Analytical Model of Optical-Field-Driven Subcycle Electron Tunneling Pulses from Two-Dimensional Materials

We develop analytical models of optical-field-driven electron tunneling from the edge and surface of free-standing two-dimensional (2D) materials. We discover a universal scaling between the tunneling current density (J) and the electric field near the barrier (F): In(J/|F|β) ∝ 1/|F| with β values of 3/2 and 1 for edge emission and vertical surface emission, respectively. At ultrahigh values of F, the current density exhibits an unexpected high-field saturation effect due to the reduced dimensionality of the 2D material, which is absent in the traditional bulk material. Our calculation reveals the dc bias as an efficient method for modulating the optical-field tunneling subcycle emission characteristics. Importantly, our model is in excellent agreement with a recent experiment on graphene. Our results offer a useful framework for understanding optical-field tunneling emission from 2D materials, which are helpful for the development of optoelectronics and emerging petahertz vacuum nanoelectronics.

Light-wave-controlled Haldane model in monolayer hexagonal boron nitride

In recent years, the stacking and twisting of atom-thin structures with matching crystal symmetry has provided a unique way to create new superlattice structures in which new properties emerge1,2. In parallel, control over the temporal characteristics of strong light fields has allowed researchers to manipulate coherent electron transport in such atom-thin structures on sublaser-cycle timescales3,4. Here we demonstrate a tailored light-wave-driven analogue to twisted layer stacking. Tailoring the spatial symmetry of the light waveform to that of the lattice of a hexagonal boron nitride monolayer and then twisting this waveform result in optical control of time-reversal symmetry breaking5 and the realization of the topological Haldane model6 in a laser-dressed two-dimensional insulating crystal. Further, the parameters of the effective Haldane-type Hamiltonian can be controlled by rotating the light waveform, thus enabling ultrafast switching between band structure configurations and allowing unprecedented control over the magnitude, location and curvature of the bandgap. This results in an asymmetric population between complementary quantum valleys that leads to a measurable valley Hall current7, which can be detected by optical harmonic polarimetry. The universality and robustness of our scheme paves the way to valley-selective bandgap engineering on the fly and unlocks the possibility of creating few-femtosecond switches with quantum degrees of freedom.

Perspectives: Light Control of Magnetism and Device Development

Accurately controlling magnetic and spin states presents a significant challenge in spintronics, especially as demands for higher data storage density and increased processing speeds grow. Approaches such as light control are gradually supplanting traditional magnetic field methods. Traditionally, the modulation of magnetism was predominantly achieved through polarized light with the help of ultrafast light technologies. With the growing demand for energy efficiency and multifunctionality in spintronic devices, integrating photovoltaic materials into magnetoelectric systems has introduced more physical effects. This development suggests that sunlight will play an increasingly pivotal role in manipulating spin orientation in the future. This review introduces and concludes the influence of various light types on magnetism, exploring mechanisms such as magneto-optical (MO) effects, light-induced magnetic phase transitions, and spin photovoltaic effects. This review briefly summarizes recent advancements in the light control of magnetism, especially sunlight, and their potential applications, providing an optimistic perspective on future research directions in this area.

Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics

The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. In this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.

Observation of interband Berry phase in laser-driven crystals

Ever since its discovery1, the notion of the Berry phase has permeated all branches of physics and plays an important part in a variety of quantum phenomena2. However, so far all its realizations have been based on a continuous evolution of the quantum state, following a cyclic path. Here we introduce and demonstrate a conceptually new manifestation of the Berry phase in light-driven crystals, in which the electronic wavefunction accumulates a geometric phase during a discrete evolution between different bands, while preserving the coherence of the process. We experimentally reveal this phase by using a strong laser field to engineer an internal interferometer, induced during less than one cycle of the driving field, which maps the phase onto the emission of higher-order harmonics. Our work provides an opportunity for the study of geometric phases, leading to a variety of observations in light-driven topological phenomena and attosecond solid-state physics.

Free light-shape focusing in extreme-ultraviolet radiation with self-evolutionary photon sieves

Extreme-ultraviolet (EUV) radiation is a promising tool, not only for probing microscopic activities but also for processing nanoscale structures and performing high-resolution imaging. In this study, we demonstrate an innovative method to generate free light-shape focusing with self-evolutionary photon sieves under a single-shot coherent EUV laser; this includes vortex focus shaping, array focusing, and structured-light shaping. The results demonstrate that self-evolutionary photon sieves, consisting of a large number of specific pinholes fabricated on a piece of Si3N4 membrane, are capable of freely regulating an EUV light field, for which high-performance focusing elements are extremely lacking, let alone free light-shape focusing. Our proposed versatile photon sieves are a key breakthrough in focusing technology in the EUV region and pave the way for high-resolution soft X-ray microscopy, spectroscopy in materials science, shorter lithography, and attosecond metrology in next-generation synchrotron radiation and free-electron lasers.

Characterizing Anomalous High-Harmonic Generation in Solids

Anomalous high-harmonic generation (HHG) arises in certain solids when irradiated by an intense laser field, originating from a Berry-curvature-induced perpendicular anomalous current. The observation of pure anomalous harmonics is, however, often prohibited by contamination from harmonics stemming from interband coherences. Here, we fully characterize the anomalous HHG mechanism, via development of an ab initio methodology for strong-field laser-solid interaction that allows a rigorous decomposition of the total current. We identify two unique properties of the anomalous harmonic yields: an overall yield increase with laser wavelength; and pronounced minima at certain laser wavelengths and laser intensities around which the spectral phases drastically change. Such signatures can be exploited to disentangle the anomalous harmonics from competing HHG mechanisms, and thus pave the way for the experimental identification and time-domain control of pure anomalous harmonics, as well as reconstruction of Berry curvatures.

Attosecond Monitoring of Nonadiabatic Molecular Dynamics by Transient X-ray Transmission Spectroscopy

Tracing the evolution of molecular coherences can provide a direct, unambiguous probe of nonadiabatic molecular processes, such as the passage through conical intersections of electronic states. Two techniques, attosecond transient absorption spectroscopy (ATAS) and Transient Redistribution of Ultrafast Electronic Coherences in Attosecond Raman Signals (TRUECARS), have been used or proposed for monitoring nonadiabatic molecular dynamics. Both techniques employ the transmission of a weak attosecond extreme-ultraviolet or X-ray probe to interrogate the molecule at controllable time delays with respect to an optical pump, thereby extracting dynamical information from transient spectral features. The connection between these techniques has not been firmly established yet. In this theoretical study, we provide a unified description of both transient transmission techniques, establishing their relationship as limits of the same pump-probe spectroscopy technique for different pulse parameter regimes. We demonstrate this by quantum dynamical simulations of thiophenol photodissociation and show how complementary coherence information can be revealed by the two techniques.

Build-up and dephasing of Floquet-Bloch bands on subcycle timescales

Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.

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.

Investigation of the Spatio-Temporal Characteristics of High-Order Harmonic Generation Using a Bohmian Trajectory Scheme

High-order harmonic generation of atoms irradiated by an ultrashort laser pulse was calculated by numerically solving the time-dependent Schrödinger equation and the Bohmian trajectory scheme. The harmonic spectra with the two schemes are quantitatively consistent. Using the wavelet behavior of the Bohmian trajectory, the spatio-temporal features of harmonic emission from different energy regions are analyzed. It is found that the spatio-temporal distribution of the harmonic well revealed the physical mechanism of harmonic generation. This method will contribute to the understanding of harmonic emission mechanisms in complex systems, which include many atoms.

Efficient All-Electron Time-Dependent Density Functional Theory Calculations Using an Enriched Finite Element Basis

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with a compactly supported numerical atom-centered basis, obtained from atomic ground-state DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on a priori error estimates to guide our choice of an adaptive finite element mesh as well as the time step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretizations. Notably, we attain a 50-100 times speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear responses by studying the absorption spectra in sodium clusters, the linear to nonlinear response transition in the green fluorescence protein chromophore, and the higher harmonic generation in the magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to ∼1000 processors, using a benchmark system of a 50-atom sodium nanocluster.

High harmonic generation enhanced by magnetic dipole resonance in an amorphous silicon metasurface

We report on the enhancement of high harmonic generation (HHG) yield in a metasurface consisting of amorphous silicon disks in a periodic array on an insulator substrate. The structure was designed and optimized using the finite-difference time-domain method for the maximum enhancement, which reaches the factor of 20-times compared to the unstructred surface. The local field is enhanced by a broadband magnetic resonance mode allowing to use ultrashort laser pulses with Fourier transform limit down to 40 fs. Due to the anisotropic structure of the metasurface, both the local-field enhancement and the HHG yield show strong polarization anisotropy.

Trajectory-controlled high-order harmonic generation in ZnO crystals

We experimentally and theoretically study high-order harmonic generation in zinc oxide crystals irradiated by mid-infrared lasers. The trajectories are mapped to the far field spatial distribution of harmonics. The divergence angles of on-axis and off-axis parts exhibit different dependences on the order of the harmonics. This observation can be theoretically reproduced by the coherent interference between the short and long trajectories with dephasing time longer than 0.5 optical cycle. Further, the relative contribution of the short and long trajectories is demonstrated to be accurately controlled by a one-color or two-color laser on the attosecond time scale. This work provides a reliable method to determine the electron dephasing time and demonstrates a versatile control of trajectory interference in the solid high-order harmonic generation.

Theoretical Approach for Electron Dynamics and Ultrafast Spectroscopy (EDUS)

In this manuscript, we present a theoretical framework and its numerical implementation to simulate the out-of-equilibrium electron dynamics induced by the interaction of ultrashort laser pulses in condensed-matter systems. Our approach is based on evolving in real time the density matrix of the system in reciprocal space. It considers excitonic and nonperturbative light-matter interactions. We show some relevant examples that illustrate the efficiency and flexibility of the approach to describe realistic ultrafast spectroscopy experiments. Our approach is suitable for modeling the promising and emerging ultrafast studies at the attosecond time scale that aim at capturing the electron dynamics and the dynamical electron-electron correlations via X-ray absorption spectroscopy.

Characterizing coherences in chemical dynamics with attosecond time-resolved x-ray absorption spectroscopy

Coherence can drive wave-like motion of electrons and nuclei in photoexcited systems, which can yield fast and efficient ways to exert materials’ functionalities beyond the thermodynamic limit. The search for coherent phenomena has been a central topic in chemical physics although their direct characterization is often elusive. Here, we highlight recent advances in time-resolved x-ray absorption spectroscopy (tr-XAS) to investigate coherent phenomena, especially those that utilize the eminent light source of isolated attosecond pulses. The unparalleled time and state sensitivities of tr-XAS in tandem with the unique element specificity render the method suitable to study valence electronic dynamics in a wide variety of materials. The latest studies have demonstrated the capabilities of tr-XAS to characterize coupled electronic–structural coherence in small molecules and coherent light–matter interactions of core-excited excitons in solids. We address current opportunities and challenges in the exploration of coherent phenomena, with potential applications for energy- and bio-related systems, potential crossings, strongly driven solids, and quantum materials. With the ongoing developments in both theory and light sources, tr-XAS holds great promise for revealing the role of coherences in chemical dynamics.

Bidirectional residual current in monolayer graphene under few-cycle laser irradiation

By numerically solving the time-dependent Schrödinger equation and semiconductor Bloch equations, the light-induced residual current in monolayer graphene driven by a circularly polarized few-cycle laser is investigated. An evident current direction reversal is disclosed when the amplitude of the driving electric field exceeds a certain threshold value, which is absent in recent investigation [Nature550, 224 (2017)10.1038/nature23900]. Here the internal physical mechanism for the current reversal is inter-optical-cycle interference under a suitable long laser wavelength. Moreover, the reversal-related laser field amplitude depends sensitively on the ratio of ponderomotive energy to photon energy.

Attosecond clocking of correlations between Bloch electrons

Delocalized Bloch electrons and the low-energy correlations between them determine key optical¹, electronic² and entanglement³ functionalities of solids, all the way through to phase transitions^4,5. To directly capture how many-body correlations affect the actual motion of Bloch electrons, subfemtosecond (1 fs = 10^-15 s) temporal precision^6-15 is desirable. Yet, probing with attosecond (1 as = 10^-18 s) high-energy photons has not been energy-selective enough to resolve the relevant millielectronvolt-scale interactions of electrons^1-5,16,17 near the Fermi energy. Here, we use multi-terahertz light fields to force electron-hole pairs in crystalline semiconductors onto closed trajectories, and clock the delay between separation and recollision with 300 as precision, corresponding to 0.7% of the driving field's oscillation period. We detect that strong Coulomb correlations emergent in atomically thin WSe₂ shift the optimal timing of recollisions by up to 1.2 ± 0.3 fs compared to the bulk material. A quantitative analysis with quantum-dynamic many-body computations in a Wigner-function representation yields a direct and intuitive view on how the Coulomb interaction, non-classical aspects, the strength of the driving field and the valley polarization influence the dynamics. The resulting attosecond chronoscopy of delocalized electrons could revolutionize the understanding of unexpected phase transitions and emergent quantum-dynamic phenomena for future electronic, optoelectronic and quantum-information technologies.

Absolute EUV reflectivity measurements using a broadband high-harmonic source and an in situ single exposure reference scheme

We present a tabletop setup for extreme ultraviolet (EUV) reflection spectroscopy in the spectral range from 40 to 100 eV by using high-harmonic radiation. The simultaneous measurements of reference and sample spectra with high energy resolution provide precise and robust absolute reflectivity measurements, even when operating with spectrally fluctuating EUV sources. The stability and sensitivity of EUV reflectivity measurements are crucial factors for many applications in attosecond science, EUV spectroscopy, and nano-scale tomography. We show that the accuracy and stability of our in situ referencing scheme are almost one order of magnitude better in comparison to subsequent reference measurements. We demonstrate the performance of the setup by reflective near-edge x-ray absorption fine structure measurements of the aluminum L_2/3 absorption edge in α-Al₂O₃ and compare the results to synchrotron measurements.

Single-shot compressed optical field topography

Femtosecond lasers are powerful in studying matter's ultrafast dynamics within femtosecond to attosecond time scales. Drawing a three-dimensional (3D) topological map of the optical field of a femtosecond laser pulse including its spatiotemporal amplitude and phase distributions, allows one to predict and understand the underlying physics of light interaction with matter, whose spatially resolved transient dielectric function experiences ultrafast evolution. However, such a task is technically challenging for two reasons: first, one has to capture in single-shot and squeeze the 3D information of an optical field profile into a two-dimensional (2D) detector; second, typical detectors are only sensitive to intensity or amplitude information rather than phase. Here we have demonstrated compressed optical field topography (COFT) drawing a 3D map for an ultrafast optical field in single-shot, by combining the coded aperture snapshot spectral imaging (CASSI) technique with a global 3D phase retrieval procedure. COFT can, in single-shot, fully characterize the spatiotemporal coupling of a femtosecond laser pulse, and live stream the light-speed propagation of an air plasma ionization front, unveiling its potential applications in ultrafast sciences.

Ultrafast bandgap narrowing and cohesion loss of photoexcited fused silica

Coupling and spatial localization of energy on ultrafast timescales and particularly on the timescale of the excitation pulse in ultrashort laser irradiated dielectric materials are key elements for enabling processing precision beyond the optical limit. Transforming matter on mesoscopic scales facilitates the definition of nanoscale photonic functions in optical glasses. On these timescales, quantum interactions induced by charge non-equilibrium become the main channel for energy uptake and transfer as well as for the material structural change. We apply a first-principles model to determine dynamic distortions of energy bands following the rapid increase in the free-carrier population in an amorphous dielectric excited by an ultrashort laser pulse. Fused silica glass is reproduced using a system of (SiO₄)^4- tetrahedra, where density functional theory extended to finite-temperature fractional occupation reproduces ground and photoexcited states. Triggered by electronic charge redistribution, a bandgap narrowing of more than 2 eV is shown to occur in fused silica under geometry relaxation. Calculations reveal that the bandgap decrease results from the rearrangement of atoms altering the bonding strength. Despite an atomic movement impacting strongly the structural stability, the observed change of geometry remains limited to 7% of the interatomic distance and occurs on the femtosecond timescale. This structural relaxation is thus expected to take place quasi-instantly following the photon energy flux. Moreover, under intense laser pulse excitation, fused silica loses its stability when an electron temperature of around 2.8 eV is reached. A further increase in the excitation energy leads to the collapse of both the structure and bandgap.

Direct observation of ultrafast exciton localization in an organic semiconductor with soft X-ray transient absorption spectroscopy

The localization dynamics of excitons in organic semiconductors influence the efficiency of charge transfer and separation in these materials. Here we apply time-resolved X-ray absorption spectroscopy to track photoinduced dynamics of a paradigmatic crystalline conjugated polymer: poly(3-hexylthiophene) (P3HT) commonly used in solar cell devices. The π→π^* transition, the first step of solar energy conversion, is pumped with a 15 fs optical pulse and the dynamics are probed by an attosecond soft X-ray pulse at the carbon K-edge. We observe X-ray spectroscopic signatures of the initially hot excitonic state, indicating that it is delocalized over multiple polymer chains. This undergoes a rapid evolution on a sub 50 fs timescale which can be directly associated with cooling and localization to form either a localized exciton or polaron pair.

A detailed understanding of ultrafast exciton dynamics is crucial for improving the efficiency of organic light-harvesting-devices. Here, the authors track exciton localization on a sub-50 fs timescale in an organic semiconductor using time resolved soft x-ray absorption spectroscopy.

Robust metallic micropatterns fabricated on quartz glass surfaces by femtosecond laser-induced selective metallization

Quartz glass has a wide range of application and commercial value due to its high light transmittance and stable chemical and physical properties. However, due to the difference in the characteristics of the material itself, the adhesion between the metal micropattern and the glass material is limited. This is one of the main things that affect the application of glass surface metallization in the industry. In this paper, micropatterns on the surface of quartz glass are fabricated by a femtosecond laser-induced backside dry etching (fs-LIBDE) method to generate the layered composite structure and the simultaneous seed layer in a single-step. This is achieved by using fs-LIBDE technology with metal base materials (Stainless steel, Al, Cu, Zr-based amorphous alloys, and W) with different ablation thresholds, where atomically dispersed high threshold non-precious metals ions are gathered across the microgrooves. On account of the strong anchor effect caused by the layered composite structures and the solid catalytic effect that is down to the seed layer, copper micropatterns with high bonding strength and high quality, can be directly prepared in these areas through a chemical plating process. After 20-min of sonication in water, no peeling is observed under repeated 3M scotch tape tests and the surface was polished with sandpapers. The prepared copper micropatterns are 18 µm wide and have a resistivity of 1.96 µΩ·cm (1.67 µΩ·cm for pure copper). These copper micropatterns with low resistivity has been proven to be used for the glass heating device and the transparent atomizing device, which could be potential options for various microsystems.

Highly efficient nonlinear optical emission from a subwavelength crystalline silicon cuboid mediated by supercavity mode

The low quantum efficiency of silicon (Si) has been a long-standing challenge for scientists. Although improvement of quantum efficiency has been achieved in porous Si or Si quantum dots, highly efficient Si-based light sources prepared by using the current fabrication technooloy of Si chips are still being pursued. Here, we proposed a strategy, which exploits the intrinsic excitation of carriers at high temperatures, to modify the carrier dynamics in Si nanoparticles. We designed a Si/SiO₂ cuboid supporting a quasi-bound state in the continuum (quasi-BIC) and demonstrated the injection of dense electron-hole plasma via two-photon-induced absorption by resonantly exciting the quasi-BIC with femtosecond laser pulses. We observed a significant improvement in quantum efficiency by six orders of magnitude to ~13%, which is manifested in the ultra-bright hot electron luminescence emitted from the Si/SiO₂ cuboid. We revealed that femtosecond laser light with transverse electric polarization (i.e., the electric field perpendicular to the length of a Si/SiO₂ cuboid) is more efficient for generating hot electron luminescence in Si/SiO₂ cuboids as compared with that of transverse magnetic polarization (i.e., the magnetic field perpendicular to the length of a Si/SiO₂ cuboid). Our findings pave the way for realizing on-chip nanoscale Si light sources for photonic integrated circuits and open a new avenue for manipulating the luminescence properties of semiconductors with indirect bandgaps.

Enhancing the efficiency of quantum emitters is essential for exploring new functionalities. Here the authors show Si cuboids that sustain bound states in the continuum enable the injection of dense electron-hole plasma and provide high quantum efficiency.

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.

New opportunities for ultrafast and highly enantio-sensitive imaging of chiral nuclear dynamics enabled by synthetic chiral light

Synthetic chiral light [D. Ayuso et al., Nat. Photon., 2019, 13, 866-871] has opened up new opportunities for ultrafast and highly efficient imaging and control of chiral matter. Here we show that the giant enantio-sensitivity enabled by such light could be exploited to probe chiral nuclear rearrangements during chemical reactions in a highly enantio-sensitive manner. Using a state-of-the-art implementation of real-time time-dependent density functional theory, we explore how the nonlinear response of the prototypical chiral molecule H₂O₂ changes as a function of its dihedral angle, which defines its handedness. The macroscopic intensity emitted from randomly oriented molecules at even harmonic frequencies (of the fundamental) depends strongly on this nuclear coordinate. Because of the ultrafast nature of such nonlinear interactions, the direct mapping between the dissymmetry factor and the nuclear geometry provides a way to probe chiral nuclear dynamics at their natural time scales. Our work paves the way for ultrafast and highly efficient imaging of enantio-sensitive dynamics in more complex chiral systems, including biologically relevant molecules.

Multiphoton Resonance in Attosecond Transient Absorption

We present the theory and simulation of attosecond transient absorption in helium atoms under the single-active-electron approximation. This study investigates the attosecond dynamics of intrinsic atomic states that interact with a field comprising vacuum ultraviolet (VUV) and extreme ultraviolet (XUV) fields. The absorption spectrum of the helium atom is obtained from the response function, which is constructed by numerically solving the three-dimensional time-dependent Schrödinger equation. We observe a fine structure near the intrinsic atomic level, which is modulated with a 0.2 fs period. Based on high-order time-dependent perturbation theory, the frequency-dependent phase of the dipole response induced by the VUV and XUV fields is analytically obtained, and the fine structure is well explained by the phase difference. In addition, the absorption fringes are dependent on the chirp of the VUV field. This study investigates the features of the attosecond transient absorption in the VUV region, which may have valuable applications in the study of ultrafast phenomena in atoms, molecules, and solids.

Reconstruction of ultrafast exciton dynamics with a phase-retrieval algorithm

The first step to gain optical control over the ultrafast processes initiated by light in solids is a correct identification of the physical mechanisms at play. Among them, exciton formation has been identified as a crucial phenomenon which deeply affects the electro-optical properties of most semiconductors and insulators of technological interest. While recent experiments based on attosecond spectroscopy techniques have demonstrated the possibility to observe the early-stage exciton dynamics, the description of the underlying exciton properties remains non-trivial. In this work we propose a new method called extended Ptychographic Iterative engine for eXcitons (ePIX), capable of reconstructing the main physical properties which determine the evolution of the quasi-particle with no prior knowledge of the exact relaxation dynamics or the pump temporal characteristics. By demonstrating its accuracy even when the exciton dynamics is comparable to the pump pulse duration, ePIX is established as a powerful approach to widen our knowledge of solid-state physics.

Proposal to generate a pair of intense independently tunable attosecond pulses from undulator radiation

We propose and numerically evaluate two schemes to generate a pair of extreme-ultraviolet monocycle pulses with gigawatt-level peak power, whose time delay and central wavelengths can be precisely controlled. The methods are based on coherent emission of radiation by an ultrarelativistic electron beam with a current profile given by a chirped sinusoid, which is generated through the interaction with a conventional broadband laser. The possibility to produce phase-locked attosecond pulses with independently tunable properties in the extreme-ultraviolet spectral region has the potential to significantly advance studies of charge dynamics in molecules of biological interests.

Spatially homogeneous few-cycle compression of Yb lasers via all-solid-state free-space soliton management

The high power and variable repetition-rate of Yb femtosecond lasers makes them very attractive for ultrafast science. However, for capturing sub-200 fs dynamics, efficient, high-fidelity and high-stability pulse compression techniques are essential. Spectral broadening using an all-solid-state free-space geometry is particularly attractive, as it is simple, robust and low-cost. However, spatial and temporal losses caused by spatio-spectral inhomogeneities have been a major challenge to date, due to coupled space-time dynamics associated with unguided nonlinear propagation. In this work, we use all-solid-state free-space compressors to demonstrate compression of 170 fs pulses at a wavelength of 1030nm from a Yb:KGW laser to ∼9.2 fs, with a highly spatially homogeneous mode. This is achieved by ensuring that the nonlinear beam propagation in periodic layered Kerr media occurs in spatial soliton modes, and by confining the nonlinear phase through each material layer to less than 1.0 rad. A remarkable spatio-spectral homogeneity of ∼0.87 can be realized, which yields a high efficiency of >50% for few-cycle compression. The universality of the method is demonstrated by implementing high-quality pulse compression under a wide range of laser conditions. The high spatiotemporal quality and the exceptional stability of the compressed pulses are further verified by high-harmonic generation. Our predictive method offers a compact and cost-effective solution for high-quality few-cycle-pulse generation from Yb femtosecond lasers, and will enable broad applications in ultrafast science and extreme nonlinear optics.

Divergence and efficiency optimization in polarization-controlled two-color high-harmonic generation

Improving the brightness of high-harmonic generation (HHG) sources is one of the major goals for next-generation ultrafast, imaging and metrology applications in the extreme-ultraviolet spectrum. Previous research efforts have demonstrated a plethora of techniques to increase the conversion efficiency of HHG. However, few studies so far have addressed how to simultaneously minimize the divergence and improve focusability, which all contribute to an increased brightness of the source. Here, we investigate how to improve both photon yield and divergence, which is directly linked to focusability, when adding the second harmonic to the fundamental driving field. We study the effects of the relative polarization in two-color HHG and compare the results to a one-color configuration. In a perpendicular two-color field, the relative phase between the two colors can be used to suppress or enhance recombination of either the long or the short trajectories. This allows to exert control over the divergence of the harmonics. In a parallel two-color field, the ionization rate is modified through the two-color phase, which selects trajectories during the ionization step. This enhances the total yield. We elaborate on the underlying mechanisms for parallel, perpendicular, and intermediate polarization angles, and confirm our experimental observations with simulations.

Two-step Brillouin zone sampling for efficient computation of electron dynamics in solids

We develop a numerical Brillouin-zone integration scheme for real-time propagation of electronic systems with time-dependent density functional theory. This scheme is based on the decomposition of a large simulation into a set of small independent simulations. The performance of the decomposition scheme is examined in both linear and nonlinear regimes by computing the linear optical properties of bulk silicon and high-order harmonic generation. The decomposition of a large simulation into a set of independent simulations can improve the efficiency of parallel computation by reducing communication and synchronization overhead and enhancing the portability of simulations across a relatively small cluster machine.

Carrier-Specific Hot Phonon Bottleneck in CH3NH3PbI3 Revealed by Femtosecond XUV Absorption

Femtosecond carrier cooling in the organohalide perovskite semiconductor CH₃NH₃PbI₃ is measured using extreme ultraviolet (XUV) and optical transient absorption spectroscopy. XUV absorption between 44 and 58 eV measures transitions from the I 4d core to the valence and conduction bands and gives distinct signals for hole and electron dynamics. The core-to-valence-band signal directly maps the photoexcited hole distribution and provides a quantitative measurement of the hole temperature. The combination of XUV and optical probes reveals that upon excitation at 400 nm, the initial hole distribution is 3.5 times hotter than the electron distribution. At an initial carrier density of 1.4 × 10²⁰ cm^-3 both carriers are subject to a hot phonon bottleneck, but at 4.2 × 10¹⁹ cm^-3 the holes cool to less than 1000 K within 400 fs. This result places significant constraints on the use of organohalide perovskites in hot-carrier photovoltaics.

All-electron real-time and imaginary-time time-dependent density functional theory within a numeric atom-centered basis function framework

Real-time time-dependent density functional theory (RT-TDDFT) is an attractive tool to model quantum dynamics by real-time propagation without the linear response approximation. Sharing the same technical framework of RT-TDDFT, imaginary-time time-dependent density functional theory (it-TDDFT) is a recently developed robust-convergence ground state method. Presented here are high-precision all-electron RT-TDDFT and it-TDDFT implementations within a numerical atom-centered orbital (NAO) basis function framework in the FHI-aims code. We discuss the theoretical background and technical choices in our implementation. First, RT-TDDFT results are validated against linear-response TDDFT results. Specifically, we analyze the NAO basis sets' convergence for Thiel's test set of small molecules and confirm the importance of the augmentation basis functions for adequate convergence. Adopting a velocity-gauge formalism, we next demonstrate applications for systems with periodic boundary conditions. Taking advantage of the all-electron full-potential implementation, we present applications for core level spectra. For it-TDDFT, we confirm that within the all-electron NAO formalism, it-TDDFT can successfully converge systems that are difficult to converge in the standard self-consistent field method. We finally benchmark our implementation for systems up to ∼500 atoms. The implementation exhibits almost linear weak and strong scaling behavior.

Temporal characterization of two-octave infrared pulses by frequency resolved optical switching

We present the temporal characterization of infrared pulses with spectra extending from 0.55 to 2.5 μm by using the frequency resolved optical switching (FROSt) technique. The pulses are obtained by broadening femtosecond pulses at 1.75 μm central wavelength in a two-stage hollow core fiber setup. This work demonstrates the capability of the FROSt technique to temporally characterize pulses with ultra-broadband spectra. Being free of phase-matching constraints, it enables the characterization of pulses with very low energy at the limit of the detection threshold and with arbitrary long pulse duration. This strength of the FROSt technique is illustrated by the characterization of supercontinua pulses whose spectra span over two octaves and with only 150 nJ energy that is spread temporally over almost 40 ps. The FROSt capabilities provide a versatile tool for the characterization of sub-cycle pulses and to study nonlinear processes such as supercontinuum generation.

Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation

We give a perspective on simulating electronic excitation and dynamics using the real-time propagation approach to time-dependent density functional theory (RT-TDDFT) in the plane-wave pseudopotential formulation. RT-TDDFT is implemented in various numerical formalisms in recent years, and its practical application often dictates the most appropriate implementation of the theory. We discuss recent developments and challenges, emphasizing numerical aspects of studying real systems. Several applications of RT-TDDFT simulation are discussed to highlight how the approach is used to study interesting electronic excitation and dynamics phenomena in recent years.

Optical Gain in Solids after Ultrafast Strong-Field Excitation

Multiphoton excitation of a solid by a few-cycle, intense laser pulse forms a very nonequilibrium distribution of charge carriers, where occupation probabilities do not necessarily decrease with energy. Within a fraction of the pulse, significant population inversion can emerge between pairs of valence-band states with a dipole-allowed transition between them. This population inversion leads to stimulated emission in a laser-excited solid at frequencies where the unperturbed solid is transparent. We establish the optimal conditions for observing this kind of strong-field-induced optical gain.

Zero→Two-Dimensional Metal Nanostructures: An Overview on Methods of Preparation, Characterization, Properties, and Applications

Metal nanostructured materials, with many excellent and unique physical and mechanical properties compared to macroscopic bulk materials, have been widely used in the fields of electronics, bioimaging, sensing, photonics, biomimetic biology, information, and energy storage. It is worthy of noting that most of these applications require the use of nanostructured metals with specific controlled properties, which are significantly dependent on a series of physical parameters of its characteristic size, geometry, composition, and structure. Therefore, research on low-cost preparation of metal nanostructures and controlling of their characteristic sizes and geometric shapes are the keys to their development in different application fields. The preparation methods, physical and chemical properties, and application progress of metallic nanostructures are reviewed, and the methods for characterizing metal nanostructures are summarized. Finally, the future development of metallic nanostructure materials is explored.

Ultrafast strong-field dissociation of vinyl bromide: An attosecond transient absorption spectroscopy and non-adiabatic molecular dynamics study

Attosecond extreme ultraviolet (XUV) and soft x-ray sources provide powerful new tools for studying ultrafast molecular dynamics with atomic, state, and charge specificity. In this report, we employ attosecond transient absorption spectroscopy (ATAS) to follow strong-field-initiated dynamics in vinyl bromide. Probing the Br M edge allows one to assess the competing processes in neutral and ionized molecular species. Using ab initio non-adiabatic molecular dynamics, we simulate the neutral and cationic dynamics resulting from the interaction of the molecule with the strong field. Based on the dynamics results, the corresponding time-dependent XUV transient absorption spectra are calculated by applying high-level multi-reference methods. The state-resolved analysis obtained through the simulated dynamics and related spectral contributions enables a detailed and quantitative comparison with the experimental data. The main outcome of the interaction with the strong field is unambiguously the population of the first three cationic states, D ₁, D ₂, and D ₃. The first two show exclusively vibrational dynamics while the D ₃ state is characterized by an ultrafast dissociation of the molecule via C-Br bond rupture within 100 fs in 50% of the analyzed trajectories. The combination of the three simulated ionic transient absorption spectra is in excellent agreement with the experimental results. This work establishes ATAS in combination with high-level multi-reference simulations as a spectroscopic technique capable of resolving coupled non-adiabatic electronic-nuclear dynamics in photoexcited molecules with sub-femtosecond resolution.

Mapping time-dependent quasi-energies of laser dressed helium

Extreme ultraviolet (EUV) transient absorption spectrum of helium dressed by a moderately intense infrared laser pulse is investigated. Strategies for correct retrieval of the time-dependent quasi-energies of helium with excitation energies covering both singly and doubly excited states are proposed. For long-lived singly excited states, the profound hyperbolic structures due to long lasting dipole can be diminished by convoluting the transient absorption spectrogram with a spectral window, allowing the time-dependent quasi-energies close to 1s2p resonance to be correctly mapped out. For short-lived doubly excited states near 2s2p resonance, the radiation dipole decays rapidly due to autoionization and the transient absorption spectrogram already recovers the main structure of quasi-energies without the convolution operation. The quantum simulation indicates that the convolution operation controls the effective decay speed of the dipole moment, which effectively builds up an instant probe that is essential for mapping time dependent quasi-energies of laser dressed systems.

Dissipative Equation of Motion for Electromagnetic Radiation in Quantum Dynamics

The dynamical description of the radiative decay of an electronically excited state in realistic many-particle systems is an unresolved challenge. In the present investigation electromagnetic radiation of the charge density is approximated as the power dissipated by a classical dipole, to cast the emission in closed form as a unitary single-electron theory. This results in a formalism of unprecedented efficiency, critical for ab initio modeling, which exhibits at the same time remarkable properties: it quantitatively predicts decay rates, natural broadening, and absorption intensities. Exquisitely accurate excitation lifetimes are obtained from time-dependent DFT simulations for C^{2+}, B^{+}, and Be, of 0.565, 0.831, and 1.97 ns, respectively, in accord with experimental values of 0.57±0.02, 0.86±0.07, and 1.77-2.5 ns. Hence, the present development expands the frontiers of quantum dynamics, bringing within reach first-principles simulations of a wealth of photophysical phenomena, from fluorescence to time-resolved spectroscopies.

Unravelling the intertwined atomic and bulk nature of localised excitons by attosecond spectroscopy

The electro-optical properties of most semiconductors and insulators of technological interest are dominated by the presence of electron-hole quasi-particles, called excitons. The manipulation of excitons in dielectrics has recently received great attention, with possible applications in different fields including optoelectronics and photonics. Here, we apply attosecond transient reflection spectroscopy in a sequential two-foci geometry and observe sub-femtosecond dynamics of a core-level exciton in bulk MgF₂ single crystals. Furthermore, we access absolute phase delays, which allow for an unambiguous comparison with theoretical calculations. Our results show that excitons surprisingly exhibit a dual atomic- and solid-like character, which manifests itself on different time scales. While the former is responsible for a femtosecond optical Stark effect, the latter dominates the attosecond excitonic response. Further theoretical investigation reveals a link with the exciton sub-femtosecond nanometric motion and allows us to envision a new route to control exciton dynamics in the close-to-petahertz regime.

Carrier-specific dynamics in 2H-MoTe2 observed by femtosecond soft x-ray absorption spectroscopy using an x-ray free-electron laser

Femtosecond carrier dynamics in layered 2H-MoTe2 semiconductor crystals have been investigated using soft x-ray transient absorption spectroscopy at the x-ray free-electron laser (XFEL) of the Pohang Accelerator Laboratory. Following above-bandgap optical excitation of 2H-MoTe2, the photoexcited hole distribution is directly probed via short-lived transitions from the Te 3d 5/2 core level (M5-edge, 572-577 eV) to transiently unoccupied states in the valence band. The optically excited electrons are separately probed via the reduced absorption probability at the Te M5-edge involving partially occupied states of the conduction band. A 400 ± 110 fs delay is observed between this transient electron signal near the conduction band minimum compared to higher-lying states within the conduction band, which we assign to hot electron relaxation. Additionally, the transient absorption signals below and above the Te M5 edge, assigned to photoexcited holes and electrons, respectively, are observed to decay concomitantly on a 1-2 ps timescale, which is interpreted as electron-hole recombination. The present work provides a benchmark for applications of XFELs for soft x-ray absorption studies of carrier-specific dynamics in semiconductors, and future opportunities enabled by this method are discussed.

Multiscale simulation of terahertz radiation process in benzimidazole crystal by impulsive stimulated Raman scattering

Comprehensive dynamics of coupled light wave and molecules in the terahertz wave generation process in an organic molecular crystal solid, 5,6-dichloro-2-methylbenzimidazole (DCMBI), induced by impulsive stimulated Raman scattering has been described by our previously developed multi-scale simulation, Maxwell + polarizable molecular dynamics method, where the propagation of macroscopic electromagnetic fields and microscopic molecular dynamics based on the force field model are numerically solved in the time domain. It has shown the behaviors of the excitation of Raman-active phonon modes by the irradiated pulse and terahertz radiation by molecular motions of infrared-active modes. Simulations of terahertz absorption and Raman spectroscopies of the DCMBI solid have also been performed to verify the applicability of the method to the terahertz optics. The calculated spectra are compared with the experimental measurements, showing good agreement. The detailed motions of the interacting electromagnetic fields and molecules occurred in the terahertz spectroscopies have also been provided, and the analyses have shown that rotational motions of the DCMBI molecules play key roles in the terahertz wave generation.

Simultaneous Observation of Carrier-Specific Redistribution and Coherent Lattice Dynamics in 2H-MoTe2 with Femtosecond Core-Level Spectroscopy

We employ few-femtosecond extreme ultraviolet (XUV) transient absorption spectroscopy to reveal simultaneously the intra- and interband carrier relaxation and the light-induced structural dynamics in nanoscale thin films of layered 2H-MoTe₂ semiconductor. By interrogating the valence electronic structure via localized Te 4d (39-46 eV) and Mo 4p (35-38 eV) core levels, the relaxation of the photoexcited hole distribution is directly observed in real time. We obtain hole thermalization and cooling times of 15 ± 5 fs and 380 ± 90 fs, respectively, and an electron-hole recombination time of 1.5 ± 0.1 ps. Furthermore, excitations of coherent out-of-plane A_1g (5.1 THz) and in-plane E_1g (3.7 THz) lattice vibrations are visualized through oscillations in the XUV absorption spectra. By comparison to Bethe-Salpeter equation simulations, the spectral changes are mapped to real-space excited-state displacements of the lattice along the dominant A_1g coordinate. By directly and simultaneously probing the excited carrier distribution dynamics and accompanying femtosecond lattice displacement in 2H-MoTe₂ within a single experiment, our work provides a benchmark for understanding the interplay between electronic and structural dynamics in photoexcited nanomaterials.

Non-adiabatic stripping of a cavity field from deep-strongly coupled electrons

Atomically strong light pulses can drive sub-optical-cycle dynamics. When the Rabi frequency - the rate of energy exchange between light and matter - exceeds the optical carrier frequency, fascinating non-perturbative strong-field phenomena emerge, such as high-harmonic generation and lightwave transport. Here, we explore a related novel subcycle regime of ultimately strong light-matter interaction without a coherent driving field. We use the vacuum fluctuations of nanoantennas to drive cyclotron resonances of two-dimensional electron gases to vacuum Rabi frequencies exceeding the carrier frequency. Femtosecond photoactivation of a switch element inside the cavity disrupts this 'deep-strong coupling' more than an order of magnitude faster than the oscillation cycle of light. The abrupt modification of the vacuum ground state causes spectrally broadband polarisation oscillations confirmed by our quantum model. In the future, this subcycle shaping of hybrid quantum states may trigger cavity-induced quantum chemistry, vacuum-modified transport, or cavity-controlled superconductivity, opening new scenarios for non-adiabatic quantum optics.

Isolated single-cycle extreme-ultraviolet pulses from undulator radiation

We propose a method to generate an isolated single-cycle pulse in the extreme-ultraviolet spectral region using a broadband conventional laser. The uncompressed laser pulse imprints a chirped sinusoid current profile onto a relativistic electron beam. As the beam propagates along a specifically tailored magnetic field of an undulator, it produces an isolated single-cycle pulse. For moderate laser intensities (0.2 mJ per pulse) and typical operating parameters of current electron accelerators, we predict a 26 as, 5 GW peak-power pulse spanning wavelengths down to 15 nm.

Simulated field-modulated x-ray absorption in titania

In this paper, we present a method to compute the x-ray absorption near-edge structure (XANES) spectra of solid-state transition metal oxides using real-time time-dependent density functional theory, including spin-orbit coupling effects. This was performed on bulk-mimicking anatase titania (TiO₂) clusters, which allows for the use of hybrid functionals and atom-centered all electron basis sets. Furthermore, this method was employed to calculate the shifts in the XANES spectra of the Ti L-edge in the presence of applied electric fields to understand how external fields can modify the electronic structure, and how this can be probed using x-ray absorption spectroscopy. Specifically, the onset of t_2g peaks in the Ti L-edge was observed to red shift and the e_g peaks were observed to blue shift with increasing fields, attributed to changes in the hybridization of the conduction band (3d) orbitals.

First-Principles Simulations of X-ray Transient Absorption for Probing Attosecond Electron Dynamics

X-ray transient absorption spectroscopy (XTAS) is a promising technique for measuring electron dynamics in molecules and solids with attosecond time resolutions. In XTAS, the elemental specificity and spatial locality of core-to-valence X-ray absorption is exploited to relate modulations in the time-resolved absorption spectra to local electron density variations around particular atoms. However, interpreting these absorption modulations and frequency shifts as a function of the time delay in terms of dynamics can be challenging. In this paper, we present a first-principles study of attosecond XTAS in a selection of simple molecules based on real-time time-dependent density functional theory (RT-TDDFT) with constrained DFT to emulate the state of the system following the interaction with a ultraviolet pump laser. In general, there is a decrease in the optical density and a blue shift in the frequency with increasing electron density around the absorbing atom. In carbon monoxide (CO), modulations in the O K-edge occur at the frequency of the valence electron dynamics, while for dioxygen (O₂) they occur at twice the frequency, due to the indistinguishability of the oxygen atoms. In 4-aminophenol (H₂NC₆H₄OH), likewise, there is a decrease in the optical density and a blue shift in the frequency for the oxygen and nitrogen K-edges with increasing charge density on the O and N, respectively. Similar effects are observed in the nitrogen K-edge for a long-range charge-transfer excitation in a benzene (C₆H₆)-tetracyanoethylene (C₆N₄; TCNE) dimer but with weaker modulations due to the delocalization of the charge across the entire TCNE molecule. Additionally, in all cases, there are pre-edge features corresponding to core transitions to depopulated orbitals. These potentially offer a background-free signal that only appears in pumped molecules.