Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids

Dephasing of Strong-Field-Driven Excitonic Autler-Townes Doublets Revealed by Time- and Spectrum-Resolved Quantum-Path Interferometry

Understanding dephasing mechanisms of strong-field-driven excitons in condensed matter is essential for their applications in quantum-state manipulation and ultrafast optical modulations. However, experimental access to exciton dephasing under strong-field conditions is challenging. In this study, using time- and spectrum-resolved quantum-path interferometry, we investigate the dephasing mechanisms of terahertz-driven excitonic Autler-Townes doublets in MoS_{2}. Our results reveal a dramatic increase in the dephasing rate beyond a threshold field strength, indicating exciton dissociation as the primary dephasing mechanism. Furthermore, we demonstrate nonperturbative high-order sideband generation in a regime where the driving fields are insufficient to dissociate excitons.

Attosecond chronoscopy of the photoemission near a bandgap of a single-element layered dielectric

We report on the energy dependence of the photoemission time delay from the single-element layered dielectric HOPG (highly oriented pyrolytic graphite). This system offers the unique opportunity to directly observe the Eisenbud-Wigner-Smith (EWS) time delays related to the bulk electronic band structure without being strongly perturbed by ubiquitous effects of transport, screening, and multiple scattering. We find the experimental streaking time shifts to be sensitive to the modulation of the density of states in the high-energy region (E ≈ 100 eV) of the band structure. The present attosecond chronoscopy experiments reveal an energy-dependent increase of the photoemission time delay when the final state energy of the excited electrons lies in the vicinity of the bandgap providing information difficult to access by conventional spectroscopy. Accompanying simulations further corroborate our interpretation.

Attosecond ionic photoionization spectroscopy

Photoionization is one of the most fundamental processes in light-matter interaction. Advanced attosecond photoelectron spectroscopy provides the possibility to characterize the ultrafast photoemission process in an extremely short attosecond time scale. Following scattering symmetry rules, residual ions encode ultrafast photoionization prints at the instant of electron removal forming an alternative electron emission chronoscope. Here, we experimentally illustrate the attosecond ion reconstruction of attosecond beating by interference of two-photon transition (RABBIT)-like interferometry through the development of high-resolution ion momentum detection in atomic photoionization processes. Our ion interferometry presents identical momentum- and time-dependent scattering phase shift, as we observed in photoelectron spectroscopy, and thus demonstrates that ion interferometry can be a possible alternative attosecond approach to resolve the photoionization process, without the electron homogeneity limitation.

Tracking electron motion within and outside of Floquet bands from attosecond pulse trains in time-resolved ARPES

Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory-it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet-Bloch bands. We formulate and employ this approach inab-initiocalculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as 'non-Floquet' bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.

Probing Photoionization Dynamics in Acetylene with Angle-Resolved Attosecond Interferometry

Photoionization of acetylene by extreme ultraviolet light results in a stand-alone contribution from the outermost valence orbital, followed by well-separated photoelectron bands from deeper molecular orbitals. This makes acetylene an ideal candidate for probing the photoionization dynamics in polyatomic molecules free from the spectral congestion often arising after interaction with an attosecond pulse train. Here, using an angle-resolved attosecond interferometric technique, we extract the photoionization time delays for the outermost valence orbital in acetylene relative to an atomic target, namely argon. Compared to argon, the photoemission from the acetylene molecule is found to be advanced by almost 28 attoseconds. The strong variation of the relative photoionization time delays as a function of the photoemission angle was interpreted using an analytical model based on semiclassical approximations to be the interplay between different short-range potentials along and perpendicular to the molecular axis. Our results highlight the importance of using attosecond time-resolved measurements to probe the nonspherical nature of the molecular potential, even in the case of relatively small, linear systems.

Separation of photoionization and measurement-induced delays

Photoionization of matter is one of the fastest electronic processes in nature. Experimental measurements of photoionization dynamics have become possible through attosecond metrology. However, all experiments reported to date contain a so-far unavoidable measurement-induced contribution, known as continuum-continuum (CC) or Coulomb-laser-coupling delay. In traditional attosecond metrology, this contribution is nonadditive for most systems and nontrivial to calculate. Here, we introduce the concept of mirror symmetry-broken attosecond interferometry, which enables the direct and separate measurement of both the native one-photon ionization delays and the CC delays. Our technique solves the longstanding challenge of experimentally isolating these two contributions. This advance opens the door to the next generation of accurate measurements and precision tests that will set standards for benchmarking the accuracy of electronic structure and electron-dynamics methods.

Time-resolved ARPES with probe energy of 6.0/7.2 eV and switchable resolution configuration

We present a detailed exposition of the design for time- and angle-resolved photoemission spectroscopy using a UV probe laser source that combines the nonlinear effects of β-BaB2O4 and KBe2BO3F2 optical crystals. The photon energy of the probe laser can be switched between 6.0 and 7.2 eV, with the flexibility to operate each photon energy setting under two distinct resolution configurations. Under the fully optimized energy resolution configuration, we achieve an energy resolution of 8.5 meV at 6.0 eV and 10 meV at 7.2 eV. Alternatively, switching to the other configuration enhances the temporal resolution, yielding a temporal resolution of 72 fs for 6.0 eV and 185 fs for 7.2 eV. We validated the performance and reliability of our system by applying it to measuring two typical materials: the topological insulator MnBi2Te4 and the excitonic insulator candidate Ta2NiSe5.

Attosecond photoionization delays in the vicinity of molecular Feshbach resonances

Temporal delays extracted from photoionization phases are currently determined with attosecond resolution by using interferometric methods. Such methods require special care when photoionization occurs near Feshbach resonances due to the interference between direct ionization and autoionization. Although theory can accurately handle these interferences in atoms, in molecules, it has to face an additional, so far insurmountable problem: Autoionization is slow, and nuclei move substantially while it happens, i.e., electronic and nuclear motions are coupled. Here, we present a theoretical framework to account for this effect and apply it to evaluate time-resolved and vibrationally resolved photoelectron spectra and photoionization phases of N₂ irradiated by a combination of an extreme ultraviolet (XUV) attosecond pulse train and an infrared pulse. We show that Feshbach resonances lead to unusual non-Franck-Condon vibrational progressions and to ionization phases that strongly vary with photoelectron energy irrespective of the vibrational state of the remaining molecular cation.

Extension of the bright high-harmonic photon energy range via nonadiabatic critical phase matching

The concept of critical ionization fraction has been essential for high-harmonic generation, because it dictates the maximum driving laser intensity while preserving the phase matching of harmonics. In this work, we reveal a second, nonadiabatic critical ionization fraction, which substantially extends the phase-matched harmonic energy, arising because of the strong reshaping of the intense laser field in a gas plasma. We validate this understanding through a systematic comparison between experiment and theory for a wide range of laser conditions. In particular, the properties of the high-harmonic spectrum versus the laser intensity undergoes three distinctive scenarios: (i) coincidence with the single-atom cutoff, (ii) strong spectral extension, and (iii) spectral energy saturation. We present an analytical model that predicts the spectral extension and reveals the increasing importance of the nonadiabatic effects for mid-infrared lasers. These findings are important for the development of high-brightness soft x-ray sources for applications in spectroscopy and imaging.

Probing Resonant Photoionization Time Delay by Self-Referenced Molecular Attoclock

Attosecond time-resolved electron tunneling dynamics have been investigated by using attosecond angular streaking spectroscopy, where a clock reference to the laser field vector is required in atomic strong-field ionization and the situation becomes complicated in molecules. Here we reveal a resonant ionization process via a transient state by developing an electron-tunneling-site-resolved molecular attoclock in Ar-Kr^{+}. Two distinct deflection angles are observed in the photoelectron angular distribution in the molecular frame, corresponding to the direct and resonant ionization pathways. We find the electron is temporally trapped in the Coulomb potential wells of the Ar-Kr^{+} before finally releasing into the continuum when the electron tunnels through the internal barrier. By utilizing the direct tunneling ionization as a self-referenced arm of the attoclock, the time delay of the electron trapped in the resonant state is revealed to be 3.50±0.04  fs. Our results give an impetus to exploring the ultrafast electron dynamics in complex systems and also endow a semiclassical presentation of the electron trapping dynamics in a quantum resonant state.

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.

Atomic partial wave meter by attosecond coincidence metrology

Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics in matter from gas to the condensed phase with attosecond temporal resolution. It has, however, not yet been possible to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attosecond chronoscopy serving as a partial wave meter to reveal the role of each partial wave from the angle-resolved photoionization phase shifts in rare gas atoms. We steer the relative ratio between different partial waves and realize a magnetic-sublevel-resolved atomic phase shift measurement. Our experimental observations are well supported by time-dependent R-matrix numerical simulations and analytical soft-photon approximation analysis. The symmetry-resolved, partial-wave analysis identifies the transition rate and phase shift property in the attosecond photoelectron emission dynamics. Our findings provide critical insights into the ubiquitous attosecond optical timer and the underlying attosecond photoionization dynamics.

Understanding the photoelectron emission time after the interaction of photon with atoms and molecules is of fundamental interest. Here the authors examine the role of partial waves to the photoionization phase shift of atoms using an attosecond clock and electron-ion coincidence spectroscopy.

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.

Necklace-structured high-harmonic generation for low-divergence, soft x-ray harmonic combs with tunable line spacing

The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wave function and, in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of linearly polarized HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme ultraviolet and soft x-ray high-harmonic combs. The on-axis HHG emission has extremely low divergence, well below that obtained when using Gaussian driving beams, which further decreases with harmonic order. This work provides a new degree of freedom for the design of harmonic combs-particularly in the soft x-ray regime, where very limited options are available. Such harmonic beams can enable more sensitive probes of the fastest correlated charge and spin dynamics in molecules, nanoparticles, and materials.

Intruder Peak-Free Transient Inner-Shell Spectra Using Real-Time Simulations

Real-time methods are convenient for simulating core-level absorption spectra but suffer from nonphysical intruder peaks when using atom-centered basis sets. In transient absorption spectra, these peaks exhibit highly nonphysical time-dependent modulations in their energies and oscillator strengths. In this paper, we address the origins of these intruder peaks and propose a straightforward and effective solution based on a filtered dipole operator. In combination with real-time time-dependent density functional theory (RT-TDDFT), we demonstrate how to compute intruder-free attosecond transient X-ray absorption spectra for the aminophenol (C₆H₇NO) oxygen and nitrogen K-edges and the α-quartz (SiO₂) silicon L-edge. Without filtering, the computed spectra are qualitatively wrong. This procedure is suitable for both static and transient inner-shell spectroscopy studies and can easily be implemented in a range of real-time methodologies.

Controlling Photon Transverse Orbital Angular Momentum in High Harmonic Generation

High harmonic generation (HHG) with longitudinal optical orbital angular momentum has attracted much attention over the past decade. Here, we present the first study on the HHG with transverse orbital angular momentum driven by the spatiotemporal optical vortex (STOV) pulses. We show that the produced spatial-resolved harmonic spectra reveal unique structures, such as the spatially spectral tilt and the fine interference patterns. We show these spatiospectral structures originate from both the macroscopic and microscopic effect of spatiotemporal optical singularity in HHG. Employing two-color counterspin and countervorticity STOV pulses, we further discuss a robust method to control the spatiotemporal topological charge and spectral structure of high-order harmonics. The conservation rule of photon transverse orbital angular momentum in HHG process is also discussed when mixing with photon spin angular momenta.

Bright, single helicity, high harmonics driven by mid-infrared bicircular laser fields

High-harmonic generation (HHG) is a unique tabletop light source with femtosecond-to-attosecond pulse duration and tailorable polarization and beam shape. Here, we use counter-rotating femtosecond laser pulses of 0.8 µm and 2.0 μm to extend the photon energy range of circularly polarized high-harmonics and also generate single-helicity HHG spectra. By driving HHG in helium, we produce circularly polarized soft x-ray harmonics beyond 170 eV-the highest photon energy of circularly polarized HHG achieved to date. In an Ar medium, dense spectra at photon energies well beyond the Cooper minimum are generated, with regions composed of a single helicity-consistent with the generation of a train of circularly polarized attosecond pulses. Finally, we show theoretically that circularly polarized HHG photon energies can extend beyond the carbon K edge, extending the range of molecular and materials systems that can be accessed using dynamic HHG chiral spectro-microscopies.

Coherent Excitation and Control of Plasmons on Gold Using Two-Dimensional Transition Metal Dichalcogenides

The hybrid combination of two-dimensional (2D) transition metal dichalcogenides (TMDs) and plasmonic materials open up novel means of (ultrafast) optoelectronic applications and manipulation of nanoscale light-matter interaction. However, control of the plasmonic excitations by TMDs themselves has not been investigated. Here, we show that the ultrathin 2D WSe₂ crystallites permit nanoscale spatially controlled coherent excitation of surface plasmon polaritons (SPPs) on smooth Au films. The resulting complex plasmonic interference patterns are recorded with nanoscale resolution in a photoemission electron microscope. Modeling shows good agreement with experiments and further indicates how SPPs can be tailored with high spatiotemporal precision using the shape of the 2D TMDs with thicknesses down to single molecular layers. We demonstrate the use of WSe₂ nanocrystals as 2D optical elements for exploring the ultrafast dynamics of SPPs. Using few-femtosecond laser pulse pairs we excite an SPP at the boundary of a WSe₂ crystal and then have a WSe₂ monolayer wedge act as a delay line inducing a spatially varying phase difference down to the attosecond time range. The observed effects are a natural yet unexplored consequence of high dielectric functional values of TMDs in the visible range that should be considered when designing metal-TMD hybrid devices. As the 2D TMD crystals are stable in air, can be defect free, can be synthesized in many shapes, and are reliably positioned on metal surfaces, using them to excite and steer SPPs adds an interesting alternative in designing hybrid structures for plasmonic control.

Attosecond intra-valence band dynamics and resonant-photoemission delays in W(110)

Time-resolved photoelectron spectroscopy with attosecond precision provides new insights into the photoelectric effect and gives information about the timing of photoemission from different electronic states within the electronic band structure of solids. Electron transport, scattering phenomena and electron-electron correlation effects can be observed on attosecond time scales by timing photoemission from valence band states against that from core states. However, accessing intraband effects was so far particularly challenging due to the simultaneous requirements on energy, momentum and time resolution. Here we report on an experiment utilizing intracavity generated attosecond pulse trains to meet these demands at high flux and high photon energies to measure intraband delays between sp- and d-band states in the valence band photoemission from tungsten and investigate final-state effects in resonant photoemission.

Accessing intraband dynamics is challenging due to simultaneous requirements on energy, momentum and time resolution. Here, the authors measure intraband delays between sp- and d-band electronic states in the valence band photoemission from W(110) using intracavity generated attosecond pulse trains.

Reconstruction of atomic resonances with attosecond streaking

Recent development of spectroscopic techniques based on attosecond radiation has given the community the right tools to study the timing of the photoelectron process. In this work we investigate the effect of Fano resonances in attosecond streaking spectrograms and the application of standard phase-reconstruction algorithms. We show that while the existence of the infrared coupling (ac-Stark shift) hinders the applicability of FROG-like methods, under certain conditions it is still possible to use standard reconstruction algorithms to retrieve the photoemission delay of the bare resonance. Finally, we propose two strategies to study the strength of IR coupling using the attosecond streaking technique.

Nonlocal mechanisms of attosecond interferometry in three-dimensional systems

Attosecond interferometry (AI) is an experimental technique based on ionizing a system with an attosecond pulse train in the presence of an assisting laser. This assisting laser pulse provides multiple pathways for the photoelectron wave packet to reach the same final states, and interference of these pathways can be used to probe the properties of matter. The mechanism of AI is well-understood for isolated atoms and molecules in the gas phase, but not so much in the condensed phase, especially if the substrate under study is transparent. Then, additional pathways open up for the electron due to (laser-assisted) scattering from neighbouring atoms. We investigate to what extent these additional pathways influence the measured photoionization delays with the help of 1D and 3D model systems. In both cases, we find that the total delay can be expressed as the sum of a local (photoionization) delay and a non-local delay, which contains the effect of electron scattering during transport. The 1D system shows that the non-local delay is an oscillatory function of the distance between the sites where ionization and scattering take place. A similar result is obtained in 3D, but the modulation depth of the non-local delay is found to strongly depend on the effective scattering cross section. We conclude that attosecond interferometry of disordered systems like liquids at low photon energies (20–30 eV) is mainly sensitive to the local delay, i.e. to changes of the photoionization dynamics induced by the immediate environment of the ionized entity, and less to electron scattering during transport through the medium. This conclusion also agrees with the interpretation of recent experimental results.

Zeptosecond birth time delay in molecular photoionization

Photoionization is one of the fundamental light-matter interaction processes in which the absorption of a photon launches the escape of an electron. The time scale of this process poses many open questions. Experiments have found time delays in the attosecond (10−18 seconds) domain between electron ejection from different orbitals, from different electronic bands, or in different directions. Here, we demonstrate that, across a molecular orbital, the electron is not launched at the same time. Rather, the birth time depends on the travel time of the photon across the molecule, which is 247 zeptoseconds (1 zeptosecond = 10−21 seconds) for the average bond length of molecular hydrogen. Using an electron interferometric technique, we resolve this birth time delay between electron emission from the two centers of the hydrogen molecule.

Attosecond electron-spin dynamics in Xe 4d photoionization

The photoionization of xenon atoms in the 70–100 eV range reveals several fascinating physical phenomena such as a giant resonance induced by the dynamic rearrangement of the electron cloud after photon absorption, an anomalous branching ratio between intermediate Xe⁺ states separated by the spin-orbit interaction and multiple Auger decay processes. These phenomena have been studied in the past, using in particular synchrotron radiation, but without access to real-time dynamics. Here, we study the dynamics of Xe 4d photoionization on its natural time scale combining attosecond interferometry and coincidence spectroscopy. A time-frequency analysis of the involved transitions allows us to identify two interfering ionization mechanisms: the broad giant dipole resonance with a fast decay time less than 50 as, and a narrow resonance at threshold induced by spin-flip transitions, with much longer decay times of several hundred as. Our results provide insight into the complex electron-spin dynamics of photo-induced phenomena.

Here the authors report experiment and theory study of the photoionization of xenon inner shell 4d electron using attosecond pulses. They have identified two ionization paths - one corresponding to broad giant dipole resonance with short decay time and the other involving spin-flip transitions.

Asymmetries in ionization of atomic superposition states by ultrashort laser pulses

Progress in ultrafast science allows for probing quantum superposition states with ultrashort laser pulses in the new regime where several linear and nonlinear ionization pathways compete. Interferences of pathways can be observed in the photoelectron angular distribution and in the past they have been analyzed for atoms and molecules in a single quantum state via anisotropy and asymmetry parameters. Those conventional parameters, however, do not provide comprehensive tools for probing superposition states in the emerging research area of bright and ultrashort light sources, such as free-electron lasers and high-order harmonic generation. We propose a new set of generalized asymmetry parameters which are sensitive to interference effects in the photoionization and the interplay of competing pathways as the laser pulse duration is shortened and the laser intensity is increased. The relevance of the parameters is demonstrated using results of state-of-the-art numerical solutions of the time-dependent Schrödinger equation for ionization of helium atom and neon atom.

Attosecond spectroscopy of liquid water

Electronic dynamics in liquids are of fundamental importance, but time-resolved experiments have so far remained limited to the femtosecond time scale. We report the extension of attosecond spectroscopy to the liquid phase. We measured time delays of 50 to 70 attoseconds between the photoemission from liquid water and that from gaseous water at photon energies of 21.7 to 31.0 electron volts. These photoemission delays can be decomposed into a photoionization delay sensitive to the local environment and a delay originating from electron transport. In our experiments, the latter contribution is shown to be negligible. By referencing liquid water to gaseous water, we isolated the effect of solvation on the attosecond photoionization dynamics of water molecules. Our methods define an approach to separating bound and unbound electron dynamics from the structural response of the solvent.

Local and Nonlocal Electron Dynamics of Au/Fe/MgO(001) Heterostructures Analyzed by Time-Resolved Two-Photon Photoemission Spectroscopy

Employing femtosecond laser pulses in front and back side pumping of Au/Fe/MgO(001) combined with detection in two-photon photoelectron emission spectroscopy, we analyze local relaxation dynamics of excited electrons in buried Fe, injection into Au across the Fe-Au interface, and electron transport across the Au layer at 0.6 to 2.0 eV above the Fermi energy. By analysis as a function of Au film thickness we obtain the electron lifetimes of bulk Au and Fe and distinguish the relaxation in the heterostructure's constituents. We also show that the excited electrons propagate through Au in a superdiffusive regime and conclude further that electron injection across the epitaxial interface proceeds ballistically by electron wave packet propagation.

Distinction of Electron Dispersion in Time-Resolved Photoemission Spectroscopy

While recent experiments provided compelling evidence for an intricate dependence of attosecond photoemission-time delays on the solid's electronic band structure, the extent to which electronic transport and dispersion in solids can be imaged in time-resolved photoelectron (PE) spectra remains poorly understood. Emphasizing the distinction between photoemission time delays measured with two-photon, two-color interferometric spectroscopy, and transport times, we demonstrate how the effect of energy dispersion in the solid on photoemission delays can, in principle, be observed in interferometric photoemission. We reveal analytically a scaling relation between the PE transport time in the solid and the observable photoemission delay and confirm this relation in numerical simulations for a model system. We trace photoemission delays to the phase difference the PE accumulates inside the solid and, in particular, predict negative photoemission delays. Based on these findings, we suggest a novel time-domain interferometric solid-state energy-momentum-dispersion imaging method.

Time-resolved momentum microscopy with a 1 MHz high-harmonic extreme ultraviolet beamline

Recent progress in laser-based high-repetition rate extreme ultraviolet (EUV) light sources and multidimensional photoelectron spectroscopy enables the build-up of a new generation of time-resolved photoemission experiments. Here, we present a setup for time-resolved momentum microscopy driven by a 1 MHz fs EUV table-top light source optimized for the generation of 26.5 eV photons. The setup provides simultaneous access to the temporal evolution of the photoelectron's kinetic energy and in-plane momentum. We discuss opportunities and limitations of our new experiment based on a series of static and time-resolved measurements on graphene.

Extreme ultraviolet time- and angle-resolved photoemission setup with 21.5 meV resolution using high-order harmonic generation from a turn-key Yb:KGW amplifier

Characterizing and controlling electronic properties of quantum materials require direct measurements of nonequilibrium electronic band structures over large regions of momentum space. Here, we demonstrate an experimental apparatus for time- and angle-resolved photoemission spectroscopy using high-order harmonic probe pulses generated by a robust, moderately high power (20 W) Yb:KGW amplifier with a tunable repetition rate between 50 and 150 kHz. By driving high-order harmonic generation (HHG) with the second harmonic of the fundamental 1025 nm laser pulses, we show that single-harmonic probe pulses at 21.8 eV photon energy can be effectively isolated without the use of a monochromator. The on-target photon flux can reach 5 × 10¹⁰ photons/s at 50 kHz, and the time resolution is measured to be 320 fs. The relatively long pulse duration of the Yb-driven HHG source allows us to reach an excellent energy resolution of 21.5 meV, which is achieved by suppressing the space-charge broadening using a low photon flux of 1.5 × 10⁸ photons/s at a higher repetition rate of 150 kHz. The capabilities of the setup are demonstrated through measurements in the topological semimetal ZrSiS and the topological insulator Sb_2-xGd_xTe₃.

Attosecond Dynamics of sp-Band Photoexcitation

We report measurements of the temporal dynamics of the valence band photoemission from the magnesium (0001) surface across the resonance of the Γ[over ¯] surface state at 134 eV and link them to observations of high-resolution synchrotron photoemission and numerical calculations of the time-dependent Schrödinger equation using an effective single-electron model potential. We observe a decrease in the time delay between photoemission from delocalized valence states and the localized core orbitals on resonance. Our approach to rigorously link excitation energy-resolved conventional steady-state photoemission with attosecond streaking spectroscopy reveals the connection between energy-space properties of bound electronic states and the temporal dynamics of the fundamental electronic excitations underlying the photoelectric effect.

Disentangling Spectral Phases of Interfering Autoionizing States from Attosecond Interferometric Measurements

We have determined spectral phases of Ne autoionizing states from extreme ultraviolet and midinfrared attosecond interferometric measurements and ab initio full-electron time-dependent theoretical calculations in an energy interval where several of these states are coherently populated. The retrieved phases exhibit a complex behavior as a function of photon energy, which is the consequence of the interference between paths involving various resonances. In spite of this complexity, we show that phases for individual resonances can still be obtained from experiment by using an extension of the Fano model of atomic resonances. As simultaneous excitation of several resonances is a common scenario in many-electron systems, the present work paves the way to reconstruct electron wave packets coherently generated by attosecond pulses in systems larger than helium.

A time- and angle-resolved photoemission spectroscopy with probe photon energy up to 6.7 eV

We present the development of a time- and angle-resolved photoemission spectroscopy based on a Yb-based femtosecond laser and a hemispherical electron analyzer. The energy of the pump photon is tunable between 1.4 and 1.9 eV, and the pulse duration is around 30 fs. We use a KBe₂BO₃F₂ nonlinear optical crystal to generate probe pulses, of which the photon energy is up to 6.7 eV, and obtain an overall time resolution of 1 ps and energy resolution of 18 meV. In addition, β-BaB₂O₄ crystals are used to generate alternative probe pulses at 6.05 eV, giving an overall time resolution of 130 fs and energy resolution of 19 meV. We illustrate the performance of the system with representative data on several samples (Bi₂Se₃, YbCd₂Sb₂, and FeSe).

Recent advances in ultrafast X-ray sources

Over more than a century, X-rays have transformed our understanding of the fundamental structure of matter and have been an indispensable tool for chemistry, physics, biology, materials science and related fields. Recent advances in ultrafast X-ray sources operating in the femtosecond to attosecond regimes have opened an important new frontier in X-ray science. These advances now enable: (i) sensitive probing of structural dynamics in matter on the fundamental timescales of atomic motion, (ii) element-specific probing of electronic structure and charge dynamics on fundamental timescales of electronic motion, and (iii) powerful new approaches for unravelling the coupling between electronic and atomic structural dynamics that underpin the properties and function of matter. Most notable is the recent realization of X-ray free-electron lasers (XFELs) with numerous new XFEL facilities in operation or under development worldwide. Advances in XFELs are complemented by advances in synchrotron-based and table-top laser-plasma X-ray sources now operating in the femtosecond regime, and laser-based high-order harmonic XUV sources operating in the attosecond regime. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Attosecond temporal confinement of interband excitation by intraband motion

High order harmonic generation (HHG) in semiconductors opens a new frontier in strong field physics and attosecond science. However, the underlying physical mechanisms are not yet fully understood and lively debated. Here, we identify and discuss carrier-wave population transfer as a novel and important dynamical effect. We find that the interband excitation occurs in an extremely short time window due to the intraband motion. Our analysis based on this finding allows for a physically intuitive interpretation of the anomalous carrier-envelope phase dependence observed in HHG from MgO and to understand the dominant role of the interband polarization as reported in a series of recent semiconductor HHG experiments. Motivated by the discovered coupling mechanism, we demonstrate that the interband excitation can be controlled by an appropriately tailored two-color field. An ultrabroad supercontinuum spectrum covering the entire plateau region can be generated which directly creates an isolated-attosecond pulse even without phase compensation. Our results provide remarkable insight into the basic physics governing the sub-cycle electron motion with significant implications for the generation of isolated-attosecond light pulses in semiconductor materials.

High-flux ultrafast extreme-ultraviolet photoemission spectroscopy at 18.4 MHz pulse repetition rate

Laser-dressed photoelectron spectroscopy, employing extreme-ultraviolet attosecond pulses obtained by femtosecond-laser-driven high-order harmonic generation, grants access to atomic-scale electron dynamics. Limited by space charge effects determining the admissible number of photoelectrons ejected during each laser pulse, multidimensional (i.e. spatially or angle-resolved) attosecond photoelectron spectroscopy of solids and nanostructures requires high-photon-energy, broadband high harmonic sources operating at high repetition rates. Here, we present a high-conversion-efficiency, 18.4-MHz-repetition-rate cavity-enhanced high harmonic source emitting 5 × 105 photons per pulse in the 25-to-60-eV range, releasing 1 × 1010 photoelectrons per second from a 10-µm-diameter spot on tungsten, at space charge distortions of only a few tens of meV. Broadband, time-of-flight photoelectron detection with nearly 100% temporal duty cycle evidences a count rate improvement between two and three orders of magnitude over state-of-the-art attosecond photoelectron spectroscopy experiments under identical space charge conditions. The measurement time reduction and the photon energy scalability render this technology viable for next-generation, high-repetition-rate, multidimensional attosecond metrology.

Photoemission time versus streaking delay in attosecond time-resolved solid state photo-emission

Time-dependent Schrodinger equation simulations for a one-dimensional model potential reveal that the delay extracted from a streaking spectrogram does not reflect the photoemission time if the streaking field inside the solid cannot be neglected.

Origins of Thermal Spin Depolarization in Half-Metallic Ferromagnet CrO_{2}

Using high-resolution spin-resolved photoemission spectroscopy, we observe a thermal spin depolarization to which all spin-polarized electrons contribute. Furthermore, we observe a distinct minority spin state near the Fermi level and a corresponding depolarization that seldom contributes to demagnetization. The origin of this depolarization has been identified as the many-body effect characteristic of half-metallic ferromagnets. Our investigation opens an experimental field of itinerant ferromagnetic physics focusing on phenomena with sub-meV energy scale.

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.

Full-field imaging of thermal and acoustic dynamics in an individual nanostructure using tabletop high harmonic beams

Imaging charge, spin, and energy flow in materials is a current grand challenge that is relevant to a host of nanoenhanced systems, including thermoelectric, photovoltaic, electronic, and spin devices. Ultrafast coherent x-ray sources enable functional imaging on nanometer length and femtosecond timescales particularly when combined with advances in coherent imaging techniques. Here, we combine ptychographic coherent diffractive imaging with an extreme ultraviolet high harmonic light source to directly visualize the complex thermal and acoustic response of an individual nanoscale antenna after impulsive heating by a femtosecond laser. We directly image the deformations induced in both the nickel tapered nanoantenna and the silicon substrate and see the lowest-order generalized Lamb wave that is partially confined to a uniform nanoantenna. The resolution achieved-sub-100 nm transverse and 0.5-Å axial spatial resolution, combined with ≈10-fs temporal resolution-represents a significant advance in full-field dynamic imaging capabilities. The tapered nanoantenna is sufficiently complex that a full simulation of the dynamic response would require enormous computational power. We therefore use our data to benchmark approximate models and achieve excellent agreement between theory and experiment. In the future, this work will enable three-dimensional functional imaging of opaque materials and nanostructures that are sufficiently complex that their functional properties cannot be predicted.

Absolute timing of the photoelectric effect

Photoemission spectroscopy is central to understanding the inner workings of condensed matter, from simple metals and semiconductors to complex materials such as Mott insulators and superconductors¹. Most state-of-the-art knowledge about such solids stems from spectroscopic investigations, and use of subfemtosecond light pulses can provide a time-domain perspective. For example, attosecond (10^-18 seconds) metrology allows electron wave packet creation, transport and scattering to be followed on atomic length scales and on attosecond timescales^2-7. However, previous studies could not disclose the duration of these processes, because the arrival time of the photons was not known with attosecond precision. Here we show that this main source of ambiguity can be overcome by introducing the atomic chronoscope method, which references all measured timings to the moment of light-pulse arrival and therefore provides absolute timing of the processes under scrutiny. Our proof-of-principle experiment reveals that photoemission from the tungsten conduction band can proceed faster than previously anticipated. By contrast, the duration of electron emanation from core states is correctly described by semiclassical modelling. These findings highlight the necessity of treating the origin, initial excitation and transport of electrons in advanced modelling of the attosecond response of solids, and our absolute data provide a benchmark. Starting from a robustly characterized surface, we then extend attosecond spectroscopy towards isolating the emission properties of atomic adsorbates on surfaces and demonstrate that these act as photoemitters with instantaneous response. We also find that the tungsten core-electron timing remains unchanged by the adsorption of less than one monolayer of dielectric atoms, providing a starting point for the exploration of excitation and charge migration in technologically and biologically relevant adsorbate systems.

Attosecond Time Delay of Retrapped Resonant Ionization

A recent ultrafast pump-probe technique has allowed measurement of time delays during photoemission in a variety of systems ranging from atoms and molecules to solids with unprecedented temporal resolution. However, identifying the underlying physics is still a challenge especially in complicated multichannel above-threshold ionization (ATI) experiments. Here we demonstrate that the time delays of different ionization pathways in ATI can be clearly resolved and extracted with a semiclassical statistical method. The remarkable phase shift of near threshold photoelectrons can be attributed to a temporary retrapping of a photoelectron by the atomic potential in a quasibound state after emerging in the continuum state. This continuum-bound-continuum scattering manifests as a new resonant effect in strong-field photoemission. Our results unify the seemingly opposing quantum Eisenbud-Wigner-Smith time delay and classical Coulomb-induced time delay by highlighting the same physical picture, which holds promise for an intuitive interpretation of time-resolved fundamental electronic processes in strong-field experiments and epistemological reexamination of the quantum-classical correspondence.

Ultrafast extreme ultraviolet photoemission without space charge

Time- and Angle-resolved photoelectron spectroscopy from surfaces can be used to record the dynamics of electrons and holes in condensed matter on ultrafast time scales. However, ultrafast photoemission experiments using extreme-ultraviolet (XUV) light have previously been limited by either space-charge effects, low photon flux, or limited tuning range. In this article, we describe XUV photoelectron spectroscopy experiments with up to 5 nA of average sample current using a tunable cavity-enhanced high-harmonic source operating at 88 MHz repetition rate. The source delivers >1011 photons/s in isolated harmonics to the sample over a broad photon energy range from 18 to 37 eV with a spot size of 58 × 100 μm2. From photoelectron spectroscopy data, we place conservative upper limits on the XUV pulse duration and photon energy bandwidth of 93 fs and 65 meV, respectively. The high photocurrent, lack of strong space charge distortions of the photoelectron spectra, and excellent isolation of individual harmonic orders allow us to observe laser-induced modifications of the photoelectron spectra at the 10-4 level, enabling time-resolved XUV photoemission experiments in a qualitatively new regime.

Revealing the Nature of the Ultrafast Magnetic Phase Transition in Ni by Correlating Extreme Ultraviolet Magneto-Optic and Photoemission Spectroscopies

By correlating time- and angle-resolved photoemission and time-resolved transverse magneto-optical Kerr effect measurements, both at extreme ultraviolet wavelengths, we uncover the universal nature of the ultrafast photoinduced magnetic phase transition in Ni. This allows us to explain the ultrafast magnetic response of Ni at all laser fluences-from a small reduction of the magnetization at low laser fluences, to complete quenching at high laser fluences. Both probe methods exhibit the same demagnetization and recovery timescales. The spin system absorbs the energy required to proceed through a magnetic phase transition within 20 fs after the peak of the pump pulse. However, the spectroscopic signatures of demagnetization of the material appear only after ≈200  fs and the subsequent recovery of magnetization on timescales ranging from 500 fs to >70  ps. We also provide evidence of two competing channels with two distinct timescales in the recovery process that suggest the presence of coexisting phases in the material.

Imaging Plasmonic Fields with Atomic Spatiotemporal Resolution

We propose a scheme for the reconstruction of plasmonic near fields at isolated nanoparticles from infrared-streaked extreme-ultraviolet photoemission spectra. Based on quantum-mechanically modeled spectra, we demonstrate and analyze the accurate imaging of the IR-streaking-pulse-induced transient plasmonic fields at the surface of gold nanospheres and nanoshells with subfemtosecond temporal and subnanometer spatial resolution.

New developments in laser-based photoemission spectroscopy and its scientific applications: a key issues review

The significant progress in angle-resolved photoemission spectroscopy (ARPES) in last three decades has elevated it from a traditional band mapping tool to a precise probe of many-body interactions and dynamics of quasiparticles in complex quantum systems. The recent developments of deep ultraviolet (DUV, including ultraviolet and vacuum ultraviolet) laser-based ARPES have further pushed this technique to a new level. In this paper, we review some latest developments in DUV laser-based photoemission systems, including the super-high energy and momentum resolution ARPES, the spin-resolved ARPES, the time-of-flight ARPES, and the time-resolved ARPES. We also highlight some scientific applications in the study of electronic structure in unconventional superconductors and topological materials using these state-of-the-art DUV laser-based ARPES. Finally we provide our perspectives on the future directions in the development of laser-based photoemission systems.