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.

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.

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.

Spiers Memorial Lecture: Prospects for photoelectron spectroscopy

An overview is presented of recent advances in photoelectron spectroscopy, focussing on advances in in situ and time-resolved measurements, and in extending the sampling depth of the technique. The future...

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.

Robust Surface States and Coherence Phenomena in Magnetically Alloyed SmB_{6}

Samarium hexaboride is a candidate for the topological Kondo insulator state, in which Kondo coherence is predicted to give rise to an insulating gap spanned by topological surface states. Here we investigate the surface and bulk electronic properties of magnetically alloyed Sm_{1-x}M_{x}B_{6} (M=Ce, Eu), using angle-resolved photoemission spectroscopy and complementary characterization techniques. Remarkably, topologically nontrivial bulk and surface band structures are found to persist in highly modified samples with up to 30% Sm substitution and with an antiferromagnetic ground state in the case of Eu doping. The results are interpreted in terms of a hierarchy of energy scales, in which surface state emergence is linked to the formation of a direct Kondo gap, while low-temperature transport trends depend on the indirect gap.

Ultrafast Dynamics of Electronic Resonances in Molecules Adsorbed on Metal Surfaces: A Wave Packet Propagation Approach

We present a wave packet propagation-based method to study the electron dynamics in molecular species in the gas phase and adsorbed on metal surfaces. It is a very general method that can be employed to any system where the electron dynamics is dominated by an active electron and the coupling between the discrete and continuum electronic states is of importance. As an example, one can consider resonant molecule-surface electron transfer or molecular photoionization. Our approach is based on a computational strategy allowing incorporating ab initio inputs from quantum chemistry methods, such as density functional theory, Hartree-Fock, and coupled cluster. Thus, the electronic structure of the molecule is fully taken into account. The electron wave function is represented on a three-dimensional grid in spatial coordinates, and its temporal evolution is obtained from the solution of the time-dependent Schrödinger equation. We illustrate our method with an example of the electron dynamics of anionic states localized on organic molecules adsorbed on metal surfaces. In particular, we study resonant charge transfer from the π* orbitals of three vinyl derivatives (acrylamide, acrylonitrile, and acrolein) adsorbed on a Cu(100) surface. Electron transfer between these lowest unoccupied molecular orbitals and the metal surface is extremely fast, leading to a decay of the population of the molecular anion on the femtosecond timescale. We detail how to analyze the time-dependent electronic wave function in order to obtain the relevant information on the system: the energies and lifetimes of the molecule-localized quasistationary states, their resonant wavefunctions, and the population decay channels. In particular, we demonstrate the effect of the electronic structure of the substrate on the energy and momentum distribution of the hot electrons injected into the metal by the decaying molecular resonance.

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.

Proper Time Delays Measured by Optical Streaking

In attosecond science it is assumed that Wigner-Smith time delays, known from scattering theory, are determined by measuring streaking shifts. Despite their wide use from atoms to solids this has never been proven. Analyzing the underlying process-energy absorption from the streaking light-we derive this relation. It reveals that only under specific conditions streaking shifts measure Wigner-Smith time delays. For the most relevant case, interactions containing long-range Coulomb tails, we show that finite streaking shifts, including relative shifts from two different orbitals, are misleading. We devise a new time-delay definition and describe a measurement technique that avoids the record of a complete streaking scan, as suggested by the relation between time delays and streaking shifts.

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.

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.

Novel beamline for attosecond transient reflection spectroscopy in a sequential two-foci geometry

We present an innovative beamline for extreme ultraviolet (XUV)-infrared (IR) pump-probe reflection spectroscopy in solids with attosecond temporal resolution. The setup uses an actively stabilized interferometer, where attosecond pulse trains or isolated attosecond pulses are produced by high-order harmonic generation in gases. After collinear recombination, the attosecond XUV pulses and the femtosecond IR pulses are focused twice in sequence by toroidal mirrors, giving two spatially separated interaction regions. In the first region, the combination of a gas target with a time-of-flight spectrometer allows for attosecond photoelectron spectroscopy experiments. In the second focal region, an XUV reflectometer is used for attosecond transient reflection spectroscopy (ATRS) experiments. Since the two measurements can be performed simultaneously, precise pump-probe delay calibration can be achieved, thus opening the possibility for a new class of attosecond experiments on solids. Successful operation of the beamline is demonstrated by the generation and characterization of isolated attosecond pulses, the measurement of the absolute reflectivity of SiO₂, and by performing simultaneous photoemission/ATRS in Ge.

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.

Investigation of valence band reconstruction methods for attosecond streaking data from surfaces

We analyze simulated streaked valence band photoemission with atomic streaking theory-based reconstruction methods to investigate the differences between atomic gas-phase streaking and valence band surface streaking. The careful distinction between atomic and surface streaking is a prerequisite to justify the application of atomic streaking theory-based reconstruction methods to surface streaking measurements. We show that neglecting the band structure underestimates the width of reconstructed photoelectron wavepackets, consistent with the Fourier transform limit of the band spectrum. We find that a fit of Gaussian wavepackets within the description of atomic streaking is adequate to a limited extent. Systematic errors that depend on the near-infrared skin depth, an inherently surface-specific property, are present in temporal widths of wavepackets reconstructed with atomic streaking theory-based methods.

Atomic scale electronic structure and response in attosecond photoemission delays: A case study using non-centrosymmetric BiTeCl

Attosecond time-resolved photoemission from the differently terminated BiTeCl surfaces yield a photoelectron streaking that cannot be explained by bulk propagation effects alone. Instead, the atomic scale electronic structure and dynamical screening for both surface terminations have to be taken into account.

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.

Refined Ptychographic Reconstruction of Attosecond Pulses

Advanced applications of attosecond pulses require the implementation of experimental techniques for a complete and accurate characterization of the pulse temporal characteristics. The method of choice is the frequency resolved optical gating for the complete reconstruction of attosecond bursts (FROG-CRAB), which requires the development of suitable reconstruction algorithms. In the last few years, various numerical techniques have been proposed and implemented, characterized by different levels of accuracy, robustness, and computational load. Many of them are based on the central momentum approximation (CMA), which may pose severe limits in the reconstruction accuracy. Alternative techniques have been successfully developed, based on the implementation of reconstruction algorithms which do not rely on this approximation, such as the Volkov-transform generalized projection algorithm (VTGPA). The main drawback is a notable increase of the computational load. We propose a new method, called refined iterative ptychographic engine (rePIE), which combines the advantages of a robust algorithm based on CMA, characterized by a fast convergence, with the accuracy of advanced algorithms not based on such approximation. The main idea is to perform a first fast iterative ptychographic engine (ePIE) reconstruction and then refine the result with just a few iterations of the VTGPA in order to correct for the error introduced by the CMA. We analyse the accuracy of the novel reconstruction method by comparing the residual error (i.e., the difference between the reconstructed and the simulated original spectrograms) when VTGPA, ePIE, and rePIE reconstructions are employed. We show that the rePIE approach is particularly useful in the case of short attosecond pulses characterized by a broad spectrum in the vacuum-ultraviolet (VUV)–extreme-ultraviolet (XUV) region.

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.

Use and mis-use of x-ray photoemission spectroscopy Ce3d spectra of Ce2O3 and CeO2

X-ray photoemission spectroscopy (XPS) work on Ce₂O₃ and CeO₂ oxides has been an active topic of research over the past four decades or so. Such research aimed to find the reasons for the unusual complexity of Ce3d spectra of the two oxides, and it studied catalytic properties of materials that contained them. I discuss how theoretical and experimental studies exploited the diagnostic potential of XPS to reach our current knowledge of the electronic properties of the two oxides. A part of these studies provided peak-fitting guidelines to resolve Ce3d spectra produced by the co-existence of both oxides into the individual spectral components arising from Ce³⁺ and Ce⁴⁺ ions. Basing myself on the analysis of several peak-fittings of Ce3d spectra carried out in studies of the catalytic applications of CeO₂-based materials, I show that more often than not they largely ignore the findings of theoretical, experimental, and methodological XPS work. I discuss typical problems that flaw Ce3d peak-fittings, and how they affect their accuracy. I argue that, although several XPS studies do list primary literature of Ce3d spectra in their bibliography, they often do so for decorative purposes, rather than practical purposes.

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.

Ultrafast quantum control of ionization dynamics in krypton

Ultrafast spectroscopy with attosecond resolution has enabled the real time observation of ultrafast electron dynamics in atoms, molecules and solids. These experiments employ attosecond pulses or pulse trains and explore dynamical processes in a pump–probe scheme that is selectively sensitive to electronic state of matter via photoelectron or XUV absorption spectroscopy or that includes changes of the ionic state detected via photo-ion mass spectrometry. Here, we demonstrate how the implementation of combined photo-ion and absorption spectroscopy with attosecond resolution enables tracking the complex multidimensional excitation and decay cascade of an Auger auto-ionization process of a few femtoseconds in highly excited krypton. In tandem with theory, our study reveals the role of intermediate electronic states in the formation of multiply charged ions. Amplitude tuning of a dressing laser field addresses different groups of decay channels and allows exerting temporal and quantitative control over the ionization dynamics in rare gas atoms.

Photoionization of atoms and molecules is a complex process and requires sensitive probes to explore the ultrafast dynamics. Here the authors combine transient absorption and photo-ion spectroscopy methods to explore and control the attosecond pulse initiated excitation, ionization and Auger decay in Kr atoms.

Angular momentum can slow down photoemission

Electrons with high angular momentum are the last to emerge from a solid