Helical-photon-dressed states determining unidirectional π-electron rotations in aromatic ring molecules

We theoretically demonstrated that helical-photon-dressed states determine the rotational directions of the π-electrons of aromatic ring molecules formed by a circularly polarized or an elliptically polarized laser. This theory was verified using a minimal three-electronic-state model under the frozen nuclei condition. The model consists of the ground state and either a doubly degenerate electronic excited state or two quasi-degenerate excited states. Three helical-photon-dressed states were derived by solving the time-dependent Schrödinger equation within the semi-classical treatment of light-molecule interactions and rotating wave approximation. The angular momenta of the two helical-photon-dressed states represent the classical rotational direction, and that of the remaining state represents the opposite rotation, that is, non-classical rotation. Classical rotation means that π-electrons have the same rotational direction as that of a given helical electric field vector and obeys the classical equations of motion. Non-classical rotation indicates that the rotational direction is opposite to that of the helical electric field vector. Non-classical rotation is forbidden in an aromatic ring molecule with high symmetry formed by a circularly polarized laser but is allowed in a low symmetric aromatic ring molecule. The sum of the angular momenta of the three dressed states is zero. This is called the sum law for the angular momentum components in this paper. Benzene (D6h) and toluene (CS) were adopted as typical aromatic ring molecules of high and low symmetries, respectively. Finally, considering the effects of nuclear vibrations in the adiabatic approximation, an expression for the π-electron angular momentum was derived and applied to toluene.

Pushing the limits of ultrafast diffraction: Imaging quantum coherences in isolated molecules

Quantum coherence governs the outcome and efficiency of photochemical reactions and ultrafast molecular dynamics. Recent ultrafast gas-phase X-ray scattering and electron diffraction have enabled the observation of femtosecond nuclear dynamics driven by vibrational coherence. However, probing attosecond electron dynamics and coupled electron-nuclear dynamics remains challenging. This article discusses advances in ultrafast X-ray scattering and electron diffraction, highlighting their potential to resolve attosecond charge migration and vibronic coupling at conical intersections. Novel techniques, such as X-ray scattering with orbital angular momentum beams and combined X-ray and electron diffraction, promise to selectively probe coherence contributions and visualize charge migration in real-space. These emerging methods could further our understanding of coherence effects in chemical reactions.

XUV-beamline for photoelectron imaging spectroscopy with shaped pulses

We introduce an extreme ultraviolet (XUV)-beamline designed for the time-resolved investigation and coherent control of attosecond (as) electron dynamics in atoms and molecules by polarization-shaped as-laser pulses. Shaped as-pulses are generated through high-harmonic generation (HHG) of tailored white-light supercontinua (WLS) in noble gases. The interaction of shaped as-pulses with the sample is studied using velocity map imaging (VMI) techniques to achieve the differential detection of photoelectron wave packets. The instrument consists of the WLS-beamline, which includes a hollow-core fiber compressor and a home-built 4f polarization pulse shaper, and the high-vacuum XUV-beamline, which combines an HHG-stage and a versatile multi-experiment vacuum chamber equipped with a home-built VMI spectrometer. The VMI spectrometer allows the detection of photoelectron wave packets from both the multiphoton ionization (MPI) of atomic or molecular samples by the tailored WLS-pulses and the single-photon ionization (SPI) by the shaped XUV-pulses. To characterize the VMI spectrometer, we studied the MPI of xenon atoms by linearly polarized WLS pulses. To validate the interplay of these components, we conducted experiments on the SPI of xenon atoms with linearly polarized XUV-pulses. Our results include the reconstruction of the 3D photoelectron momentum distribution (PMD) and initial findings on the coherent control of the PMD by tuning the spectrum of the XUV-pulses with the spectral phase of the WLS. Our results demonstrate the performance of the entire instrument for HHG-based photoelectron imaging spectroscopy with prototypical shaped pulses. Perspectively, we will employ polarization-tailored WLS-pulses to generate polarization-shaped as-pulses.

Self-Heterodyne Diffractive Imaging of Ultrafast Electron Dynamics Monitored by Single-Electron Pulses

The direct imaging of time-evolving molecular charge densities on atomistic scale and at femtosecond resolution has long been an elusive task. In this theoretical study, we propose a self-heterodyne electron diffraction technique based on single electron pulses. The electron is split into two beams, one passes through the sample and its interference with the second beam produces a heterodyne diffraction signal that images the charge density. Application to probing the ultrafast electronic dynamics in Mg-phthalocyanine demonstrates its potential for imaging chemical dynamics.

Simulating Attochemistry: Which Dynamics Method to Use?

Attochemistry aims to exploit the properties of coherent electronic wavepackets excited via attosecond pulses to control the formation of photoproducts. Such molecular processes can, in principle, be simulated with various nonadiabatic dynamics methods, yet the impact of the approximations underlying the methods is rarely assessed. The performances of widely used mixed quantum-classical approaches, Tully surface hopping, and classical Ehrenfest methods are evaluated against the high-accuracy DD-vMCG quantum dynamics. This comparison is conducted for the valence ionization of fluorobenzene. Analyzing the nuclear motion induced in the branching space of the nearby conical intersection, the results show that the mixed quantum-classical methods reproduce quantitatively the average motion of a quantum wavepacket when initiated on a single electronic state. However, they fail to properly capture the nuclear motion induced by an electronic wavepacket along the derivative coupling, the latter originating from the quantum electronic coherence property, key to attochemistry.

Manipulating Attosecond Charge Migration in Molecules by Optical Cavities

The ultrafast electronic charge dynamics in molecules upon photoionization while the nuclear motions are frozen is known as charge migration. In a theoretical study of the quantum dynamics of photoionized 5-bromo-1-pentene, we show that the charge migration process can be induced and enhanced by placing the molecule in an optical cavity, and can be monitored by time-resolved photoelectron spectroscopy. The collective nature of the polaritonic charge migration process is investigated. We find that, unlike spectroscopy, molecular charge dynamics in a cavity is local and does not show many-molecule collective effects. The same conclusion applies to cavity polaritonic chemistry.

Attochemistry Regulation of Charge Migration

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-C₆H₄-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 → C₆H₄ delocalized → R localized mechanism. Interestingly, the hole contrast on the acceptor functional group increases with increasing electron-donating strength. This trend is well-described by the Hammett σ value of the group, which is a commonly used metric for quantifying the effect of functionalization on the chemical reactivity of benzene derivatives. These results suggest that simple attochemistry principles and a density-based picture can be used to predict and understand CM.

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially 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 regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L_2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.

Stimulated-Raman-scattering amplification of attosecond XUV pulses with pulse-train pumps and application to local in-depth plasma-density measurement

We present a scheme for amplifying an extreme-ultraviolet (XUV) seed isolated attosecond pulse via stimulated Raman scattering of a pulse-train pump. At sufficient seed and pump intensity, the amplification is nonlinear, and the amplitude of the seed pulse can reach that of the pump, one order of magnitude higher than the initial seed amplitude. In the linear amplification regime, we find that the spectral signature of the pump pulse train is imprinted on the spectrum of the amplified seed pulse. Since the spectral signature is imprinted with its frequency downshifted by the plasma frequency, it is possible to deduce the electron density in the region of interaction. This region can be of micrometer length scale longitudinally. By varying the delay between the seed and the pump, this scheme provides a local electron-density measurement inside solid-density plasmas that cannot be probed with optical frequencies, with micrometer resolution.

Attosecond spectroscopy for the investigation of ultrafast dynamics in atomic, molecular and solid-state physics

Since the first demonstration of the generation of attosecond pulses (1 as = 10^-18s) in the extreme-ultraviolet spectral region, several measurement techniques have been introduced, at the beginning for the temporal characterization of the pulses, and immediately after for the investigation of electronic and nuclear ultrafast dynamics in atoms, molecules and solids with unprecedented temporal resolution. The attosecond spectroscopic tools established in the last two decades, together with the development of sophisticated theoretical methods for the interpretation of the experimental outcomes, allowed to unravel and investigate physical processes never observed before, such as the delay in photoemission from atoms and solids, the motion of electrons in molecules after prompt ionization which precede any notable nuclear motion, the temporal evolution of the tunneling process in dielectrics, and many others. This review focused on applications of attosecond techniques to the investigation of ultrafast processes in atoms, molecules and solids. Thanks to the introduction and ongoing developments of new spectroscopic techniques, the attosecond science is rapidly moving towards the investigation, understanding and control of coupled electron-nuclear dynamics in increasingly complex systems, with ever more accurate and complete investigation techniques. Here we will review the most common techniques presenting the latest results in atoms, molecules and solids.

Modeling Potential-Dependent Electrochemical Activation Barriers: Revisiting the Alkaline Hydrogen Evolution Reaction

Accurate theoretical simulation of electrochemical activation barriers is key to understanding electrocatalysis and guides the design of more efficient catalysts. Providing a detailed picture of proton transfer processes encounters several challenges: the constant potential requirement during charge transfer, the different time scales involved in the processes, and the thermal fluctuation of the solvent. Hence, it is prohibitively expensive computationally to apply density functional theory (DFT) calculations in modeling the potential-dependent activation barrier at the electrode-solvent interface, and the results are dubious. To address these challenges, we have developed an analytical approach based on charge conservation and decoupled potential energy surfaces to compute charge transfer barriers. The method makes it possible to simulate an electrochemical process at different potentials and explicitly include thermal fluctuations of the solvent at the electrode-solvent interface. We use the Pt-catalyzed alkaline hydrogen evolution reaction (HER) as our benchmark reaction, and we model the microkinetics of HER with consideration of the spatial fluctuations between the metal surface and the first solvent layer at room temperature. The distribution of water-metal distances has a large effect on the barriers of the charge transfer processes, and an accurate account of the statistical fluctuation in the reaction network leads to a several orders of magnitude increase in HER current as compared to transfer from a static solvent. The trends of the different reaction mechanisms in HER were successfully simulated with our model, and the theoretical I-V curves obtained are in good qualitative agreement with experimental results.

Ultrafast Valence-Electron Dynamics in Oxazole Monitored by X-ray Diffraction Following a Stimulated X-ray Raman Excitation

Direct imaging of the ultrafast quantum motion of valence electrons in molecules is essential for understanding many elementary chemical and physical processes. We present a simulation study of valence-electron dynamics of oxazole. A valence-state electronic wavepacket is prepared with an attosecond soft X-ray pulse through a stimulated resonant X-ray Raman process and then probed with time-resolved off-resonant single-molecule X-ray diffraction. We find that the time dependent diffraction signal originates solely from the electronic coherences and can be detected by existing experimental techniques. We thus provide a feasible way of imaging electron dynamics in molecules. Moreover, the created electronic coherences and subsequent electron dynamics can be manipulated by the resonant X-ray Raman excitation tuned to different core-excited states.

Attochemistry: Is Controlling Electrons the Future of Photochemistry?

Controlling matter with light has always been a great challenge, leading to the ever-expanding field of photochemistry. In addition, since the first generation of light pulses of attosecond (1 as = 10^-18 s) duration, a great deal of effort has been devoted to observing and controlling electrons on their intrinsic time scale. Because of their short duration, attosecond pulses have a large spectral bandwidth populating several electronically excited states in a coherent manner, i.e., an electronic wavepacket. Because of interference, such a wavepacket has a new electronic distribution implying a potentially different and totally new reactivity as compared to traditional photochemistry, leading to the novel concept of "attochemistry". This nascent field requires the support of theory right from the start. In this Perspective, we discuss the opportunities offered by attochemistry, the related challenges, and the current and future state-of-the-art developments in theoretical chemistry needed to model it accurately.

Unlocking the Double Bond in Protonated Schiff Bases by Coherent Superposition of S1 and S2

The primary event occurring during the E-to-Z photoisomerization reaction of retinal protonated Schiff base (rPSB) is single-to-double bond inversion. In this work we examine the nuclear dynamics that occurs when the initial excited state is a superposition of the S₁ and S₂ electronic excited states that might be created in a laser experiment. The nuclear dynamics is dominated by double bond inversion that is parallel to the derivative coupling vector of S₁ and S₂. Thus, the molecule behaves as if it were at a conical intersection even if the states are nondegenerate.

Electron Dynamics with the Time-Dependent Density Matrix Renormalization Group

In this work, we simulate the electron dynamics in molecular systems with the time-dependent density matrix renormalization group (TD-DMRG) algorithm. We leverage the generality of the so-called tangent-space TD-DMRG formulation and design a computational framework in which the dynamics is driven by the exact nonrelativistic electronic Hamiltonian. We show that by parametrizing the wave function as a matrix product state, we can accurately simulate the dynamics of systems including up to 20 electrons and 32 orbitals. We apply the TD-DMRG algorithm to three problems that are hardly targeted by time-independent methods: the calculation of molecular (hyper)polarizabilities, the simulation of electronic absorption spectra, and the study of ultrafast ionization dynamics.

Real-time dynamics of strongly correlated fermions using auxiliary field quantum Monte Carlo

Spurred by recent technological advances, there is a growing demand for computational methods that can accurately predict the dynamics of correlated electrons. Such methods can provide much-needed theoretical insights into the electron dynamics probed via time-resolved spectroscopy experiments and observed in non-equilibrium ultracold atom experiments. In this article, we develop and benchmark a numerically exact Auxiliary Field Quantum Monte Carlo (AFQMC) method for modeling the dynamics of correlated electrons in real time. AFQMC has become a powerful method for predicting the ground state and finite temperature properties of strongly correlated systems mostly by employing constraints to control the sign problem. Our initial goal in this work is to determine how well AFQMC generalizes to real-time electron dynamics problems without constraints. By modeling the repulsive Hubbard model on different lattices and with differing initial electronic configurations, we show that real-time AFQMC is capable of accurately capturing long-lived electronic coherences beyond the reach of mean field techniques. While the times to which we can meaningfully model decrease with increasing correlation strength and system size as a result of the exponential growth of the dynamical phase problem, we show that our technique can model the short-time behavior of strongly correlated systems to very high accuracy. Crucially, we find that importance sampling, combined with a novel adaptive active space sampling technique, can substantially lengthen the times to which we can simulate. These results establish real-time AFQMC as a viable technique for modeling the dynamics of correlated electron systems and serve as a basis for future sampling advances that will further mitigate the dynamical phase problem.

On the quantum and classical control of laser-driven isomerization in the Wigner representation

We investigate the validity of the classical approximation to the numerically exact quantum dynamics for infrared laser-driven control of isomerization processes. To this end, we simulate the fully quantum mechanical dynamics both by wavepacket propagation in position space and by propagating the Wigner function in phase space employing a quantum-mechanical correction term. A systematic comparison is made with purely classical propagation of the Wigner function. On the example of a one-dimensional double well potential, we identify two complementary classes of pulse sequences that invoke either a quantum mechanically or a classically dominated control mechanism. The quantum control relies on a sequence of excitations and de-excitations between the system's eigenstates on a time scale far exceeding the characteristic vibrational oscillation periods. In contrast, the classical control mechanism is based on a short and strong few-cycle field exerting classical-like forces driving the wavepacket to the target potential well where it is slowed down and finally trapped. While in the first case, only the quantum mechanical propagation correctly describes the field-induced population transfer, the short pulse case is also amenable to a purely classical description. These findings shed light on the applicability of classical approximations to simulate laser-controlled dynamics and may offer a guideline for novel control experiments in more complex systems that can be analyzed and interpreted utilizing efficient state-of-the-art classical trajectory simulations based on ab initio molecular dynamics.

Spontaneous electron emission vs dissociation in internally hot silver dimer anions

Referring to a recent experiment, we theoretically study the process of a two-channel decay of the diatomic silver anion (Ag₂ ^-), namely, the spontaneous electron ejection giving Ag₂ + e^- and the dissociation leading to Ag^- + Ag. The ground state potential energy curves of the silver molecules of diatomic neutral and negative ions were calculated using proper pseudo-potentials and atomic basis sets. We also estimated the non-adiabatic electronic coupling between the ground state of Ag₂ ^- and the ground state of Ag₂ + e^-, which, in turn, allowed us to estimate the minimal and mean values of the electron autodetachment lifetimes. The relative energies of the rovibrational levels allow the description of the spontaneous electron emission process, while the description of the rotational dissociation is treated with the quantum dynamics method as well as time-independent methods. The results of our calculations are verified by comparison with the experimental data.

Coupled nuclear and electron dynamics in the vicinity of a conical intersection

Ultrafast optical techniques allow us to study ultrafast molecular dynamics involving both nuclear and electronic motion. To support interpretation, theoretical approaches are needed that can describe both the nuclear and electron dynamics. Hence, we revisit and expand our ansatz for the coupled description of the nuclear and electron dynamics in molecular systems (NEMol). In this purely quantum mechanical ansatz, the quantum-dynamical description of the nuclear motion is combined with the calculation of the electron dynamics in the eigenfunction basis. The NEMol ansatz is applied to simulate the coupled dynamics of the molecule NO₂ in the vicinity of a conical intersection (CoIn) with a special focus on the coherent electron dynamics induced by the non-adiabatic coupling. Furthermore, we aim to control the dynamics of the system when passing the CoIn. The control scheme relies on the carrier envelope phase of a few-cycle IR pulse. The laser pulse influences both the movement of the nuclei and the electrons during the population transfer through the CoIn.

Molecular Modes of Attosecond Charge Migration

First-principles calculations are employed to elucidate the modes of attosecond charge migration (CM) in halogenated hydrocarbon chains. We use constrained density functional theory (DFT) to emulate the creation of a localized hole on the halogen and follow the subsequent dynamics via time-dependent DFT. We find low-frequency CM modes (∼1  eV) that propagate across the molecule and study their dependence on length, bond order, and halogenation. We observe that the CM speed (∼4  Å/fs) is largely independent of molecule length, but is lower for triple-bonded versus double-bonded molecules. Additionally, as the halogen mass increases, the hole travels in a more particlelike manner as it moves across the molecule. These heuristics will be useful in identifying molecules and optimal CM detection methods for future experiments, especially for halogenated hydrocarbons which are promising targets for ionization-triggered CM.

Control of nuclear dynamics in the benzene cation by electronic wavepacket composition

The study of coupled electron-nuclear dynamics driven by coherent superpositions of electronic states is now possible in attosecond science experiments. The objective is to understand the electronic control of chemical reactivity. In this work we report coherent 8-state non-adiabatic electron-nuclear dynamics simulations of the benzene radical cation. The computations were inspired by the extreme ultraviolet (XUV) experimental results in which all 8 electronic states were prepared with significant population. Our objective was to study the nuclear dynamics using various bespoke coherent electronic state superpositions as initial conditions in the Quantum-Ehrenfest method. The original XUV measurements were supported by Multi-configuration time-dependent Hartree (MCTDH) simulations, which suggested a model of successive passage through conical intersections. The present computations support a complementary model where non-adiabatic events are seen far from a conical intersection and are controlled by electron dynamics involving non-adjacent adiabatic states. It proves to be possible to identify two superpositions that can be linked with two possible fragmentation paths.

Waveform control of molecular dynamics close to a conical intersection

Conical intersections are ubiquitous in chemical systems but, nevertheless, extraordinary points on the molecular potential energy landscape. They provide ultra-fast radiationless relaxation channels, their topography influences the product branching, and they equalize the timescales of the electron and nuclear dynamics. These properties reveal optical control possibilities in the few femtosecond regime. In this theoretical study, we aim to explore control options that rely on the carrier envelope phase of a few-cycle IR pulse. The laser interaction creates an electronic superposition just before the wave packet reaches the conical intersection. The imprinted phase information is varied by the carrier envelope phase to influence the branching ratio after the conical intersection. We test and analyze this scenario in detail for a model system and show to what extent it is possible to transfer this type of control to a realistic system like uracil.

Opening a new route to multiport coherent XUV sources via intracavity high-order harmonic generation

High-order harmonic generation (HHG) is currently utilized for developing compact table-top radiation sources to provide highly coherent extreme ultraviolet (XUV) and soft X-ray pulses; however, the low repetition rate of fundamental lasers, which is typically in the multi-kHz range, restricts the area of application for such HHG-based radiation sources. Here, we demonstrate a novel method for realizing a MHz-repetition-rate coherent XUV light source by utilizing intracavity HHG in a mode-locked oscillator with an Yb:YAG thin disk laser medium and a 100-m-long ring cavity. We have successfully implemented HHG by introducing two different rare gases into two separate foci and picking up each HH beam. Owing to the two different HH beams generated from one cavity, this XUV light source will open a new route to performing a time-resolved measurement with an XUV-pump and XUV-probe scheme at a MHz-repetition rate with a femtosecond resolution.

Ultrafast X-ray photoelectron diffraction in triatomic molecules by circularly polarized attosecond light pulses

We theoretically study ultrafast photoelectron diffraction in triatomic molecules with cyclic geometry by ultrafast circular soft X-ray attosecond pulses.

Progress and Perspectives of Electrochemical CO2 Reduction on Copper in Aqueous Electrolyte

To date, copper is the only heterogeneous catalyst that has shown a propensity to produce valuable hydrocarbons and alcohols, such as ethylene and ethanol, from electrochemical CO₂ reduction (CO₂R). There are variety of factors that impact CO₂R activity and selectivity, including the catalyst surface structure, morphology, composition, the choice of electrolyte ions and pH, and the electrochemical cell design. Many of these factors are often intertwined, which can complicate catalyst discovery and design efforts. Here we take a broad and historical view of these different aspects and their complex interplay in CO₂R catalysis on Cu, with the purpose of providing new insights, critical evaluations, and guidance to the field with regard to research directions and best practices. First, we describe the various experimental probes and complementary theoretical methods that have been used to discern the mechanisms by which products are formed, and next we present our current understanding of the complex reaction networks for CO₂R on Cu. We then analyze two key methods that have been used in attempts to alter the activity and selectivity of Cu: nanostructuring and the formation of bimetallic electrodes. Finally, we offer some perspectives on the future outlook for electrochemical CO₂R.

A fast and adaptable method for high accuracy integration of the time-dependent Schrödinger equation

We present an adaptable, fast, and robust method for integrating the time-dependent Schrödinger equation. We apply the method to calculations of High Harmonic (HHG) and Above Threshold Ionisation (ATI) spectra for a single atomic electron in an intense laser field. Our approach implements the stabilized bi-conjugate gradient method (BiCG-STAB) for solving a sparse linear system to evolve the electronic wavefunction in time. The use of this established method makes the propagation scheme less restrictive compared to other schemes which may have particular requirements for the form of the equation, such as use of a three-point finite-difference approximation for spatial derivatives. Our method produces converged solutions significantly faster than existing methods, particularly if high accuracy is required. We demonstrate that this approach is suitable for a range of different parameters and show that in many circumstances significant gains can be made with the use of a fourth-order time propagator as opposed to the more common second-order Crank-Nicolson (CN) method.

An efficient approximate algorithm for nonadiabatic molecular dynamics

We propose a modification to the nonadiabatic surface hopping calculation method formulated in a paper by Yu et al. [Phys. Chem. Chem. Phys. 16, 25883 (2014)], which is a multidimensional extension of the Zhu-Nakamura theory with a practical diabatic gradient estimation algorithm. In our modification, their diabatic gradient estimation algorithm, which is based on a simple interpolation of the adiabatic potential energy surfaces, is replaced by an algorithm using the numerical derivatives of the adiabatic gradients. We then apply the algorithm to several models of nonadiabatic dynamics, both analytic and ab initio models, to numerically demonstrate that our method indeed widens the applicability and robustness of their method. We also discuss the validity and limitations of our new nonadiabatic surface hopping method while considering in mind potential applications to excited-state dynamics of biomolecules or unconventional nonadiabatic dynamics such as radiation decay processes in ultraintense X-ray fields.

Attosecond Pulse Shaping by Multilayer Mirrors

The emerging research field of attosecond science allows for the temporal investigation of one of the fastest dynamics in nature: electron dynamics in matter. These dynamics are responsible for chemical and biological processes, and the ability to understand and control them opens a new door of fundamental science, with the possibility to influence all lives if medical issues can thereby be addressed. Multilayer optics are key elements in attosecond experiments; they are used to tailor attosecond pulses with well-defined characteristics to facilitate detailed and accurate insight into processes, e.g., photoemission, Auger decay, or (core-) excitons. Based on the investigations and research efforts from the past several years, multilayer mirrors today are routinely used optical elements in attosecond beamlines. As a consequence, the generation of ultrashort pulses, combined with their dispersion control, has proceeded from the femtosecond range in the visible/infrared spectra to the attosecond range, covering the extreme ultraviolet and soft X-ray photon range up to the water window. This article reviews our work on multilayer optics over the past several years, as well as the impact from other research groups, to reflect on the scientific background of their nowadays routine use in attosecond physics.

Atomic and Molecular Processes in a Strong Bicircular Laser Field

With the development of intense femtosecond laser sources it has become possible to study atomic and molecular processes on their own subfemtosecond time scale. Table-top setups are available that generate intense coherent radiation in the extreme ultraviolet and soft-X-ray regime which have various applications in strong-field physics and attoscience. More recently, the emphasis is moving from the generation of linearly polarized pulses using a linearly polarized driving field to the generation of more complicated elliptically polarized polychromatic ultrashort pulses. The transverse electromagnetic field oscillates in a plane perpendicular to its propagation direction. Therefore, the two dimensions of field polarization plane are available for manipulation and tailoring of these ultrashort pulses. We present a field that allows such a tailoring, the so-called bicircular field. This field is the superposition of two circularly polarized fields with different frequencies that rotate in the same plane in opposite directions. We present results for two processes in a bicircular field: High-order harmonic generation and above-threshold ionization. For a wide range of laser field intensities, we compare high-order harmonic spectra generated by bicircular fields with the spectra generated by a linearly polarized laser field. We also investigate a possibility of introducing spin into attoscience with spin-polarized electrons produced in high-order above-threshold ionization by a bicircular field.

The Ehrenfest method with fully quantum nuclear motion (Qu-Eh): Application to charge migration in radical cations

An algorithm is described for quantum dynamics where an Ehrenfest potential is combined with fully quantum nuclear motion (Quantum-Ehrenfest, Qu-Eh). The method is related to the single-set variational multi-configuration Gaussian approach (vMCG) but has the advantage that only a single quantum chemistry computation is required at each time step since there is only a single time-dependent potential surface. Also shown is the close relationship to the "exact factorization method." The quantum Ehrenfest method is compared with vMCG for study of electron dynamics in a modified bismethylene-adamantane cation system. Illustrative examples of electron-nuclear dynamics are presented for a distorted allene system and for HCCI⁺ where one has a degenerate Π system.

Attosecond Pump-Probe Spectroscopy of Charge Dynamics in Tryptophan

Attosecond pump-probe experiments performed in small molecules have allowed tracking charge dynamics in the natural time scale of electron motion. That this is also possible in biologically relevant molecules is still a matter of debate, because the large number of available nuclear degrees of freedom might destroy the coherent charge dynamics induced by the attosecond pulse. Here we investigate extreme ultraviolet-induced charge dynamics in the amino acid tryptophan. We find that, although nuclear motion and nonadiabatic effects introduce some decoherence in the moving electron wave packet, these do not significantly modify the coherence induced by the attosecond pulse during the early stages of the dynamics, at least for molecules in their equilibrium geometry. Our conclusions are based on elaborate theoretical calculations and the experimental observation of sub-4 fs dynamics, which can only be reasonably assigned to electronic motion. Hence, attosecond pump-probe spectroscopy appears as a promising approach to induce and image charge dynamics in complex molecules.

Real-Time Imaging of Ultrafast Charge Dynamics in Tetrafluoromethane from Attosecond Pump-Probe Photoelectron Spectroscopy

A pump-probe experiment in the tetrafluoro-methane (CF₄ ) molecule has been theoretically simulated, allowing one to access electron dynamics in its natural time scale: the attosecond. The chosen pump and probe pulses can be currently produced in most attosecond laboratories. In this scheme, CF₄ is first ionized by an extreme UV (XUV) attosecond pulse and the charge dynamics induced in the corresponding cation is probed with a few-femtosecond visible light (VIS) pulse. We demonstrate that modulations in the calculated photoelectron spectra with the pump-probe delay reflect the dynamics of the XUV-induced electronic wave packet. In particular, from the analysis of these modulations in the interval of time delays where the pump and probe pulses do not overlap any more, one has access to the amplitudes and phases of the different components of the electronic wave packet generated by the attosecond pulse. These reflect a complex dynamics that basically consists of very fast charge fluctuations occurring all over the molecule without any preference for a particular molecular site.

Helicity asymmetry in strong-field ionization of atoms by a bicircular laser field

Ionization of atoms by an intense bicircular laser field is considered, which consists of two coplanar corotating or counterrotating circularly polarized field components with frequencies that are integer multiples of a fundamental frequency. Emphasis is on the effect of a reversal of the helicities of the two field components on the photoelectron spectra. The velocity maps of the liberated electrons are calculated using the direct strong-field approximation (SFA) and its improved version (ISFA), which takes into account rescattering off the parent ion. Under the SFA all symmetries of the driving field are preserved in the velocity map while the ISFA violates certain reflection symmetries. This allows one to assess the significance of rescattering in actual data obtained from an experiment or a numerical simulation.

Universal route to optimal few- to single-cycle pulse generation in hollow-core fiber compressors

Gas-filled hollow-core fiber (HCF) pulse post-compressors generating few- to single-cycle pulses are a key enabling tool for attosecond science and ultrafast spectroscopy. Achieving optimum performance in this regime can be extremely challenging due to the ultra-broad bandwidth of the pulses and the need of an adequate temporal diagnostic. These difficulties have hindered the full exploitation of HCF post-compressors, namely the generation of stable and high-quality near-Fourier-transform-limited pulses. Here we show that, independently of conditions such as the type of gas or the laser system used, there is a universal route to obtain the shortest stable output pulse down to the single-cycle regime. Numerical simulations and experimental measurements performed with the dispersion-scan technique reveal that, in quite general conditions, post-compressed pulses exhibit a residual third-order dispersion intrinsic to optimum nonlinear propagation within the fiber, in agreement with measurements independently performed in several laboratories around the world. The understanding of this effect and its adequate correction, e.g. using simple transparent optical media, enables achieving high-quality post-compressed pulses with only minor changes in existing setups. These optimized sources have impact in many fields of science and technology and should enable new and exciting applications in the few- to single-cycle pulse regime.

Quantum control of coherent π-electron ring currents in polycyclic aromatic hydrocarbons

We present results for quantum optimal control (QOC) of the coherent π electron ring currents in polycyclic aromatic hydrocarbons (PAHs). Since PAHs consist of a number of condensed benzene rings, in principle, there exist various coherent ring patterns. These include the ring current localized to a designated benzene ring, the perimeter ring current that flows along the edge of the PAH, and the middle ring current of PAHs having an odd number of benzene rings such as anthracene. In the present QOC treatment, the best target wavefunction for generation of the ring current through a designated path is determined by a Lagrange multiplier method. The target function is integrated into the ordinary QOC theory. To demonstrate the applicability of the QOC procedure, we took naphthalene and anthracene as the simplest examples of linear PAHs. The mechanisms of ring current generation were clarified by analyzing the temporal evolutions of the electronic excited states after coherent excitation by UV pulses or (UV+IR) pulses as well as those of electric fields of the optimal laser pulses. Time-dependent simulations of the perimeter ring current and middle ring current of anthracene, which are induced by analytical electric fields of UV pulsed lasers, were performed to reproduce the QOC results.

Population density gratings induced by few-cycle optical pulses in a resonant medium

Creation, erasing and ultrafast control of population density gratings using few-cycle optical pulses coherently interacting with resonant medium is discussed. In contrast to the commonly used schemes, here the pulses do not need to overlap in the medium, interaction between the pulses is mediated by excitation of polarization waves. We investigate the details of the dynamics arising in such ultrashort pulse scheme and develop an analytical theory demonstrating the importance of the phase memory effects in the dynamics.

Photoinduced Ultrafast Charge Transfer and Charge Migration in Small Gold Clusters Passivated by a Chromophoric Ligand

Because the development of attopulses, charge migration induced by short optical pulses has been extensively investigated. We report a computational purely electronic dynamical study of ultrafast few femtoseconds (fs) charge transfer and charge migration in realistic passivated stoichiometric Au₁₁ and Au₂₀ gold nanoclusters functionalized by a bipyridine ligand. We show that a net significant amount of electronic charge (0.1 to 0.4 |e| where |e| is the electron charge) is permanently transferred from the bipyridine chromophore to the gold cluster during the short 5-6 fs UV-vis strong pulse. This electron transfer to the metallic core is induced by the optical excitation of electronic states with a partial charge transfer character involving the chromophore before the onset of nuclei motion. In addition, the photoexcitation by the strong fs pulse builds a nonequilibrium electronic density that beats between the chromophore and the metallic core around the average of the transferred value. Modular systems made of a donor chromophore that can be photoexcited in the UV-vis range coupled to an efficient acceptor that could trap the charge are of interest for applications to nanodevices. Our study provides understanding on the very early, purely electronic dynamics built by the fs optical excitation and the initial charge separation step.

Pumping and probing vibrational modulated coupled electronic coherence in HCN using short UV fs laser pulses: a 2D quantum nuclear dynamical study

The coupled electronic-nuclear coherent dynamics induced by a short strong VUV fs pulse in the low excited electronic states of HCN is probed by transient absorption spectroscopy with a second weaker fs UV pulse. The nuclear time-dependent Schrodinger equation is solved on a 2D nuclear grid with several electronic states with a Hamiltonian including the dipole coupling to the pump and the probe electric fields. The two internal nuclear coordinates describe the motion of the light H atom. There is a band of several excited electronic states at about 8 eV above the ground state (GS) that is transiently accessed by the pump pulse. We tailored the pump so as to selectively populate the lowest 1A'' electronic state thereby the pulse creates an electronic coherence with the GS. Our simulations show that this electronic coherence is modulated by the nuclear motion and persists all the way to dissociation on the 1A'' state. Transient absorption spectra computed as a function of the delay time between the pump and the probe pulses provide a detailed probe of the electronic amplitude and its phase, as well as of the modulation of the electronic coherence by the nuclear motion, both bound and dissociative.

Development of a 10 kHz high harmonic source up to 140 eV photon energy for ultrafast time-, angle-, and phase-resolved photoelectron emission spectroscopy on solid targets

We present a newly developed high harmonic beamline for time-, angle-, and carrier-envelope phase-resolved extreme ultraviolet photoemission spectroscopy on solid targets for the investigation of ultrafast band structure dynamics in the low-fs to sub-fs time regime. The source operates at a repetition rate of 10 kHz and is driven by 5 fs few-cycle near-infrared laser pulses generating high harmonic radiation with photon energies up to 120 eV at a feasible flux. The experimental end station consists of a complementary combination of photoelectron detectors which are able to spectroscopically address electron dynamics both in real and in k-space. The versatility of the source is completed by a phase-meter which allows for tracking the carrier-envelope phase for each pulse and which is synchronized to the photoelectron detectors, thus enabling phase sensitive measurements on the one hand and the selection of single attosecond pulses for ultimate time resolution in pump-probe experiments on the other hand. We demonstrate the applicability of the source by an angle- and carrier-envelope phase-resolved photoemission measurement on a tungsten (110) surface with 95 eV extreme ultraviolet radiation.

Generation of unipolar half-cycle pulses via unusual reflection of a single-cycle pulse from an optically thin metallic or dielectric layer

We propose a strikingly simple method to form approximately unipolar half-cycle optical pulses via reflection of a single-cycle optical pulse from a thin flat metallic or dielectric layer. Unipolar pulses in reflection arise due to specifics of one-dimensional pulse propagation. Namely, we show that the field emitted by the layer is proportional to the velocity of the oscillating charges in the medium, instead of their acceleration. Besides, the oscillation velocity of the charges can be forced to keep a constant sign throughout the pulse duration. That is, reflection of ultrashort pulses from broad-area layers with nanometer-scale thickness can be very different from the common reflection in the case of longer pulses and thicker layers. This suggests a possibility of unusual transformations of few-cycle light pulses in completely linear optical systems.