clusters. We find a continuous increase of the delay for clusters containing up to 4-5 molecules and little change towards larger clusters. We show that these…
Ultrafast laser excitation can trigger multiplex coherent dynamics in molecules. Here, we report attosecond transient absorption experiments addressing simultaneous probing of electronic and vibrational dynamics in a prototype molecule, deuterium bromide (DBr), following its strong-field ionization. Electronic and vibrational coherences in the ionic X$^2Π_{3/2}$ and X$^2Π_{1/2}$ states are characterized in the Br-$3d$ core-level absorption spectra via quantum beats with 12.6-fs and 19.9-fs periodicities, respectively. Polarization scans reveal that the phase of the electronic quantum beats dep…
Preparation and control of electronic wave packets in neutral molecules via attosecond x-ray processes
Technical University of Denmark（丹麦技术大学）；University of Hamburg（汉堡大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；The Hamburg Centre for Ultrafast Imaging（汉堡超快成像中心）；Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；Q-Chem, Inc.（Q-Chem公司）；University of Southern California（南加州大学）
The use of semiclassical models based on the Strong Field Approximation (SFA) is ubiquitous in strong field multi-photon ionization and underlies many key developments in attosecond science, including the description of High Harmonic Generation (HHG). However, such models are notably lacking in streaking experiments, which use an attosecond pulse to initiate single-photon ionization and a lower frequency infrared pulse to provide timing information. Here, we introduce a classical Wigner propagation (CWP) method, which analogously to semiclassical models in strong field ionization, treats the i…
In this work, we present a time-dependent (TD) selected configuration interaction method based on our recently-introduced adaptive configuration interaction (ACI). We show that ACI, in either its ground or excited state formalisms, is capable of building a compact basis for use in real-time propagation of wave functions for computing electron dynamics. TD-ACI uses an iteratively selected basis of determinants in real-time propagation capable of capturing strong correlation effects in both ground and excited states, all with an accuracy---and associated cost---tunable by the user. We apply TD-A…
Shape resonances in physics and chemistry arise from the spatial confinement of a particle by a potential barrier. In molecular photoionization, these barriers prevent the electron from escaping instantaneously, so that nuclei may move and modify the potential, thereby affecting the ionization process. By using an attosecond two-color interferometric approach in combination with high spectral resolution, we have captured the changes induced by the nuclear motion on the centrifugal barrier that sustains the well-known shape resonance in valence-ionized N$_2$. We show that despite the nuclear mo…
The shifted Tietz-Wei (sTW) oscillator is as good as traditional Morse potential in simulating the atomic interaction in diatomic molecules. By using the Pekeris-type approximation to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schrödinger equation with this typical molecular model via the exact quantization rule (EQR). The energy spectrum for a set of diatomic molecules ($NO \left(a^4Π_i\right)$, $NO \left(B^2Π_r\right)$, $NO \left(L'^2ϕ\right)$, $NO \left(b^4Σ^{-}\right)$, $ICl\left(X^1Σ_g^{+}\right)$, $ICl\left(A^3Π_1\right)$ and $ICl\left(A'^3Π_2\right…
Time-resolved investigations of ultrafast electronic and molecular dynamics were not possible until recently. The typical time scale of these processes is in the picosecond to attosecond realm. The tremendous technological progress in recent years made it possible to generate ultrashort pulses, which can be used to trigger, to watch, and to control atomic and molecular motion. This tutorial focuses on experimental and theoretical advances which are used to study the dynamics of electrons and molecules in the presence of ultrashort pulses. In the first part, the rotational dynamics of molecules…
We investigate theoretically charge migration following prompt double ionization of a polyatomic molecule (C$_2$H$_4$BrI) and find that for double ionization, correlation-driven charge migration appears to be particularly prominent, i.e., we observe exceptionally rich dynamics solely driven by the electron-electron interaction even in the situation when the electrons are emitted from outer-valence orbitals. These strongly correlated electron dynamics are witnessed in the theoretically determined time-resolved transient absorption cross section. Strikingly, features in the cross section can be …
We propose an imaging technique to follow core-hole wave-packet oscillations in the nitrogen molecule. In this scheme, an attosecond x-ray pulse core-ionizes the nitrogen molecule and a subsequent attosecond x-ray pulse probes the evolution of the electron dynamics. We can image the oscillation of the core-hole between the two atomic sites by measuring the angular correlation between photoelectrons. Analytical relations for the angular correlation are derived based on the plane-wave approximation for the photoelectron wave function. We validate these results with a scattering calculation for t…
Time-dependent Hole States in Multiconfigurational Time-Dependent Hartree-Fock Approaches: Applications in Photoionization of Water Molecule
Shanghai Jiao Tong University（上海交通大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论数学科学中心（iTHEMS））；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心（R-CCS））；The University of Tokyo（东京大学）
Linear off-resonant X-ray Raman techniques are capable of detecting the ultrafast electronic coherences generated when a photoexcited wave packet passes through a conical intersection. A hybrid femtosecond or attosecond probe pulse is employed to excite the system and stimulate the emission of the signal photon, where both fields are components of a hybrid pulse scheme. In this paper, we investigate how attosecond pulse trains, as provided by high-harmonic generation processes, perform as probe pulses in the framework of this spectroscopic technique, instead of single Gaussian pulses. We explo…
We report a three-dimensional numerical implementation of multiconfiguration time-dependent Hartree-Fock (MCTDHF) based on a multi-resolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully compute high-harmonic generation (HHG) of H2 and H2O. The present implementation will open a way to the first-principle theoretical study of intense-field and attosecond-pulse induced ultrafast phenomena in general molecules.
High harmonic spectroscopy can access structural and dynamical information on molecular systems encoded in amplitude and phase of high harmonic generation (HHG) signals4. However, measurement of the harmonic phase is a daunting task. Here we present a precise measurement of HHG phase difference between two isotopes of molecular hydrogen using the advanced extreme-ultraviolet (XUV) Gouy phase interferometer. The measured phase difference is about 200 mrad, corresponding to 3 attoseconds (1 as = 10^-18 s) time delay which is nearly independent of harmonic order. The measurements agree very well …
Expressions for the two-dimensional Stimulated x-ray Raman Spectroscopy (2D-SXRS) signal obtained using attosecond x-ray pulses are derived. The 1D- and 2D-SXRS signals are calculated for trans-N-methyl acetamide (NMA) with broad bandwidth (FWHM ~14.2eV, 181 as) pulses tuned to the oxygen and nitrogen K-edges. Crosspeaks in 2D signals reveal electronic Franck-Condon overlaps between valence orbitals and relaxed orbitals in the presence of the core hole.
Irradiation of a molecular system by an intense laser field can trigger dynamics of both electronic and nuclear subsystems. The lighter electrons usually move on much faster, attosecond time scale but the slow nuclear rearrangement damps ultrafast electronic oscillations, leading to the decoherence of the electronic dynamics within a few femtoseconds. We show that a simple, single-trajectory semiclassical scheme can evaluate the electronic coherence time in polyatomic molecules accurately by demonstrating an excellent agreement with full-dimensional quantum calculations. In contrast to numeric…
High-order harmonic generation in polyatomic molecules generally involves multiple channels, each associated with a different orbital. Their unambiguous assignment remains a major challenge for high-harmonic spectroscopy. Here we present a multi-modal approach, using unaligned SF$_6$ molecules as an example, where we combine methods from extreme-ultraviolet spectroscopy, above-threshold ionization and attosecond metrology. Channel-resolved above-threshold ionization measurements reveal that strong-field ionization opens four channels. Two of them, identified by monitoring the ellipticity depen…
Attosecond nonlinear Fourier transform (NFT) pump probe spectroscopy is an experimental technique which allows investigation of the electronic excitation, ionization, and unimolecular dissociation processes. The NFT spectroscopy utilizes ultrafast multiphoton ionization in the extreme ultraviolet spectral range and detects the dissociation products of the unstable ionized species. In this paper, a quantum mechanical description of NFT spectra is suggested, which is based on the second order perturbation theory in molecule-light interaction and the high level ab initio calculations of CO2 and C…
A nonadiabatic scheme for the description of the coupled electron and nuclear motions in the ozone molecule was proposed recently. An initial coherent nonstationary state was prepared as a superposition of the ground state and the excited Hartley band. In this situation neither the electrons nor the nuclei are in a stationary state. The multiconfiguration time dependent Hartree method was used to solve the coupled nuclear quantum dynamics in the framework of the adiabatic separation of the time-dependent Schrödinger equation. The resulting wave packet shows an oscillation of the electron densi…
High-order harmonic generation is a powerful and sensitive tool for probing atomic and molecular structures, combining in the same measurement an unprecedented attosecond temporal resolution with a high spatial resolution, of the order of the angstrom. Imaging of the outermost molecular orbital by high-order harmonic generation has been limited for a long time to very simple molecules, like nitrogen. Recently we demonstrated a technique that overcame several of the issues that have prevented the extension of molecular orbital tomography to more complex species, showing that molecular imaging c…
Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult with increasing structural complexity, given that a global extremum must be found in a multi-dimensional solution space. Worse, pre-calculating many thousands of molecular configurations for all orientations becomes simply intractable. As a remedy, here, we propose a machine learning algorithm with a convolutional neural network which can be trained with a lim…
We introduce and experimentally demonstrate a method, where the two intrinsic time scales of a molecule, the slow nuclear motion and the fast electronic motion, are simultaneously measured in a photo-electron photo-ion coincidence experiment. In our experiment, elliptically polarized, 750~nm, 4.5~fs laser pulses were focused to an intensity of $9\times10^{14}\mathrm{W/cm}^2$ onto H$_2$. Using coincidence imaging, we directly observe the nuclear wavepacket evolving on the \ssg{} state of H$_2^+$ during its first roundtrip with attosecond temporal and picometer spatial resolution. The demonstrat…
Structural information on electronically excited neutral molecules can be indirectly retrieved, largely through pump-probe and rotational spectroscopy measurements with the aid of calculations. Here, we demonstrate the direct structural retrieval of neutral carbonyl disulfide (CS$_2$) in the B$^1$B$_2$ excited electronic state using laser-induced electron diffraction (LIED). We unambiguously identify the ultrafast symmetric stretching and bending of the field-dressed neutral CS$_2$ molecule with combined picometer and attosecond resolution using intrapulse pump-probe excitation and measurement…
Charge migration (CM) is a coherent attosecond process that involves the movement of localized holes across a molecule. To determine the relationship between a molecule's structure and the CM dynamics it exhibits, we perform systematic studies of para-functionalized bromobenzene molecules (X-C$_6$H$_4$-R) using real-time time-dependent density functional theory. We initiate valence-electron dynamics by emulating rapid strong-field ionization leading to a localized hole on the bromine atom. The resulting CM, which takes on the order of 1 fs, occurs via an X localized to C$_6$H$_4$ delocalized t…
Measuring and controlling the ionization dynamics by intense laser fields has recently led to important breakthroughs, from the investigation of tunneling time delays to attosecond molecular imaging by electron holography. In these experiments, extracting the subtle influence of the ionic potential on the departing electrons is of capital importance, and often challenging. Here we show that molecular chirality naturally provides a solution to this issue by breaking the symmetry of the photoionization process along the laser propagation direction. Using counter-rotating bicircular bichromatic l…
Coherent light pulses of few to hundreds of femtoseconds (fs) duration have prolifically served the field of ultrafast phenomena. While fs pulses address mainly dynamics of nuclear motion in molecules or lattices in the gas, liquid or condensed matter phase, the advent of attosecond pulses has in recent years provided direct experimental access to ultrafast electron dynamics. However, there are processes involving nuclear motion in molecules and in particular coupled electronic and nuclear motion that possess few fs or even sub-fs dynamics. In the present work we have succeeded in addressing s…
