Resonance Effects in Photoemission Time Delays

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.

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.

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.

Phase stabilization of an attosecond beamline combining two IR colors

We present a phase-stabilized attosecond pump-probe beamline involving two separate infrared wavelengths for high-harmonic generation (HHG) and pump or probe. The output of a Ti:sapphire laser is partly used to generate attosecond pulses via HHG and partly to pump an optical parametric amplifier (OPA) that converts the primary Ti:sapphire radiation to a longer wavelength. The attosecond pulse and down-converted infrared are recombined after a more than 20-m-long Mach-Zehnder interferometer that spans across two laboratories and separate optical tables. We demonstrate a technique for active stabilization of the relative phase of the pump and probe to within 450 as rms, without the need for an auxiliary continuous wave (cw) laser. The long-term stability of our system is demonstrated with an attosecond photoelectron streaking experiment. While the technique has been shown for one specific OPA output wavelength (1560 nm), it should also be applicable to other OPA output wavelengths. Our setup design permits tuning of the OPA wavelength independently from the attosecond pulse generation. This approach yields new possibilities for studying the wavelength-dependence of field-driven attosecond electron dynamics in various systems.

Accuracy and precision of the RABBIT technique

One of the most ubiquitous techniques within attosecond science is the so-called reconstruction of attosecond beating by interference of two-photon transitions (RABBIT). Originally proposed for the characterization of attosecond pulses, it has been successfully applied to the accurate determination of time delays in photoemission. Here, we examine in detail, using numerical simulations, the effect of the spatial and temporal properties of the light fields and of the experimental procedure on the accuracy of the method. This allows us to identify the necessary conditions to achieve the best temporal precision in RABBIT measurements. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

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.

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.

Orientation-dependent stereo Wigner time delay and electron localization in a small molecule

Attosecond metrology of atoms has accessed the time scale of the most fundamental processes in quantum mechanics. Transferring the time-resolved photoelectric effect from atoms to molecules considerably increases experimental and theoretical challenges. Here we show that orientation- and energy-resolved measurements characterize the molecular stereo Wigner time delay. This observable provides direct information on the localization of the excited electron wave packet within the molecular potential. Furthermore, we demonstrate that photoelectrons resulting from the dissociative ionization process of the CO molecule are preferentially emitted from the carbon end for dissociative ²Σ states and from the center and oxygen end for the ²Π states of the molecular ion. Supported by comprehensive theoretical calculations, this work constitutes a complete spatially and temporally resolved reconstruction of the molecular photoelectric effect.

Generation of coherent extreme ultraviolet radiation from α-quartz using 50 fs laser pulses at a 1030 nm wavelength and high repetition rates

Coherent extreme ultraviolet (EUV) radiation using high-harmonic generation (HHG) in α-quartz is demonstrated from 10 to 200 kHz, using 50 fs laser pulses at the center wavelength of 1030 nm. The EUV radiation extends beyond 25 eV in the nondamaging regime. The number of photons generated in a single harmonic order at 15.6 eV is measured to be ≈(3.5±2.5)×10¹⁰ per second which, to the best of our knowledge, is a first and record value reported to date using EUV HHG from solids. This Letter demonstrates one of the first all-solid-state EUV sources based on industrial-grade fiber lasers, enabling the possibility of bringing reliable EUV sources to the mass market.

Few-femtosecond extreme-ultraviolet pulses fully reconstructed by a ptychographic technique

Sub-10-fs pulses tunable in the extreme-ultraviolet (XUV) spectral region are particularly important in many research fields: from atomic and molecular spectroscopy to the study of relaxation processes in solids and transition phase processes, from holography to free-electron laser injection. A crucial prerequisite for all applications is the accurate measurement of the temporal characteristics of these pulses. To fulfill this purpose, many phase retrieval algorithms have been successfully applied to reconstruct XUV attosecond pulses. Nevertheless, their extension to XUV femtosecond pulses is not trivial and has never been investigated/reported so far. We demonstrate that ultrashort XUV pulses, produced by high-order harmonic generation, spectrally filtered by a time-delay compensated monochromator, can be fully characterized, in terms of temporal intensity and phase, by employing the ptychographic reconstruction technique while other common reconstruction algorithms fail. This allows us to report on the generation and complete temporal characterization of XUV pulses with duration down to 5 fs, which constitute the shortest XUV pulse ever achieved via a time-delay compensated monochromator.

Anisotropic photoemission time delays close to a Fano resonance

Electron correlation and multielectron effects are fundamental interactions that govern many physical and chemical processes in atomic, molecular and solid state systems. The process of autoionization, induced by resonant excitation of electrons into discrete states present in the spectral continuum of atomic and molecular targets, is mediated by electron correlation. Here we investigate the attosecond photoemission dynamics in argon in the 20–40 eV spectral range, in the vicinity of the 3s⁻¹np autoionizing resonances. We present measurements of the differential photoionization cross section and extract energy and angle-dependent atomic time delays with an attosecond interferometric method. With the support of a theoretical model, we are able to attribute a large part of the measured time delay anisotropy to the presence of autoionizing resonances, which not only distort the phase of the emitted photoelectron wave packet but also introduce an angular dependence.

Ionization time delays are of interest in understanding the photoionization mechanism in atoms and molecules in ultra-short time scales. Here the authors investigate the angular dependence of photoionization time delays in the presence of an autoionizing resonance in argon atom using RABBITT technique.

Attosecond Time Delay in Photoionization of Noble-Gas and Halogen Atoms

Ultrafast processes are now accessible on the attosecond time scale due to the availability of ultrashort XUV laser pulses. Noble-gas and halogen atoms remain important targets due to their giant dipole resonance and Cooper minimum. Here, we calculate photoionization cross section, asymmetry parameter and Wigner time delay using the time-dependent local-density approximation (TDLDA), which includes the electron correlation effects. Our results are consistent with experimental data and other theoretical calculations. The asymmetry parameter provides an extra layer of access to the phase information of the photoionization processes. We find that halogen atoms bear a strong resemblance on cross section, asymmetry parameter and time delay to their noble-gas neighbors. Our predicted time delay should provide a guidance for future experiments on those atoms and related molecules.

Characterizing isolated attosecond pulses with angular streaking

We present a reconstruction algorithm for isolated attosecond pulses, which exploits the phase dependent energy modulation of a photoelectron ionized in the presence of a strong laser field. The energy modulation due to a circularly polarized laser field is manifest strongly in the angle-resolved photoelectron momentum distribution, allowing for complete reconstruction of the temporal and spectral profile of an attosecond burst. We show that this type of reconstruction algorithm is robust against counting noise and suitable for single-shot experiments. This algorithm holds potential for a variety of applications for attosecond pulse sources.

Erratum: Resonance Effects in Photoemission Time Delays [Phys. Rev. Lett. 115, 133001 (2015)]

This corrects the article DOI: 10.1103/PhysRevLett.115.133001.

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.

Attosecond dynamics through a Fano resonance: Monitoring the birth of a photoelectron

The dynamics of quantum systems are encoded in the amplitude and phase of wave packets. However, the rapidity of electron dynamics on the attosecond scale has precluded the complete characterization of electron wave packets in the time domain. Using spectrally resolved electron interferometry, we were able to measure the amplitude and phase of a photoelectron wave packet created through a Fano autoionizing resonance in helium. In our setup, replicas obtained by two-photon transitions interfere with reference wave packets that are formed through smooth continua, allowing the full temporal reconstruction, purely from experimental data, of the resonant wave packet released in the continuum. In turn, this resolves the buildup of the autoionizing resonance on an attosecond time scale. Our results, in excellent agreement with ab initio time-dependent calculations, raise prospects for detailed investigations of ultrafast photoemission dynamics governed by electron correlation, as well as coherent control over structured electron wave packets.

Gouy phase shift for annular beam profiles in attosecond experiments

Attosecond pump-probe measurements are typically performed by combining attosecond pulses with more intense femtosecond, phase-locked infrared (IR) pulses because of the low average photon flux of attosecond light sources based on high-harmonic generation (HHG). Furthermore, the strong absorption of materials at the extreme ultraviolet (XUV) wavelengths of the attosecond pulses typically prevents the use of transmissive optics. As a result, pump and probe beams are typically recombined geometrically with a center-hole mirror that reflects the larger IR beam and transmits the smaller XUV, which leads to an annular beam profile of the IR. This modification of the IR beam can affect the pump-probe measurements because the propagation that follows the reflection on the center-hole mirror can strongly deviate from that of an ideal Gaussian beam. Here we present a detailed experimental study of the Gouy phase of an annular IR beam across the focus using a two-foci attosecond beamline and the RABBITT (reconstruction of attosecond beating by interference of two-photon transitions) technique. Our measurements show a Gouy phase shift of the truncated beam as large as 2π and a corresponding rate of 50 as/mm time delay change across the focus in a RABBITT measurement. These results are essential for attosecond pump-probe experiments that compare measurements of spatially separated targets.

Comparison of attosecond streaking and RABBITT

Recent progress in the generation of ultra-short laser pulses has enabled the measurement of photoionization time delays with attosecond precision. For single photoemission time delays the most common techniques are based on attosecond streaking and the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT). These are pump-probe techniques employing an extreme-ultraviolet (XUV) single attosecond pump pulse for streaking or an attosecond pump pulse train for RABBITT, and a phase-locked infrared (IR) probe pulse. These techniques can only extract relative timing information between electrons originating from different initial states within the same atom or different atoms. Here we address the question whether the two techniques give identical timing information. We present a complete study, supported by both experiments and simulations, comparing these two techniques for the measurement of the photoemission time delay difference between valence electrons emitted from the Ne 2p and Ar 3p ground states. We highlight not only the differences and similarities between the two techniques, but also critically investigate the reliability of the methods used to extract the timing information.

Attosecond science in atomic, molecular, and condensed matter physics

Attosecond science represents a new frontier in atomic, molecular, and condensed matter physics, enabling one to probe the exceedingly fast dynamics associated with purely electronic dynamics in a wide range of systems. This paper presents a brief discussion of the technology required to generate attosecond light pulses and gives representative examples of attosecond science carried out in several laboratories. Attosecond transient absorption, a very powerful method in attosecond science, is then reviewed and several examples of gas phase and condensed phase experiments that have been carried out in the Leone/Neumark laboratories are described.

Ptychographic reconstruction of attosecond pulses

We demonstrate a new attosecond pulse reconstruction modality which uses an algorithm that is derived from ptychography. In contrast to other methods, energy and delay sampling are not correlated, and as a result, the number of electron spectra to record is considerably smaller. Together with the robust algorithm, this leads to a more precise and fast convergence of the reconstruction.

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.