Photoemission Delays Research Articles

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.

Attosecond delay in the molecular photoionization of asymmetric molecules.

We report theoretical calculations of the delay in photoemission from CO with particular emphasis on the role of the ultrafast electronic bound dynamics. We study the delays in photoionization in the HOMO and HOMO-1 orbitals of the CO molecule by looking into the stereo Wigner time delay technique. That compares the delay in photoemission from electrons emitted to the left and right to extract structural and dynamical information of the ionization process. For this we apply two techniques: The attosecond streak camera and the time of flight technique. Although they should provide the same results we have found large discrepancies of up to 36 in the case of HOMO, while for the HOMO-1 we obtain the same results with the two techniques. We have found that the large time delays observed in the HOMO orbital with the streaking technique are a consequence of the resonant transition triggered by the streaking field. This resonant transition produces a bound electron wavepacket that modifies the measurements of delay in photoionization. As a result of this observation, our technique allows us to reconstruct the bound wavepacket dynamics induced by the streaking field. By measuring the expected value of the electron momentum along the polarization direction after the streaking field has finished, we can recover the relative phase between the complex amplitudes of the HOMO and LUMO orbitals. These theoretical calculations pave the way for the measurement of ultrafast bound-bound electron transitionsand its crucial role for the delay in photoemission observation.

Extracting attosecond delays from spectrally overlapping interferograms

Attosecond interferometry is becoming an increasingly popular technique for measuring the dynamics of photoionization in real time. Whereas early measurements focused on atomic systems with very simple photoelectron spectra, the technique is now being applied to more complex systems including isolated molecules and solids. The increase in complexity translates into an augmented spectral congestion, unavoidably resulting in spectral overlap in attosecond interferograms. Here, we discuss currently used methods for phase retrieval and introduce two new approaches for determining attosecond photoemission delays from spectrally overlapping photoelectron spectra. We show that the previously used technique, consisting in the spectral integration of the areas of interest, does in general not provide reliable results. Our methods resolve this problem, thereby opening the technique of attosecond interferometry to complex systems and fully exploiting its specific advantages in terms of spectral resolution compared to attosecond streaking.

Control of photoemission delay in resonant two-photon transitions

SynopsisIn contrast to one-photon transitions and non-resonant multiphoton transitions, time delay in resonant multi-photon electron emission can exhibit large positive and negative values that have no scattering equivalent, due to the interference of multiple ionization paths.

Control of photoemission delay in resonant two-photon transitions

The photoelectron emission time delay $\ensuremath{\tau}$ associated with one-photon absorption, which coincides with half the Wigner delay ${\ensuremath{\tau}}_{\mathrm{W}}$ experienced by an electron scattered off the ionic potential, is a fundamental descriptor of the photoelectric effect. Although it is hard to access directly from experiment, it is possible to infer it from the time delay of two-photon transitions, ${\ensuremath{\tau}}^{(2)}$, measured with attosecond pump-probe schemes, provided that the contribution of the probe stage can be factored out. In the absence of resonances, $\ensuremath{\tau}$ can be expressed as the energy derivative of the one-photon ionization amplitude phase, $\ensuremath{\tau}={\ensuremath{\partial}}_{E}arg{D}_{Eg}$, and, to a good approximation, $\ensuremath{\tau}={\ensuremath{\tau}}^{(2)}\ensuremath{-}{\ensuremath{\tau}}_{\mathrm{cc}}$, where ${\ensuremath{\tau}}_{\mathrm{cc}}$ is associated with the dipole transition between Coulomb functions. Here we show that, in the presence of a resonance, the correspondence between $\ensuremath{\tau}$ and ${\ensuremath{\partial}}_{E}arg{D}_{Eg}$ is lost. Furthermore, while ${\ensuremath{\tau}}^{(2)}$ can still be written as the energy derivative of the two-photon ionization amplitude phase, ${\ensuremath{\partial}}_{E}arg{D}_{Eg}^{(2)}$, it does not have any scattering counterpart. Indeed, ${\ensuremath{\tau}}^{(2)}$ can be much larger than the lifetime of an intermediate resonance in the two-photon process or more negative than the lower bound imposed on scattering delays by causality. Finally, we show that ${\ensuremath{\tau}}^{(2)}$ is controlled by the frequency of the probe pulse, ${\ensuremath{\omega}}_{\mathrm{IR}}$, so that by varying ${\ensuremath{\omega}}_{\mathrm{IR}}$, it is possible to radically alter the photoelectron group delay.

Spin Polarization and Attosecond Time Delay in Photoemission from Spin Degenerate States of Solids.

After photon absorption, electrons from a dispersive band of a solid require a finite time in the photoemission process before being photoemitted as free particles, in line with recent attosecond-resolved photoemission experiments. According to the Eisenbud-Wigner-Smith model, the time delay is due to a phase shift of different transitions that occur in the process. Such a phase shift is also at the origin of the angular dependent spin polarization of the photoelectron beam, observable in spin degenerate systems without angular momentum transfer by the incident photon. We propose a semiquantitative model which permits us to relate spin and time scales in photoemission from condensed matter targets and to better understand spin- and angle-resolved photoemission spectroscopy (SARPES) experiments on spin degenerate systems. We also present the first experimental determination by SARPES of this time delay in a dispersive band, which is found to be greater than 26 as for electrons emitted from the sp-bulk band of the model system Cu(111).

Wigner photoemission time delay from endohedral anions

Characteristic features of Wigner photoemission time delay from endohedral anions A@${\mathrm{C}}_{60}{}^{q}$ along with their dependence on the anion charge $q$ are unraveled. Specifically, significant enhancement of the time delay in the innermost dipole photoionization channels near threshold is found, owing to the presence of the Coulomb confined resonances (CRs). Moreover, it is shown that interchannel coupling of the inner-shell Coulomb CRs with outer-shell photoionization channels results in resonantly enhanced time delay in the release of the outer-shell photoelectron well above, several hundreds eV, the outer-shell thresholds. It is also demonstrated that, and explained why, photoionization cross sections of the innermost subshells as well as outer subshells (near the inner-subshell threshold) depends only very weakly on the anion charge $q$, but the dependence of the corresponding time delays on $q$ can be significant. Furthermore, Coulomb CRs are found to emerge in the innermost quadrupole photoionization channels as well, thereby causing considerable time delay in the quadrupole photoemission. These findings are illustrated in calculations of the photoionization of inner and outer subshells of the endohedral anions Ne@${\text{C}}_{60}{}^{\ensuremath{-}1}$ and Ne@${\mathrm{C}}_{60}{}^{\ensuremath{-}5}$ that were chosen as case studies.

Attosecond Time Delay in Photoemission and Electron Scattering near Threshold.

We study the time delay in the primary photoemission channel near the opening of an additional channel and compare it with the Wigner time delay in elastic scattering of the photoelectron near the corresponding inelastic threshold. The photoemission time delay near threshold is significantly enhanced, to a measurable 40 as, in comparison to the corresponding elastic scattering delay. The enhancement is due to the different lowest order of interelectron interaction coupling the primary and additional photoemission channels. We illustrate these findings by considering photodetachment from the H^{-} negative ion, and compare it with electron scattering on the hydrogen atom near the first excitation threshold. Other threshold processes of atomic photoionization and molecular photofragmentation, where photoemission time delay is enhanced, are identified. This opens the possibility of studying threshold behavior utilizing attosecond chronoscopy.

Attosecond photoemission dynamics encoded in real-valued continuum wave functions

The dynamics of photoemission is fully encoded in the continuum wave functions selected by the transitions. Using numerical simulations on simple benchmark models, we show how scattering phase shifts and photoemission delays can be retrieved from this unambiguously defined class of wave functions. In contrast with standard scattering waves inherited from collision theory, they are real-valued for one-photon transitions and provide a clear-cut interpretation of the delays recently discussed in the framework of attosecond science.

Light-Matter Interaction at Surfaces in the Spatiotemporal Limit of Macroscopic Models.

What is the spatiotemporal limit of a macroscopic model that describes the optoelectronic interaction at the interface between different media? This fundamental question has become relevant for time-dependent photoemission from solid surfaces using probes that resolve attosecond electron dynamics on an atomic length scale. We address this fundamental question by investigating how ultrafast electron screening affects the infrared field distribution for a noble metal such as Cu(111) at the solid-vacuum interface. Attosecond photoemission delay measurements performed at different angles of incidence of the light allow us to study the detailed spatiotemporal dependence of the electromagnetic field distribution. Surprisingly, comparison with Monte Carlo semiclassical calculations reveals that the macroscopic Fresnel equations still properly describe the observed phase of the IR field on the Cu(111) surface on an atomic length and an attosecond time scale.

Attosecond time-resolved streaked photoemission from Mg-covered W(110) surfaces

We formulate a quantum-mechanical model for infrared-streaked photoelectron (PE) emission by ultrashort extreme ultraviolet (XUV) pulses from an adsorbate-covered metal surface, exposing the influence of microscopic PE dispersion in substrate and adsorbate on the interpretation of streaked photoemission spectra and photoemission time delays. We validate this numerical model first by reproducing measured relative photoemission delays (a) between valence-band and $2p$-core-level (CL) PEs emitted from clean Mg(0001) surfaces and (b) between conduction-band (CB) and $4f$-CL PEs from clean W(110) surfaces at two XUV-pulse central photon energies. Next, applying this model to ultrathin Mg adsorbate layers on W(110) substrates, we reproduce (i) the measured nonmonotonic dependence of relative photoemission delays between CB and $\mathrm{Mg}(2p$) PEs and (ii) the monotonic dependence of relative delays between $\mathrm{W}(4f$) and $\mathrm{Mg}(2p$) PEs in a recent experiment [S. Neppl et al., Nature (London) 517, 342 (2015)].

Photoionization dynamics: Transition and scattering delays

SynopsisThe advent of attosecond science, with main objectives to probe and to control ultrafast dynamics in quantum systems, brought in the past few years a fresh look on photoemission. This very fundamental process was indeed recently revisited in the time domain, in a series of pioneering experiments that were soon accompanied by an intense theoretical activity devoted to the interpretation of the reported “photoemission delays”. At the conference, we will present some contributions of our group to this topic, with a focus on the characterization of photoemission dynamics in terms of “scattering delay” and “transition delay” as evidenced in numerical experiments performed on simple model systems.

Energy-dependent photoemission delays from noble metal surfaces by attosecond interferometry

How quanta of energy and charge are transported on both atomic spatial and ultrafast time scales is at the heart of modern technology. Recent progress in ultrafast spectroscopy has allowed us to directly study the dynamical response of an electronic system to interaction with an electromagnetic field. Here, we present energy-dependent photoemission delays from the noble metal surfaces Ag(111) and Au(111). An interferometric technique based on attosecond pulse trains is applied simultaneously in a gas phase and a solid state target to derive surface-specific photoemission delays. Experimental delays on the order of 100 as are in the same time range as those obtained from simulations. The strong variation of measured delays with excitation energy in Ag(111), which cannot be consistently explained invoking solely electron transport or initial state localization as supposed in previous work, indicates that final state effects play a key role in photoemission from solids.

Angular resolved time delay in photoemission

We investigate theoretically the relative time delay of photoelectrons originating from different atomic subshells of noble gases. This quantity was measured via attosecond streaking and studied theoretically by Schultze et al (2010 Science 328 1658) for neon. A substantial discrepancy was found between the measured and the calculated values of the relative time delay. Several theoretical studies were put forward to resolve this issue, e.g., by including correlation effects. In the present paper we explore a further aspect, namely the directional dependence of time delay. In contrast to neon, for argon target a strong angular dependence of the time delay is found near the Cooper minimum.

Attosecond Time-Resolved Photoelectron Dispersion and Photoemission Time Delays

We compute spectrograms and relative time delays for laser-assisted photoemission by single attosecond extreme ultraviolet pulses from valence band (VB) and 2p core levels (CLs) of a Mg(0001) surface within a quantum-mechanical model. Comparing the time-dependent dispersion of photoelectron (PE) wave packets for VB and CL emission, we find striking differences in their dependence on the (i)electron mean free path (MFP) in the solid, (ii)screening of the streaking laser field, and (iii)chirp of the attosecond pulse. The relative photoemission delay between VB and 2p PEs is shown to be sensitive to the electron MFP and screening of the streaking laser field inside the solid. Our model is able to reproduce a recent attosecond-streaking experiment [S. Neppl et al., Phys. Rev. Lett. 109, 087401 (2012)], which reveals no relative streaking time delay between VB and 2p PEs.

Time-resolved photoemission on the attosecond scale: opportunities and challenges

The interaction of laser pulses of sub-femtosecond duration with matter opened up the opportunity to explore electronic processes on their natural time scale. One central conceptual question posed by the observation of photoemission in real time is whether the ejection of the photoelectron wavepacket occurs instantaneously, or whether the response time to photoabsorption is finite leading to a time delay in photoemission. Recent experimental progress exploring attosecond streaking and RABBIT techniques find relative time delays between the photoemission from different atomic substates to be of the order of -20 attoseconds. We present ab initio simulations for both one- and two-electron systems which allow the determination of both absolute and relative time delays with -1 attosecond precision. We show that the intrinsic time shift of the photoionization process encoded in the Eisenbud-Wigner-Smith delay time can be unambiguously disentangled from measurement-induced time delays in a pump-probe setting when the photoionized electronic wavepacket is probed by a modestly strong infrared streaking field. We identify distinct contributions due to initial-state polarization, Coulomb-laser coupling in the final continuum state as well as final-state interaction with the entangled residual ionic state. Extensions to multi-electron systems and to the extraction of time information in the presence of decohering processes are discussed.

Attosecond streaking of shake-up and Auger electrons in xenon

We present first results of simultaneous attosecond streaking measurements of shake-up electrons and Auger electrons emitted from xenon. We extract relative photo-emission delays for electrons emitted from the 4d, 5s and 5p subshell, as well as for the 5p −2 5d correlation satellite (shake-up electrons).

Effect of wave-function localization on the time delay in photoemission from surfaces

We investigate streaking time delays in the photoemission from a solid model surface as a function of the degree of localization of the initial-state wave functions. We consider a one-dimensional slab with lattice constant alatt of attractive Gaussian-shaped core potentials of width σ . The parameter σ/alatt thus controls the overlap between adjacent core potentials and localization of the electronic eigenfunctions on the lattice points. Small values of σ/alatt � 1 yield lattice eigenfunctions that consist of localized atomic wave functions modulated by a “Bloch-envelope” function, while the eigenfunctions become delocalized for larger values of σ/alatt 0.4. By numerically solving the time-dependent Schr¨ odinger equation, we calculate photoemission spectra from which we deduce a characteristic bimodal shape of the band-averaged photoemission time delay: as the slab eigenfunctions become increasingly delocalized, the time delay quickly decreases near σ/alatt = 0.3 from relatively large values below σ/alatt ∼ 0.2 to much smaller delays above σ/alatt ∼ 0.4. This change in wave-function localization facilitates the interpretation of a recently measured apparent relative time delay between the photoemission from core and conduction-band levels of a tungsten surface.

Streaking and Wigner time delays in photoemission from atoms and surfaces

Streaked photoemission metrology allows the observation of an apparent relative time delay between the detection of photoelectrons from different initial electronic states. This relative delay is obtained by recording the photoelectron yield as a function of the delay between an ionizing ultrashort extended ultraviolet (XUV) pulse and a streaking infrared (IR) pulse. Theoretically, photoemission delays can be defined based on i) the phase shift the photoelectron wavefunction accumulates during the release and propagation of the photoelectron (``Wigner delay") and, alternatively, ii) the streaking trace in the calculated photoemission spectrum (``streaking delay"). We investigate the relation between Wigner and streaking delays in the photoemission from atomic and solid-surface targets. For solid targets and assuming a vanishing IR-skin depth, both Wigner and streaking delays can be interpreted as an average propagation time needed by photoelectrons to reach the surface, while the two delays differ for non-vanishing skin depths. For atomic targets, the difference between Wigner and streaking delays depends on the range of the ionic potential.