Photoemission Time Delays Research Articles

Sub-attosecond time delays of photoemission from asymmetric cores of molecules

We theoretically study the extreme ultraviolet (XUV) photoemission of the asymmetric molecular ion HeH2+ beyond the dipole approximation. Based on the double-slit interference of the photoelectron emitted from two atomic cores, we propose a scheme to obtain the XUV photoemission time delays originated from different physical mechanisms. In our study, two types of sub-attosecond photoemission time delays are identified and extracted from the observable photoelectron momentum distributions. One is the so-called birth time delay, originated from the travel time of the photon across the molecule, and the other is the escaping time delay of the photoelectron from two different cores. The present study shows the observable evidence demonstrating that in single-photon ionization, it takes more time for the photoelectron escaping from the helium nucleus than that from the proton. Published by the American Physical Society 2024

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.

Modifications in the angular photoemission time delay in Ar@C60q=−1 : Coulomb confinement resonance as an amplifier of the spin-orbit-interaction-activated interchannel coupling effect

Coulomb confinement resonances (CCRs) are the main features of the photoionization spectra of an atom inside an anionic fullerene. These CCRs can act as an amplifier to spin-orbit-interaction-activated interchannel coupling (SOIAIC) and can lead to discernible signatures of relativistic effects even for low $Z$ confined atomic systems. The present paper demonstrates this intriguing feature by studying angular photoemission time delay of the $2{p}_{3/2}$ subshell of $\mathrm{Ar}@{\mathrm{C}}_{60}^{\ensuremath{-}1}$ in the vicinity of the $2{p}_{1/2}$ ionization threshold. Here $2{p}_{1/2}$ CCR functions as an amplifier to the SOIAIC and, thereby, induces significant modifications in the $2{p}_{3/2}$ angular time delay through the interchannel coupling. Moreover, the effects of the SOIAIC for the spin-up and spin-down photoelectrons are found to be different. All of these suggest that angle-resolved time-delay measurements can reveal the relativistic effects even for the low Z confined atomic systems, and $\mathrm{Ar}@{\mathrm{C}}_{60}^{\ensuremath{-}1}$ is a potential candidate for such experimental scrutiny. The impact of the model parameters on the predicted feature is also critically examined by using different sets of parameters. All of those calculations showed the existence of SOIAIC enabled structures in the angular time-delay profile.

Ensemble effects on the reconstruction of attosecond pulses and photoemission time delays

A crucial prerequisite for a detailed interpretation of the experimental results obtained with the most common attosecond spectroscopic techniques is a careful characterization of the attosecond extreme-ultraviolet (XUV) and femtosecond infrared (IR) pulses used in the measurements. A commonly adopted approach is based on the measurement of the spectra of the photoelectrons produced by the interaction of the attosecond pulses with a noble gas in the presence of a delayed IR pulse. Feeding the resulting spectrogram to reconstruction algorithms, it is then possible to retrieve the temporal properties of the XUV and IR pulses. To date, all reconstruction techniques are based on the assumption that the spectrogram is produced by the interaction of a single atom with a two-color (XUV-IR) field. In this work, we numerically investigate the effect of the actual XUV and IR beam spatial distributions, and we analyze their impact on the retrieval of the temporal characteristics of the XUV and IR pulses and on the determination of the photoemission time delays. We show that the impact of the ensemble effects can be severe, leading to notable variation of the photoelectron spectrograms, depending on the ratio between the XUV and IR beam spot sizes and on the IR peak intensity. We demonstrate that the photoemission time delay can be retrieved with great accuracy even in the presence of large deformations of the photoelectron spectrograms by employing suitable reconstruction procedures.

A multiple scattering theoretical approach to time delay in high energy core-level photoemission of heteronuclear diatomic molecules

We present analytical expressions of momentum-resolved core-level photoemission time delay in a molecular frame of a heteronuclear diatomic molecule upon photoionization by a linearly polarized soft x-ray attosecond pulse. For this purpose, we start to derive a general expression of photoemission time delay based on the first order time dependent perturbation theory within the one electron and single channel model in the fixed-in-space system (atoms, molecules and crystals) and apply it to the core-level photoemission within the electric dipole approximation. By using multiple scattering theory and applying series expansion, plane wave and muffin-tin approximations, the core-level photoemission time delay is divided into three components, , and , which are atomic photoemission time delay, delays caused by the propagation of photoelectron among the surrounding atoms and the scattering of photoelectron by them, respectively. We applied a single scattering approximation to and obtained for a linearly polarized soft x-ray field with polarization vector parallel to the molecular axis for a heteronuclear diatomic molecule, where is the angle of measured photoelectron from the molecular axis. The core-level photoemission time delay is approximated well with this simplified expression in the high energy regime ( a.u.−1, where is the amplitude of photoelectron momentum ), and the validity of this estimated result is confirmed by comparing it with multiple scattering calculations for C 1s core-level photoemission time delay of CO molecules. shows a characteristic dependence on θ, it becomes zero at θ = 0°, exhibits extended x-ray absorption fine structure type oscillation with period at θ = 180°, where R is the bondlength, and gives just the travelling time of photoelectron from the absorbing atom to the neighbouring atom at θ = 90°. We confirmed these features also in the numerical results performed by multiple scattering calculations.

Theoretical study of the molecular-frame photoemission time delay for K -shell photoionization of N2

Photoelectron emission Wigner time delay for $K$-shell ionization of a nitrogen molecule is studied theoretically in the frame of a molecular reference for parallel and perpendicular orientations of the molecule with respect to the electric field vector of linearly polarized ionizing light. Electronic structure calculations are performed by the single center method for photoelectron kinetic energies from 5 to 20 eV and at different levels of approximation. Thereby, the influence of core relaxation effects and interchannel coupling on the $1s$-photoemission time delays, computed across the ${\ensuremath{\sigma}}^{*}$-shape resonance, is investigated in detail. The present theoretical results can be considered as reliable predictions for future experiments.

Scattering effects from neighboring atoms in core-level WSe2 photoemission

Methods of attosecond science originally developed to investigate systems in the gas phase are currently being adapted to obtain temporal information on the electron dynamics that takes place in condensed-matter systems. In particular, streaking measurements have recently been performed to determine photoemission time delays from the ${\mathrm{WSe}}_{2}$ dichalcogenide. In this work we present a fully atomistic description of the photoemission process in ${\mathrm{WSe}}_{2}$ and provide angularly resolved photoemission cross sections and time delays from the W $4f$, Se $3d$ and Se $4s$ core states of the system. Since these states are spatially localized, we propose a cluster approach in which we build up from smaller to larger clusters, so that we can assess the importance of scattering effects by each new layer of neighboring atoms. We use a static-exchange density functional theory method with $B$-spline functions, where a one-center angular-momentum expansion is supplemented by off-center expansions with fewer partial waves. This enhances convergence in comparison with a one-center expansion, which would require very high angular momenta to characterize the localized fast oscillations near each off-center atomic core. We find that the photoemission delays and fully differential cross sections are strongly affected by scattering events that take place off the neighboring atoms, implying the need to consider their effects for quantitative descriptions of the photoemission process.

Precise measurement of attosecond dynamics of NO molecular shape resonance

Shape resonance is an important and ubiquitous phenomenon in the process of molecular scattering and photoionization. The study of the attosecond photoemission time delay in the vicinity of the shape resonance is of great significance for understanding its intrinsic origin on a nature time scale of electron motion. In this paper, an advanced attosecond coincidence interferometer consisting of a near-infrared femtosecond light source and an extreme ultraviolet attosecond pulse train is used to study the shape resonance process of the 4σ electron of nitric oxide molecules via reconstructing attosecond harmonic beating by measuring the interference of two-photon transitions (RABBIT). The energy dependent effective ionization time delay in the vicinity of the resonance energy region is reported. By comparing the relationship between the two-photon transition delay and the one-photon transition delay, it is found that the Wigner delay of the single-photon process is the main reason for the two-photon transition delay changing with energy. The effect of continuum-continuum delay is further explored. Theoretical calculations of the initial state (bound state) and final state (resonance state) electron wave function orbits of the resonance show that the shape resonance assisted time delay is dominated by the electrons trapped in the centrifugal potential barrier.

Attosecond photoemission delay in the inhomogeneous field.

We investigate the photoemission process of the hydrogen atom in a spatial-dependent infrared (IR) field. The results show that the inhomogeneous field induces an additional contribution to the photoemission time delay, which results in the increase (decrease) of the photoemission time delay due to the enhancement (decay) of the IR field intensity in space when compared to the case in the homogeneous field. Based on the photoemission time delay in the inhomogeneous field, we demonstrate a method to extract the inhomogeneous parameter that is vital for characterizing the spatial distribution of IR field. The proposed method might pave an accessible route toward describing the plasmon-enhanced fields in the vicinity of a nanostructure.

Two-center interference and stereo Wigner time delay in photoionization of asymmetric molecules

We present numerical simulations of the time delay in photoemission of asymmetric diatomic molecules using the technique of reconstruction of attosecond beating by interference of two-photon transitions (RABITT) by solving the time-dependent Schr\"odinger equation. Our results show an obvious time delay between photoelectrons emitted to the left and right and this relative time delay oscillates as the photoelectron energy changes. More interestingly, the amplitude of this oscillation increases when the asymmetry degree of diatomic molecules decreases. With the method of the selected continuum wave functions, we calculate the Wigner time delay in photoionization. The obtained stereo Wigner time delay also oscillates with photoelectron energy. This oscillation is traced back to two-center interferences and it could explain the relative time delay in the RABITT measurement. Furthermore, our results indicate that the continuum-continuum time delay in photoemission of heteronuclear molecules is asymmetric.

Determination of the photoemission position in single-photon ionization with attosecond streaking spectroscopy

Attosecond metrology can directly measure attosecond emission time of photoexcited electrons from matter, providing unprecedented understanding of transition processes of electrons from bound to continuum states. However, some fundamental details of the electron dynamics in the entire emission process upon photoexcitation still remain debatable or unknown. The photoemission time delays deduced from attosecond streaking spectroscopy originate from photoelectron propagation in the coupled Coulomb-laser fields, encoding the spatial and spectral information of electrons upon photoexcitation. Here we demonstrate that attosecond photoemission delays can be used to image picometer-resolved photoemission position via a classical model. The electronic dynamics in the laser-assisted single-photon ionization process is fully captured by a quantum path-integral model. We trace the imaged photoemission position to the average position of spatially coherent superposition of electron waves upon photoexcitation and, in particular, predict emission position coinciding with the orbital radius of the ground state of hydrogen-like atoms, in contrast with previous predictions.

An eikonal approximation model for two-color two-photon attosecond interferometric spectrum

The emission time of photoelectrons from atoms, molecules and solids can be accurately measured on an attosecond scale by using two-color two-photon attosecond interferometric spectroscopy, which helps us to understand the ultrafast electronic dynamics in laser-assisted single photoionization. Understanding the photoelectron emission time depends on the physical model, and the relevant theoretical model provides a better physical explanation and numerical prediction for the photoemission time delay. Although the numerical solution of the time-dependent Schrödinger equation can accurately predict the photoelectron emission time, but it cannot provide a physical explanation. Although some other current theoretical models can provide a more reasonable corresponding physical process, the quantitative prediction of the photoemission time delay has a large deviation. Therefore, we improve the exisating eikonal approximation model. Comparing with the existing eikonal approximation model, we use a more accurate final state wave function and calculate the photoelectron trajectory more accurately when calculating the phase accumulated in the photoelectron propagation process, so we can predict the photoemission time delay more accurately. By comparing our numerical simulation results, we find that when the final kinetic energy of photoelectron is low, the calculated results from the existing theoretical model are greatly different from those from the time-dependent Schrödinger equation, reaching tens of attoseconds. The resultsfrom the existing theoretical model are closer to those from the time-dependent Schrödinger equation with the increase of final kinetic energy of photoelectron. However, no matter what the final kinetic energy of the photoelectron is, the difference between the calculation result from the improved eikonal approximation model and that from the time-dependent Schrödinger equation is always very small. Therefore, our improved eikonal approximation model is closer to the results from the time-dependent Schrödinger equation than the existing theoretical model, which greatly deeps our understanding of the ultra-fast process of photoelectron emission.

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.

Effects of spin-orbit-interaction-activated interchannel coupling on photoemission time delay

Effects of spin-orbit-interaction-activated interchannel coupling on photoemission time delay

Strong dependence of photoionization time delay on energy and angle in the neighborhood of Fano resonances

We uncover dramatic variations of the Wigner photoemission time delay with energy and angle in the vicinity of a Fano resonance with the time delay taking opposite signs at different angles at the same energy as well as at the opposite sides of the resonance at the same angle. These variations are illustrated by choosing the Ne $2s\ensuremath{\rightarrow}3p$ autoionizing state as a case study. Moreover, we demonstrate the existence of strikingly significant changes in time delay due to relativistic effects despite Ne being a low-$Z$ atom. This finding shows the possibility for utilizing time delay chronoscopy as a route towards experimental probing of relativistic interactions and the phases of individual transition matrix elements upon atomic photoionization of low-$Z$ atoms. Finally, we develop a practical parametrization to model and explain the angle and energy variation of the autoionizing resonance time delay in the nonrelativistic limit.

Using a passively stable attosecond beamline for relative photoemission time delays at high XUV photon energies.

We present and demonstrate an experimental scheme that enables overlap-free reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) measurements at high extreme-ultraviolet (XUV) photon energies. A compact passively-stabilized attosecond beamline employing a multilayer (ML) mirror allows us to obtain XUV pulses consisting of only two odd high-harmonic orders from an attosecond pulse train (APT). We compare our new technique to existing schemes that are used to perform RABBITT measurements and discuss how our scheme resolves the limitations imposed by spectral complexity of the harmonic comb at high photon energies. We further demonstrate first applications of our scheme for rare gases and gas mixtures, and show that this scheme can be extended to gas-molecule mixtures.

Attosecond-Resolved Electron Dynamics in Many-Electron Atoms: Quantitative Theory and Comparison with Measurements

A variety of processes originating from the interaction of atomic or molecular N-electron states with strong and/or hypershort radiation pulses can be understood quantitatively only by first determining with good accuracy the solutions of the many-electron time-dependent Schrödinger equation (METDSE) that describe the corresponding physics. The METDSE is solvable nonperturbatively via the state-specific expansion approach (SSEA). SSEA solutions have been used, or can be used, for quantitative explanation and numerically reliable predictions of quantities that have been measured or are measurable in modern laser-driven experiments that can track, with hypershort (attosecond) time resolution, the effects of electron rearrangements in atoms and molecules. The calculations take into account in a transparent way the interplay between the phenomena and the electronic structures of the physically significant states in discrete and multichannel continuous spectra, including multiply- and inner-hole–excited resonance states. The discussion focuses on novel topics of time-resolved many-electron physics and includes a comparison of our predictions to recent quantitative measurements of attosecond-resolved generation of the profile of the ( 2 s 2 p ) 1 P o doubly excited resonance state of helium during photoionization and of the relative time delay in photoemission of the (2s,2p) electrons of neon.

Angle-resolved Wigner time delay in atomic photoionization: The 4d subshell of free and confined Xe

The angular dependence of photoemission time delay for the inner $n{d}_{3/2}$ and $n{d}_{5/2}$ subshells of free and confined Xe is studied in the dipole relativistic random phase approximation. A finite spherical annular well potential is used to model the confinement due to fullerene ${C}_{60}$ cage. Near cancellations in a variety of the dipole amplitudes, Cooper-like minima, are found. The effects of confinement on the angular dependence, primarily confinement resonances, are demonstrated and detailed.

Photoemission and photoionization time delays and rates.

Ionization and, in particular, ionization through the interaction with light play an important role in fundamental processes in physics, chemistry, and biology. In recent years, we have seen tremendous advances in our ability to measure the dynamics of photo-induced ionization in various systems in the gas, liquid, or solid phase. In this review, we will define the parameters used for quantifying these dynamics. We give a brief overview of some of the most important ionization processes and how to resolve the associated time delays and rates. With regard to time delays, we ask the question: how long does it take to remove an electron from an atom, molecule, or solid? With regard to rates, we ask the question: how many electrons are emitted in a given unit of time? We present state-of-the-art results on ionization and photoemission time delays and rates. Our review starts with the simplest physical systems: the attosecond dynamics of single-photon and tunnel ionization of atoms in the gas phase. We then extend the discussion to molecular gases and ionization of liquid targets. Finally, we present the measurements of ionization delays in femto- and attosecond photoemission from the solid–vacuum interface.

Angle-dependent time delay in two-color XUV+IR photoemission of He and Ne

We solve the time-dependent Schr\odinger equation for a noble gas atom (He and Ne) driven by an ionizing XUV and dressing IR fields. From this solution we deduce an angular dependence of the photoemission time delay as measured by the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) technique. We use a recent angle-resolved RABBITT measurement on helium [S. Heuser et al., Phys. Rev. A 94, 063409 (2016)] to test and calibrate our theoretical model. Based on this calibration, we find no significant difference between the time delay in He measured in the angle-integrated RABBITT experiments [C. Palatchi et al., J. Phys. B 47, 245003 (2014) and D. Gu\'enot et al., J. Phys. B 47, 245602 (2014)] and measured or calculated in the polarization axis direction. The angular dependence of the photoemission time delay of Ne is shown to be qualitatively different from He because of the different orbital character of the valence $2p$ orbital. The angular momentum projection dependence of the time delay in Ne is also investigated.