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 covered in Section 3. Throughout the remainder of the chapter, we report on selected applications in molecular attosecond physics, thereby addressing specific phenomena mediated by purely electronic dynamics: charge localization in molecular hydrogen, charge migration in biorelevant molecules, high-harmonic spectroscopy, and delays in molecular photoionization.
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…
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 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 t…
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 …
First principle theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, specially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regime. Especially for TAS, full four-component (4c) RT simulations are fe…
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…
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…
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…
The recent demonstration of isolated attosecond pulses from an X-ray free-electron laser (XFEL) opens the possibility for probing ultrafast electron dynamics at X-ray wavelengths. An established experimental method for probing ultrafast dynamics is X-ray transient absorption spectroscopy, where the X-ray absorption spectrum is measured by scanning the central photon energy and recording the resultant photoproducts. The spectral bandwidth inherent to attosecond pulses is wide compared to the resonant features typically probed, which generally precludes the application of this technique in the a…
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…
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…
We analyze the attosecond electron dynamics in hydrogen molecular ion driven by an external intense laser field using ab-initio numerical simulations of the corresponding time-dependent Schr{ö}dinger equation and Bohmian trajectories. To this end, we employ a one-dimensional model of the molecular ion in which the motion of the protons is frozen. The results of the Bohmian trajectory calculations do agree well with those of the ab-initio simulations and clearly visualize the electron transfer between the two protons in the field. In particular, the Bohmian trajectory calculations confirm the r…
Probing of Core Excitons in Solid NaF with Polarization-Selective Attosecond Time-Resolved Four-Wave Mixing Spectroscopy
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of Regensburg（雷根斯堡大学）；Lund University（隆德大学）
We present the first fully ab initio calculations for attosecond transient absorption spectroscopy of atomic krypton with overlapping pump and probe pulses. Within the time-dependent configuration interaction singles (TDCIS) approach, we describe the pump step (strong-field ionization using a near-infrared pulse) as well as the probe step (resonant electron excitation using an extreme- ultraviolet pulse) from first principles. We extent our TDCIS model and account for the spin-orbit splitting of the occupied orbitals. We discuss the spectral features seen in a recent attosecond transient absor…
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 …
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…
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…
Molecular absorption and photo-electron spectra can be efficiently predicted with real-time time-dependent density-functional theory (TDDFT). We show here how these techniques can be easily extended to study time-resolved pump-probe experiments in which a system response (absorption or electron emission) to a probe pulse, is measured in an excited state. This simulation tool helps to interpret the fast evolving attosecond time-resolved spectroscopic experiments, where the electronic motion must be followed at its natural time-scale. We show how the extra degrees of freedom (pump pulse duration…
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…
Core-level signature of long-range density-wave order and short-range excitonic correlations probed by attosecond broadband spectroscopy
University of California at Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；Tsung-Dao Lee Institute and Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University（上海交通大学桐江书院与张江高等研究院）
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…
Zepto to Attosecond core-level photoemission time delays in homonuclear diatomic molecules and non-dipole effects in the framework of Multiple Scattering theory
Two- and multi-dimensional spectroscopy is used in physics and chemistry to obtain structural and dynamical information that would otherwise be invisible by the projection into a one-dimensional data set such as a single emission or absorption spectrum. Here, we introduce a qualitatively new two-dimensional spectroscopy method by employing the carrier-envelope phase (CEP). Instead of measuring spectral vs. spectral information, the combined application of spectral interferometry and CEP control allows the measurement of otherwise inseparable temporal events on an attosecond time scale. As a sp…
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 …
