Understanding attosecond streaking.

This tutorial provides an overview on the theory of attosecond streaking, a pump-probe scheme to extract timing information of ionization processes that has been widely used in the past decade. Emphasis is put on the origin of the Coulomb-laser-coupling (CLC) term, which is crucial in the interpretation of streaking delays. Having gained a proper understanding of how the CLC terms in various publications relate to each other, we will be able to analyze in which regime the streaking delay can be split into a measurement-induced CLC term and a `pure' ionization delay and under which conditions this splitting may break down. Thus we address the long-standing question of the validity of the widely applied interpretation of the streaking delay as a sum of the CLC term and a `pure' ionization delay.

Time-dependent Extension of Grimme's Continuous Chirality Measure for Electronic Chirality Flips in Femto- and Attosecond Time Domains.

Grimme's Continuous Chirality Measure (CCM ) was developed for comparisons of the chirality of the electronic wave functions of molecules, typically in their ground states. For example, CCM=14.5, 1.2,  and 0.0 for alanine, hydrogen-peroxide, and for achiral molecules, respectively. Well-designed laser pulses can excite achiral molecules from the electronic ground state to time-dependent chiral superposition states, with chirality flips in the femto- or even attosecond (fs or as) time domains. Here we provide a time-dependent extension CCM(t) of Grimme's CCM for trailing the electronic chirality flips. As examples, we consider two laser driven electronic wavefunctions which represent flips between opposite electronic enantiomers of oriented NaK within 4.76 fs and 433 as. The corresponding  CCM(t) vary respectively from 14.5 or from 13.3 to 0.0, and back.

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

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

Controlling laser-dressed resonance line shape using attosecond extreme-ultraviolet pulse with a spectral minimum.

High-harmonic generation from a gas target exhibits sharp spectral features and rapid phase variation near the Cooper minimum. By applying spectral filtering, shaped isolated attosecond pulses can be generated where the pulse is split into two in the time domain. Using such shaped extreme-ultraviolet (XUV) pulses, we theoretically study attosecond transient absorption (ATA) spectra of helium [Formula: see text] autoionizing state which is resonantly coupled to the [Formula: see text] dark state by a time-delayed infrared laser. Our simulations show that the asymmetric [Formula: see text] Fano line shape can be readily tuned into symmetric Lorentzian within the time delay of a few tens of attoseconds. Such efficient control is due to the destructive interference in the generation of the [Formula: see text] state when it is excited by a strongly shaped XUV pulse. This is to be compared to prior experiments where tuning the line shape of a Fano resonance would take tens of femtoseconds. We also show that the predicted ATA spectral line shape can be observed experimentally after propagation in a gas medium. Our results suggest that strongly shaped attosecond XUV pulses offer the opportunity for controlling and probing fine features of narrow resonances on the few-ten attoseconds timescale.

High-harmonic spectroscopy of low-energy electron-scattering dynamics in liquids.

High-harmonic spectroscopy is an all-optical nonlinear technique with inherent attosecond temporal resolution. It has been applied to a variety of systems in the gas phase and solid state. Here we extend its use to liquid samples. By studying high-harmonic generation over a broad range of wavelengths and intensities, we show that the cut-off energy is independent of the wavelength beyond a threshold intensity and that it is a characteristic property of the studied liquid. We explain these observations with a semi-classical model based on electron trajectories that are limited by the electron scattering. This is further confirmed by measurements performed with elliptically polarized light and with ab-initio time-dependent density functional theory calculations. Our results propose high-harmonic spectroscopy as an all-optical approach for determining the effective mean free paths of slow electrons in liquids. This regime is extremely difficult to access with other methodologies, but is critical for understanding radiation damage to living tissues. Our work also indicates the possibility of resolving subfemtosecond electron dynamics in liquids offering an all-optical approach to attosecond spectroscopy of chemical processes in their native liquid environment.

Scattering of Attosecond Laser Pulses on a DNA Molecule during Its Nicking and Bending.

It is well known that X-ray crystallography is based on X-ray diffraction (XRD) for atoms and molecules. The diffraction pattern arises as a result of scattering of incident radiation, which makes it possible to determine the structure of the scattering substance. With the advent of ultrashort radiation sources, the theory and interpretation of X-ray diffraction analysis have remained the same. This work shows that when an attosecond laser pulse is scattered on a DNA molecule, including during its nicking and bending, the pulse duration is an important characteristic of the scattering. In this case, the diffraction pattern changes significantly compared to the previously known scattering theory. The results obtained must be used in XRD theory to study DNA structures, their mutations and damage, since the previously known theory can produce large errors and, therefore, the DNA structure can be "decoding" incorrectly.

High harmonic generation in solids: particle and wave perspectives.

High harmonic generation (HHG) from gas-phase atoms (or molecules) has opened up a new frontier in ultrafast optics, where attosecond time resolution and angstrom spatial resolution are accessible. The fundamental physical pictures of HHG are always explained by the laser-induced recollision of particle-like electron motion, which lay the foundation of attosecond spectroscopy. In recent years, HHG has also been observed in solids. One can expect the extension of attosecond spectroscopy to the condensed matter if a description capable of resolving the ultrafast dynamics is provided. Thus, a large number of theoretical studies have been proposed to understand the underlying physics of solid HHG. Here, we revisit the recollision picture in solid HHG and show some challenges of current particle-perspective methods, and present the recently developed wave-perspective Huygens-Fresnel picture for understanding dynamical systems within the ambit of strong-field physics.

Theoretical Description of Attosecond X-ray Absorption Spectroscopy of Frenkel Exciton Dynamics.

Frenkel excitons are responsible for the transport of light energy in many molecular systems. Coherent electron dynamics govern the initial stage of Frenkel-exciton transfer. Capability to follow coherent exciton dynamics in real time will help to reveal their actual contribution to the efficiency of light-harvesting. Attosecond X-ray pulses are the tool with the necessary temporal resolution to resolve pure electronic processes with atomic sensitivity. We describe how attosecond X-ray pulses can probe coherent electronic processes during Frenkel-exciton transport in molecular aggregates. We analyze time-resolved absorption cross section taking broad spectral bandwidth of an attosecond pulse into account. We demonstrate that attosecond X-ray absorption spectra can reveal delocalization degree of coherent exciton transfer dynamics.

Attosecond electron-beam technology: a review of recent progress.

Electron microscopy and diffraction with ultrashort pulsed electron beams are capable of imaging transient phenomena with the combined ultrafast temporal and atomic-scale spatial resolutions. The emerging field of optical electron beam control allowed the manipulation of relativistic and sub-relativistic electron beams at the level of optical cycles. Specifically, it enabled the generation of electron beams in the form of attosecond pulse trains and individual attosecond pulses. In this review, we describe the basics of the attosecond electron beam control and overview the recent experimental progress. High-energy electron pulses of attosecond sub-optical cycle duration open up novel opportunities for space-time-resolved imaging of ultrafast chemical and physical processes, coherent photon generation, free electron quantum optics, electron-atom scattering with shaped wave packets and laser-driven particle acceleration. Graphical Abstract.

Monitoring Argon L-Shell Auger Decay Using 250-eV Attosecond X-ray Pulses.

Electron correlation describes the interaction between electrons in a multi-electron system. It plays an important role in determining the speed of relaxation of atoms and molecules excited by XUV/X-ray pulses, such as the argon decay rate. Most research on electron correlation has centered on the role of correlation in stationary states. A time-resolved experimental study of electron correlation is a grand challenge due to the required temporal resolution and photon energy. In this research, we investigated Auger decay in argon using 200-attosecond X-ray pulses reaching the carbon K-edge. At such a high photon energy, ionization occurs not only from the outer most levels (3s and 3p), but also from the 2p core shells. We have measured a lifetime of 4.9 fs of L-shell vacancies of argon in pump-probe experiments with a home-built high-resolution time-of-flight spectrometer.

Nuclear-Electron Correlation Effects and Their Photoelectron Imprint in Molecular XUV Ionisation.

The ionisation of molecules by attosecond XUV pulses is accompanied by complex correlated dynamics, such as the creation of coherent electron wave packets in the parent ion, their interplay with nuclear wave packets, and a correlated photoelectron moving in a multi-centred potential. Additionally, these processes are influenced by the dynamics prior to and during the ionisation. To fully understand and subsequently control the ionisation process on different time scales, a profound understanding of electron and nuclear correlation is needed. Here, we investigate the effect of nuclear-electron correlation in a correlated two-electron and one-nucleus quantum model system. Solving the time-dependent Schrödinger equation allows to monitor the correlation impact pre, during, and post-XUV ionisation. We show how an initial nuclear wave packet displaced from equilibrium influences the post-ionisation dynamics by means of momentum conservation between the target and parent ion, whilst the attosecond electron population remains largely unaffected. We calculate time-resolved photoelectron spectra and their asymmetries and demonstrate how the coupled electron-nuclear dynamics are imprinted on top of electron-electron correlation on the photoelectron properties. Finally, our findings give guidelines towards when correlation resulting effects have to be incorporated and in which instances the exact correlation treatment can be neglected.

The time-resolved atomic, molecular and optical science instrument at the Linac Coherent Light Source.

The newly constructed time-resolved atomic, molecular and optical science instrument (TMO) is configured to take full advantage of both linear accelerators at SLAC National Accelerator Laboratory, the copper accelerator operating at a repetition rate of 120 Hz providing high per-pulse energy as well as the superconducting accelerator operating at a repetition rate of about 1 MHz providing high average intensity. Both accelerators power a soft X-ray free-electron laser with the new variable-gap undulator section. With this flexible light source, TMO supports many experimental techniques not previously available at LCLS and will have two X-ray beam focus spots in line. Thereby, TMO supports atomic, molecular and optical, strong-field and nonlinear science and will also host a designated new dynamic reaction microscope with a sub-micrometer X-ray focus spot. The flexible instrument design is optimized for studying ultrafast electronic and molecular phenomena and can take full advantage of the sub-femtosecond soft X-ray pulse generation program.

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.

Attosecond Photoionization Dynamics: from Molecules over Clusters to the Liquid Phase.

Photoionization is a process taking place on attosecond time scales. How its properties evolve from isolated particles to the condensed phase is an open question of both fundamental and practical relevance. Here, we review recent work that has advanced the study of photoionization dynamics from atoms to molecules, clusters and the liquid phase. The first measurements of molecular photoionization delays have revealed the attosecond dynamics of electron emission from a molecular shape resonance and their sensitivity to the molecular potential. Using electron-ion coincidence spectroscopy these measurements have been extended from isolated molecules to clusters. A continuous increase of the delays with the water-cluster size has been observed up to a size of 4-5 molecules, followed by a saturation towards larger clusters. Comparison with calculations has revealed a correlation of the time delay with the spatial extension of the created electron hole. Using cylindrical liquid-microjet techniques, these measurements have also been extended to liquid water, revealing a delay relative to isolated water molecules that was very similar to the largest water clusters studied. Detailed modeling based on Monte-Carlo simulations confirmed that these delays are dominated by the contributions of the first two solvation shells, which agrees with the results of the cluster measurements. These combined results open the perspective of experimentally characterizing the delocalization of electronic wave functions in complex systems and studying their evolution on attosecond time scales.

All-optical attosecond time domain interferometry.

Interferometry, a key technique in modern precision measurements, has been used for length measurement in engineering metrology and astronomy. An analogous time-domain interferometric technique would represent a significant complement to spatial domain applications and require the manipulation of interference on extreme time and energy scales. Here, we report an all-optical interferometer using laser-driven high order harmonics as attosecond temporal slits. By controlling the phase of the temporal slits with an external field, a time domain interferometer that preserves both attosecond temporal resolution and hundreds of meV energy resolution is implemented. We apply this exceptional temporal resolution to reconstruct the waveform of an arbitrarily polarized optical pulse, and utilize the provided energy resolution to interrogate the abnormal character of the transition dipole near the Cooper minimum in argon. This novel attosecond interferometry paves the way for high precision measurements in the time-energy domain using all-optical approaches.

Multi-resolution electron spectrometer array for future free-electron laser experiments.

The design of an angular array of electron time-of-flight (eToF) spectrometers is reported, intended for non-invasive spectral, temporal, and polarization characterization of single shots of high-repetition rate, quasi-continuous, short-wavelength free-electron lasers (FELs) such as the LCLS II at SLAC. This array also enables angle-resolved, high-resolution eToF spectroscopy to address a variety of scientific questions on ultrafast and nonlinear light-matter interactions at FELs. The presented device is specifically designed for the time-resolved atomic, molecular and optical science endstation (TMO) at LCLS II. In its final version, the spectrometer comprises up to 20 eToF spectrometers aligned to collect electrons from the interaction point, which is defined by the intersection of the incoming FEL radiation and a gaseous target. The full composition involves 16 spectrometers forming a circular equiangular array in the plane normal to the X-ray propagation and four spectrometers at 54.7° angle relative to the principle linear X-ray polarization axis with orientations in the forward and backward direction of the light propagation. The spectrometers are capable of independent and minimally chromatic electrostatic lensing and retardation, in order to enable simultaneous angle-resolved photo- and Auger-Meitner electron spectroscopy with high energy resolution. They are designed to ensure an energy resolution of 0.25 eV across an energy window of up to 75 eV, which can be individually centered via the adjustable retardation to cover the full range of electron kinetic energies relevant to soft X-ray methods, 0-2 keV. The full spectrometer array will enable non-invasive and online spectral-polarimetry measurements, polarization-sensitive attoclock spectroscopy for characterizing the full time-energy structure of SASE or seeded LCLS II pulses, and support emerging trends in molecular-frame spectroscopy measurements.

The 2021 ultrafast spectroscopic probes of condensed matter roadmap.

In the 60 years since the invention of the laser, the scientific community has developed numerous fields of research based on these bright, coherent light sources, including the areas of imaging, spectroscopy, materials processing and communications. Ultrafast spectroscopy and imaging techniques are at the forefront of research into the light-matter interaction at the shortest times accessible to experiments, ranging from a few attoseconds to nanoseconds. Light pulses provide a crucial probe of the dynamical motion of charges, spins, and atoms on picosecond, femtosecond, and down to attosecond timescales, none of which are accessible even with the fastest electronic devices. Furthermore, strong light pulses can drive materials into unusual phases, with exotic properties. In this roadmap we describe the current state-of-the-art in experimental and theoretical studies of condensed matter using ultrafast probes. In each contribution, the authors also use their extensive knowledge to highlight challenges and predict future trends.

Angular dynamics of small nanoparticles induced by non-vortex electron beams.

In this work, we present a theoretical study of the angular dynamics of small nanoparticles induced by fast non-vortex electron beams. General expressions for the torque and the angular momentum transferred from an electron to an arbitrary-but small-nanoparticle are obtained using a full-retarded classical electrodynamics approach, within the small particle limit. We applied this methodology to study a particular case of interest: the angular dynamics of spherical nanoparticles with homogeneous and isotropic electromagnetic responses. We analytically calculate the total angular momentum transferred from a swift electron to such nanoparticles, finding that it is electric in nature and it is always in a direction determined by the electron trajectory relative to the center of the nanoparticle. We realize that it is possible to represent the angular momentum transferred as the product of two functions: the extinction cross-section of the nanoparticle and a function that only contains information about the swift electron. We present numerical results for the total angular momentum transferred from a swift electron to an aluminum and a gold nanoparticle. We also present an analysis of the temporal behavior of the torque and the electric dipole moment induced within the nanoparticle by the swift electron. We compare the angular momentum transfer calculated in this work with a previously reported case of vortex beams, finding that, for both aluminum and gold nanoparticles, our results are two orders of magnitude smaller. Finally, we consider a particular case of a frictionless gold spherical nanoparticle of radius a=5nm, obtaining that it can spin with an angular frequency up to 29.3Hz.

Thermal Nonlinear Klein-Gordon Equation for Nano-/Micro-Sized Metallic Particle-Attosecond Laser Pulse Interaction.

In this study, a rigorous analytical solution to the thermal nonlinear Klein-Gordon equation in the Kozlowski version is provided. The Klein-Gordon heat equation is solved via the Zhukovsky "state-of-the-art" mathematical techniques. Our study can be regarded as an initial approximation of attosecond laser-particle interaction when the prevalent phenomenon is photon-electron interaction. The electrons interact with the laser beam, which means that the nucleus does not play a significant role in temperature distribution. The particle is supposed to be homogenous with respect to thermophysical properties. This theoretical approach could prove useful for the study of metallic nano-/micro-particles interacting with attosecond laser pulses. Specific applications for Au "nano" particles with a 50 nm radius and "micro" particles with 110, 130, 150, and 1000 nm radii under 100 attosecond laser pulse irradiation are considered. First, the cross-section is supposed to be proportional to the area of the particle, which is assumed to be a perfect sphere of radius R or a rotation ellipsoid. Second, the absorption coefficient is calculated using a semiclassical approach, taking into account the number of atoms per unit volume, the classical electron radius, the laser wavelength, and the atomic scattering factor (10 in case of Au), which cover all the basic aspects for the interaction between the attosecond laser and a nanoparticle. The model is applicable within the 100-2000 nm range. The main conclusion of the model is that for a range inferior to 1000 nm, a competition between ballistic and thermal phenomena occurs. For values in excess of 1000 nm, our study suggests that the thermal phenomena are dominant. Contrastingly, during the irradiation with fs pulses, this value is of the order of 100 nm. This theoretical model's predictions could be soon confirmed with the new EU-ELI facilities in progress, which will generate pulses of 100 as at a 30 nm wavelength.

Scattering of Ultrashort X-ray Pulses by Various Nanosystems.

Currently, the study of the scattering of ultrashort X-ray pulses (USPs) by various objects is an urgent task, in connection with the creation of powerful sources of USP generation. In this paper, the theory of the scattering of attosecond pulses by polyatomic structures is developed taking into account the magnetic component of USPs. It is shown that the scattering spectra depend not only on the structure of the target, but also on other characteristics of USPs. Results are presented of the calculation of the scattering spectra on various nanosystems, such as rings, groups of rings, carbon nanotubes (CNTs), and groups of co-directed CNTs (forest CNTs). The calculation results are presented in an analytical form, which allows a general analysis of the expressions. It was found that taking the magnetic component of the momentum into the scattering spectra into account leads to the generation of the second harmonic. In this case, the spectra have characteristic features and differ from the scattering spectra at the carrier frequency, which can complement ultra-high-resolution X-ray analysis. It is shown that the scattering spectra of some structures, for example, forest CNTs, have a strictly specified radiation direction and such material in the field of such USPs is non-reflective (completely black).