Atomic transient recorder

Carrier-envelope-phase-independent field sampling of single-cycle transients using homochromatic attosecond streaking

The recent development of homochromatic attosecond streaking (HAS) has enabled a novel, highly precise method for ultrafast metrology of attosecond electron pulses as well as for real-time sampling of the instantaneous field waveforms of light transients. Here, we evaluate the potential of HAS as a method for precisely sampling the field waveform of non-phase-stabilized single-cycle transients of light. We show that the extreme nonlinearity of field emission and the core properties of HAS as a field sampling technique allow one to track the waveform of a single carrier-envelope phase (CEP) setting whose field dynamics results in the most energetic electron cutoff. Our results establish HAS as a robust, compact, all-solid-state method for characterizing light fields with attosecond-level precision and as a powerful tool in light field synthesis.

Correlation-driven attosecond photoemission delay in the plasmonic excitation of C60 fullerene

Extreme light confinement in plasmonic nanosystems enables novel applications in photonics, sensor technology, energy harvesting, biology, and quantum information processing. Fullerenes represent an extreme case for nanoplasmonics: They are subnanometer carbon-based molecules showing high-energy and ultrabroad plasmon resonances; however, the fundamental mechanisms driving the plasmonic response and the corresponding collective electron dynamics are still elusive. Here, we uncover the dominant role of electron correlations in the dynamics of the giant plasmon resonance (GPR) of the subnanometer system C60 by using attosecond photoemission chronoscopy. We find a characteristic photoemission delay of up to about 300 attoseconds that is purely induced by coherent large-scale electron correlations in the plasmonic potential. These results provide insights into the nature of the plasmon resonances in subnanometer systems and open perspectives for advancing nanoplasmonic applications.

Design of a compact, high-resolution velocity-map imaging spectrometer for attosecond spectroscopy

We present the design of a VMI spectrometer optimized for attosecond spectroscopy in the 0-40 eV energy range. It is based on a compact three-electrode configuration where the lens shape, size, and material have been optimized using numerical simulations to improve the spectral resolution by a factor of ∼5 relative to the initial design [Eppink and Parker, Rev. Sci. Instrum. 68, 3477-3484 (1997)] while keeping a flat spectral response in the 10-40 eV range. The experimental performance is tested using an attosecond source based on high-order harmonic generation. A good agreement is observed between the measured and simulated spectral resolution. At low kinetic energy, the electrostatic lens remains the limiting factor, while the high energy range is mostly affected by the resolution of the camera objective.

Time Delays as Attosecond Probe of Interelectronic Coherence and Entanglement

Attosecond chronoscopy enables the exploration of correlated electron dynamics in real time. One key observable of attosecond physics is the determination of "time zero" of photoionization, the time delay with which the wave packet of the ionized electron departs from the ionic core. This observable has become accessible by experimental advances in attosecond streaking and reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) techniques. In this Letter, we explore photoionization time delays by strong extreme ultraviolet fields beyond the linear-response limit. We identify novel signatures in time delays signifying strong coupling between atoms and light fields and the light-field dressing of the ion. As a prototypical case, we study the interelectronic coherence and entanglement in helium driven by a strong extreme ultraviolet field. By the numerical solution of the time-dependent Schrödinger equation in its full dimensionality, we show that the time delay of the photoionized electron allows one to monitor the ultrafast variations of coherence dynamics and entanglement in real time.

XUV-beamline for photoelectron imaging spectroscopy with shaped pulses

We introduce an extreme ultraviolet (XUV)-beamline designed for the time-resolved investigation and coherent control of attosecond (as) electron dynamics in atoms and molecules by polarization-shaped as-laser pulses. Shaped as-pulses are generated through high-harmonic generation (HHG) of tailored white-light supercontinua (WLS) in noble gases. The interaction of shaped as-pulses with the sample is studied using velocity map imaging (VMI) techniques to achieve the differential detection of photoelectron wave packets. The instrument consists of the WLS-beamline, which includes a hollow-core fiber compressor and a home-built 4f polarization pulse shaper, and the high-vacuum XUV-beamline, which combines an HHG-stage and a versatile multi-experiment vacuum chamber equipped with a home-built VMI spectrometer. The VMI spectrometer allows the detection of photoelectron wave packets from both the multiphoton ionization (MPI) of atomic or molecular samples by the tailored WLS-pulses and the single-photon ionization (SPI) by the shaped XUV-pulses. To characterize the VMI spectrometer, we studied the MPI of xenon atoms by linearly polarized WLS pulses. To validate the interplay of these components, we conducted experiments on the SPI of xenon atoms with linearly polarized XUV-pulses. Our results include the reconstruction of the 3D photoelectron momentum distribution (PMD) and initial findings on the coherent control of the PMD by tuning the spectrum of the XUV-pulses with the spectral phase of the WLS. Our results demonstrate the performance of the entire instrument for HHG-based photoelectron imaging spectroscopy with prototypical shaped pulses. Perspectively, we will employ polarization-tailored WLS-pulses to generate polarization-shaped as-pulses.

Attosecond delays in X-ray molecular ionization

The photoelectric effect is not truly instantaneous but exhibits attosecond delays that can reveal complex molecular dynamics1-7. Sub-femtosecond-duration light pulses provide the requisite tools to resolve the dynamics of photoionization8-12. Accordingly, the past decade has produced a large volume of work on photoionization delays following single-photon absorption of an extreme ultraviolet photon. However, the measurement of time-resolved core-level photoionization remained out of reach. The required X-ray photon energies needed for core-level photoionization were not available with attosecond tabletop sources. Here we report measurements of the X-ray photoemission delay of core-level electrons, with unexpectedly large delays, ranging up to 700 as in NO near the oxygen K-shell threshold. These measurements exploit attosecond soft X-ray pulses from a free-electron laser to scan across the entire region near the K-shell threshold. Furthermore, we find that the delay spectrum is richly modulated, suggesting several contributions, including transient trapping of the photoelectron owing to shape resonances, collisions with the Auger-Meitner electron that is emitted in the rapid non-radiative relaxation of the molecule and multi-electron scattering effects. The results demonstrate how X-ray attosecond experiments, supported by comprehensive theoretical modelling, can unravel the complex correlated dynamics of core-level photoionization.

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.

All-optical subcycle microscopy on atomic length scales

Bringing optical microscopy to the shortest possible length and time scales has been a long-sought goal, connecting nanoscopic elementary dynamics with the macroscopic functionalities of condensed matter. Super-resolution microscopy has circumvented the far-field diffraction limit by harnessing optical nonlinearities1. By exploiting linear interaction with tip-confined evanescent light fields2, near-field microscopy3,4 has reached even higher resolution, prompting a vibrant research field by exploring the nanocosm in motion5-19. Yet the finite radius of the nanometre-sized tip apex has prevented access to atomic resolution20. Here we leverage extreme atomic nonlinearities within tip-confined evanescent fields to push all-optical microscopy to picometric spatial and femtosecond temporal resolution. On these scales, we discover an unprecedented and efficient non-classical near-field response, in phase with the vector potential of light and strictly confined to atomic dimensions. This ultrafast signal is characterized by an optical phase delay of approximately π/2 and facilitates direct monitoring of tunnelling dynamics. We showcase the power of our optical concept by imaging nanometre-sized defects hidden to atomic force microscopy and by subcycle sampling of current transients on a semiconducting van der Waals material. Our results facilitate access to quantum light-matter interaction and electronic dynamics at ultimately short spatio-temporal scales in both conductive and insulating quantum materials.

Ionization Pathway Interference in Photoionization Time Delays in Molecules

The photoionization time-delay in linear conjugated molecules is computed using the Wigner scattering approach. We find that, in general, there are two additive contributions to the ionization time-delays. One originates from interferences between various ionization pathways that belong to different cationic eigenstates, while the other is due to time delays associated with each pathway and originates due to electron-electron correlations in the molecule. The former contribution scales up rapidly with the conjugation length, leading to larger time delays, as observed in recent experiments, while the latter is much less sensitive to the molecular conjugation.

Compact realization of all-attosecond pump-probe spectroscopy

The ability to perform attosecond-pump attosecond-probe spectroscopy (APAPS) is a longstanding goal in ultrafast science. While first pioneering experiments demonstrated the feasibility of APAPS, the low repetition rates (10 to 120 Hz) and the large footprints of existing setups have so far hindered the widespread exploitation of APAPS. Here, we demonstrate two-color APAPS using a commercial laser system at 1 kHz, straightforward post-compression in a hollow-core fiber, and a compact high-harmonic generation (HHG) setup. The latter enables the generation of intense extreme-ultraviolet (XUV) pulses by using an out-of-focus HHG geometry and by exploiting a transient blueshift of the driving laser in the HHG medium. Near-isolated attosecond pulses are generated, as demonstrated by one-color and two-color XUV-pump XUV-probe experiments. Our concept allows selective pumping and probing on extremely short timescales in many laboratories and permits investigations of fundamental processes that are not accessible by other pump-probe techniques.

Spatiotemporal imaging and shaping of electron wave functions using novel attoclock interferometry

Electrons detached from atoms by photoionization carry valuable information about light-atom interactions. Characterizing and shaping the electron wave function on its natural timescale is of paramount importance for understanding and controlling ultrafast electron dynamics in atoms, molecules and condensed matter. Here we propose a novel attoclock interferometry to shape and image the electron wave function in atomic photoionization. Using a combination of a strong circularly polarized second harmonic and a weak linearly polarized fundamental field, we spatiotemporally modulate the atomic potential barrier and shape the electron wave functions, which are mapped into a temporal interferometry. By analyzing the two-color phase-resolved and angle-resolved photoelectron interference, we are able to reconstruct the spatiotemporal evolution of the shaping on the amplitude and phase of electron wave function in momentum space within the optical cycle, from which we identify the quantum nature of strong-field ionization and reveal the effect of the spatiotemporal properties of atomic potential on the departing electron. This study provides a new approach for spatiotemporal shaping and imaging of electron wave function in intense light-matter interactions and holds great potential for resolving ultrafast electronic dynamics in molecules, solids, and liquids.

Real-Time Extension of TAO-DFT

Thermally assisted occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Moreover, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

Charge Migration in HCCI Cations Probed by Strong Field Ionization: Time-Dependent Configuration Interaction and Vibrational Wavepacket Simulations

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations and results in charge migration between the CC π orbital and the iodine π-type lone pair. This charge migration causes oscillations in the rate of strong field ionization of the cation to the dication that can be monitored using intense few-cycle probe pulses. The dynamics and strong field ionization of the coherent superposition the X and A states of HCCI⁺ have been modeled by time-dependent configuration interaction (TDCI) simulations. When the nuclei are allowed to move, the electronic wavefunctions need to be multiplied by vibrational wavefunctions. Nuclear motion has been modeled by vibrational packets moving on quadratic approximations to the potential energy surfaces for the X and A states of the cation. The overlap of the vibrational wavepackets decays in about 10-15 fs. Consequently, the oscillations in the strong field ionization decay on the same time scale. A revival of the vibrational overlap and in the oscillations of the strong field ionization is seen at 60-110 fs. TDCI simulations show that the decay and revival of the charge migration can be monitored by strong field ionization with intense 2- and 4-cycle linearly polarized 800 nm pulses. The revival is also seen with 7-cycle pulses.

Symmetry-aware deep neural networks for high harmonic spectroscopy in solids

Neural networks are a prominent tool for identifying and modeling complex patterns, which are otherwise hard to detect and analyze. While machine learning and neural networks have been finding applications across many areas of science and technology, their use in decoding ultrafast dynamics of quantum systems driven by strong laser fields has been limited so far. Here we use standard deep neural networks to analyze simulated noisy spectra of highly nonlinear optical response of a 2-dimensional gapped graphene crystal to intense few-cycle laser pulses. We show that a computationally simple 1-dimensional system provides a useful "nursery school" for our neural network, allowing it to be retrained to treat more complex 2D systems, recovering the parametrized band structure and spectral phases of the incident few-cycle pulse with high accuracy, in spite of significant amplitude noise and phase jitter. Our results offer a route for attosecond high harmonic spectroscopy of quantum dynamics in solids with a simultaneous, all-optical, solid-state based complete characterization of few-cycle pulses, including their nonlinear spectral phase and the carrier envelope phase.

Quench dynamics of Fano-like resonances in the presence of the on-dot superconducting pairing

We explore the electron dynamics of a system composed of double quantum dot embedded between metallic and superconducting leads in a "T-shape" geometry. In nanoscopic systems, where electron transfer between electrodes can be realized via different paths, interference effects play an important role. For double quantum dot system in the chosen geometry, interference of electrons transferred between electrodes via the interfacial quantum dot and electrons scattered on the side dot gives rise to Fano-like interference. If such a system is additionally coupled to a superconducting electrode, together with the well-understood Fano resonance an additional resonance appears on the opposite side of the Fermi level. In the recent work (Barański et al. in Sci Rep 10:2881, 2020), we showed that this resonance occurs solely as a result of the local pairing of non-scattered electrons with scattered ones. In this work, considering the quench dynamics, we explore how much time is required for formation of each of these resonances. In particular, (i) we analyze the charge oscillations between subsystems; (ii) we estimate the time required for each resonance to achieve stable equilibrium upon an abrupt change of interdot connection; (iii) we discuss a typical energy and time scales for experiments on similar architectures.

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L_2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.

Near-unity uniformity and efficiency broadband meta-beam-splitter/combiner

Subwavelength planar structured interfaces, also known as metasurfaces, are ultra-thin optical elements modulating the amplitude, phase, and polarization of incident light using nanostructures called meta-atoms. The optical properties of such metasurfaces can be controlled across wavelengths by selecting geometries and materials of the meta-atoms. Given recent technological developments in optical device miniaturization, components for beam splitting and beam combining are sought for use within these devices as two quintessential components of every optical setup. However, realizing such devices using metasurfaces typically leads to poor uniformity of diffraction orders and narrow-band operation. Using a modified version of particle swarm optimization, we propose and numerically demonstrate a broadband, reciprocal metasurface beam combiner/splitter with uniformity > 97% and diffraction efficiency > 90% in the continuous band from λ=1525 nm to λ=1575 nm. The proposed approach significantly extends the current state of the art of metasurfaces design in terms of uniformity, bandwidth, and efficiency, and opens the door for devices requiring high power or near-unit uniformity.

Ultra-broadband all-optical sampling of optical waveforms

Optical-field sampling techniques provide direct access to the electric field of visible and near-infrared light. The existing methods achieve the necessary bandwidth using highly nonlinear light-matter interaction that involves ionization of atoms or generation of charge carriers in solids. We demonstrate an alternative, all-optical approach for measuring electric fields of broadband laser pulses, which offers an advantage in terms of sensitivity and signal-to-noise ratio and extends the detection bandwidth of optical methods to the petahertzdomain.

Artificial intelligence for online characterization of ultrashort X-ray free-electron laser pulses

X-ray free-electron lasers (XFELs) as the world’s brightest light sources provide ultrashort X-ray pulses with a duration typically in the order of femtoseconds. Recently, they have approached and entered the attosecond regime, which holds new promises for single-molecule imaging and studying nonlinear and ultrafast phenomena such as localized electron dynamics. The technological evolution of XFELs toward well-controllable light sources for precise metrology of ultrafast processes has been, however, hampered by the diagnostic capabilities for characterizing X-ray pulses at the attosecond frontier. In this regard, the spectroscopic technique of photoelectron angular streaking has successfully proven how to non-destructively retrieve the exact time–energy structure of XFEL pulses on a single-shot basis. By using artificial intelligence techniques, in particular convolutional neural networks, we here show how this technique can be leveraged from its proof-of-principle stage toward routine diagnostics even at high-repetition-rate XFELs, thus enhancing and refining their scientific accessibility in all related disciplines.

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.

Deep learning in attosecond metrology

Time-resolved photoelectron spectroscopy provides a versatile tool for investigating electron dynamics in gaseous, liquid, and solid samples on sub-femtosecond time scales. The extraction of information from spectrograms recorded with the attosecond streak camera remains a difficult challenge. Common algorithms are highly specialized and typically computationally heavy. In this work, we apply deep neural networks to map from streaking traces to near-infrared pulses as well as electron wavepackets and extensively benchmark our results on simulated data. Additionally, we illustrate domain-shift to real-world data. We also attempt to quantify the model predictive uncertainty. Our deep neural networks display competitive retrieval quality and superior tolerance against noisy data conditions, while reducing the computational time by orders of magnitude.

Ionization of HCCI Neutral and Cations by Strong Laser Fields Simulated With Time Dependent Configuration Interaction

Strong field ionization of neutral iodoacetylene (HCCI) can produce a coherent superposition of the X and A cations. This superposition results in charge migration between the CC π orbital and the iodine π-type lone pair which can be monitored by strong field ionization with short, intense probe pulses. Strong field ionization of the X and A states of HCCI cation was simulated with time-dependent configuration interaction using singly ionized configurations and singly excited, singly ionized configurations (TD-CISD-IP) and an absorbing boundary. Studies with static fields were used to obtain the 3-dimensional angular dependence of instantaneous ionization rates by strong fields and the orbitals involved in producing the cations and dications. The frequency of charge oscillation is determined by the energy separation of the X and A states; this separation can change depending on the direction and strength of the field. Furthermore, fields along the molecular axis can cause extensive mixing between the field-free X and A configurations. For coherent superpositions of the X and A states, the charge oscillations are characterized by two frequencies-the driving frequency of the laser field of the probe pulse and the intrinsic frequency due to the energy separation between the X and A states. For linear and circularly polarized pulses, the ionization rates show marked differences that depend on the polarization direction of the pulse, the carrier envelope phase and initial phase of the superposition. Varying the initial phase of the superposition at the beginning of the probe pulse is analogous to changing the delay between the pump and probe pulses. The charge oscillation in the coherent superposition of the X and A states results in maxima and minima in the ionization yield as a function of the superposition phase.

The speed limit of optoelectronics

Light-field driven charge motion links semiconductor technology to electric fields with attosecond temporal control. Motivated by ultimate-speed electron-based signal processing, strong-field excitation has been identified viable for the ultrafast manipulation of a solid's electronic properties but found to evoke perplexing post-excitation dynamics. Here, we report on single-photon-populating the conduction band of a wide-gap dielectric within approximately one femtosecond. We control the subsequent Bloch wavepacket motion with the electric field of visible light. The resulting current allows sampling optical fields and tracking charge motion driven by optical signals. Our approach utilizes a large fraction of the conduction-band bandwidth to maximize operating speed. We identify population transfer to adjacent bands and the associated group velocity inversion as the mechanism ultimately limiting how fast electric currents can be controlled in solids. Our results imply a fundamental limit for classical signal processing and suggest the feasibility of solid-state optoelectronics up to 1 PHz frequency.

Electro-optic characterization of synthesized infrared-visible light fields

The measurement and control of light field oscillations enable the study of ultrafast phenomena on sub-cycle time scales. Electro-optic sampling (EOS) is a powerful field characterization approach, in terms of both sensitivity and dynamic range, but it has not reached beyond infrared frequencies. Here, we show the synthesis of a sub-cycle infrared-visible pulse and subsequent complete electric field characterization using EOS. The sampled bandwidth spans from 700 nm to 2700 nm (428 to 110 THz). Tailored electric-field waveforms are generated with a two-channel field synthesizer in the infrared-visible range, with a full-width at half-maximum duration as short as 3.8 fs at a central wavelength of 1.7 µm (176 THz). EOS detection of the complete bandwidth of these waveforms extends it into the visible spectral range. To demonstrate the power of our approach, we use the sub-cycle transients to inject carriers in a thin quartz sample for nonlinear photoconductive field sampling with sub-femtosecond resolution.

Electron Dynamics and Correlations During High-Order Harmonic Generation in Be

We investigate theoretically the high-order harmonic generation in beryllium atom irradiated by a short 1850 nm linearly polarized laser pulse in the intermediate strong-field ionization regime with the Keldysh parameter of 0.85. To this end, the respective time-dependent Schrödinger equation is solved by the time-dependent restricted-active-space configuration-interaction (TD-RASCI) method. By systematically increasing the active space of included configurations, we demonstrate an individual effect of different physical processes evoked by the pulse, which, all together, significantly enrich and extend the computed high-order harmonic generation spectrum.

Photo-Ionization Time Delay in Linearly Extended π-Conjugated Molecular Systems

We calculate the photo-ionization time delay for extended, linear, π-conjugated molecules. Ionization can be realized as scattering of an electron from bound to continuum states due to interaction with an ionizing radiation field. This allows us to use the Wigner method, whereby the rate of change in phase of the scattered electron wave packet with respect to the electron energy gives a measure of the ionization time delay. An analytical expression for ionization time delay is obtained using a model system that shows how interference between different ionization pathways leads to a finite time delay, even if there is a zero time delay corresponding to individual pathways. It is observed that the ionization time delay increases linearly as the size of the chain increases. We compute the ionization time delay also using computational chemistry and compare the results with those obtained from the model system. In qualitative agreement with the model calculation, we find that the ionization time delay increases linearly with increasing conjugation.

A Single-Molecule Digital Full Adder

A specifically designed aza-starphene molecule is presented where contacting one, two, and/or three single Al adatoms allows this molecule to function as a "3-inputs & 2-outputs" digital full adder on a Au(111) surface. Sequentially positioning single Al adatoms with atomic precision to interact with aza-starphene, inputs one classical digit per Al, which is converted to quantum information by the molecule. The intramolecular logical calculations do not require a solid-state digital full adder cascade-like architecture. The measured Boolean truth table results in part from the quantum level repulsion effect and in part from a nonlinear magnetic effect also intrinsic to the aza-starphene molecule with its contacted Al adatoms.

Temporal characterization of electron dynamics in attosecond XUV and infrared laser fields

We use a Wigner distribution-like function based on the strong field approximation theory to obtain the time-energy distributions and the ionization time distributions of electrons ionized by an XUV pulse alone and in the presence of an infrared (IR) pulse. In the case of a single XUV pulse, although the overall shape of the ionization time distribution resembles the XUV-envelope, its detail shows dependence on the emission direction of the electron and the carrier-envelope phase of the pulse, which mainly results from the low-energy interference structure. It is further found that the electron from the counter-rotating term plays an important role in the interference. In the case of the two-color pulse, both the time-energy distributions and the ionization time distributions change with varying IR field. Our analysis demonstrates that the IR field not only modifies the final electron kinetic energy but also changes the electron's emission time, which is attributed to the change of the electric field induced by the IR pulse. Moreover, the ionization time distributions of the photoelectrons emitted from atoms with higher ionization energy are also given, which show less impact of the IR field on the electron dynamics.

High-Order Phase-Dependent Asymmetry in the Above-Threshold Ionization Plateau

Above-threshold ionization spectra from cesium are measured as a function of the carrier-envelope phase (CEP) using laser pulses centered at 3.1  μm wavelength. The directional asymmetry in the energy spectra of backscattered electrons oscillates three times, rather than once, as the CEP is changed from 0 to 2π. Using the improved strong-field approximation, we show that the unusual behavior arises from the interference of few quantum orbits. We discuss the conditions for observing the high-order CEP dependence, and draw an analogy with time-domain holography with electron wave packets.

Topical Issue on many particle spectroscopy of atoms, molecules, clusters and surfaces editorial: Editorial

Many particle spectroscopy is a subject of continued interest to many experimental and theoretical groups worldwide. It is based on the coincidence spectroscopy of minimum two particles coming from the same elementary process. It is a very powerful tool for studying not just atoms and molecules but also more extended electronic systems such as clusters and surfaces. Due to the large variety of its applications, it is really an interdisciplinary research field. This Topical Issue presents a state-of-the-art description of current research activities in the field of many particle spectroscopy. The contributions to this Issue represent original research results on both experimental and theoretical studies, involving the interaction of various projectiles, like photons, electrons, ions with atoms, molecules, clusters and surfaces.

Nonlocal mechanisms of attosecond interferometry in three-dimensional systems

Attosecond interferometry (AI) is an experimental technique based on ionizing a system with an attosecond pulse train in the presence of an assisting laser. This assisting laser pulse provides multiple pathways for the photoelectron wave packet to reach the same final states, and interference of these pathways can be used to probe the properties of matter. The mechanism of AI is well-understood for isolated atoms and molecules in the gas phase, but not so much in the condensed phase, especially if the substrate under study is transparent. Then, additional pathways open up for the electron due to (laser-assisted) scattering from neighbouring atoms. We investigate to what extent these additional pathways influence the measured photoionization delays with the help of 1D and 3D model systems. In both cases, we find that the total delay can be expressed as the sum of a local (photoionization) delay and a non-local delay, which contains the effect of electron scattering during transport. The 1D system shows that the non-local delay is an oscillatory function of the distance between the sites where ionization and scattering take place. A similar result is obtained in 3D, but the modulation depth of the non-local delay is found to strongly depend on the effective scattering cross section. We conclude that attosecond interferometry of disordered systems like liquids at low photon energies (20–30 eV) is mainly sensitive to the local delay, i.e. to changes of the photoionization dynamics induced by the immediate environment of the ionized entity, and less to electron scattering during transport through the medium. This conclusion also agrees with the interpretation of recent experimental results.

Attosecond streaking using a rescattered electron in an intense laser field

When an atom or molecule is exposed to a strong laser field, an electron can tunnel out from the parent ion and moves along a specific trajectory. This ultrafast electron motion is sensitive to a variation of the laser field. Thus, it can be used as a fast temporal gate for the temporal characterization of the laser field. Here, we demonstrate a new type of attosecond streaking wherein a rescattered electron trajectory is manipulated by an ultrashort laser pulse. The vector potential of the laser pulse is directly recorded in the photoelectron spectra of the rescattered electron. In contrast to high harmonic generation methods, our approach has no directional ambiguity in space, leading to complete in situ temporal characterization. In addition, it provides timing information on ionization and re-scattering events. Therefore, our approach can be a useful tool for the investigation of strong-field processes triggered by rescattering, such as non-sequential double ionization and laser-induced electron diffraction.

Interatomic and Intermolecular Coulombic Decay

Interatomic or intermolecular Coulombic decay (ICD) is a nonlocal electronic decay mechanism occurring in weakly bound matter. In an ICD process, energy released by electronic relaxation of an excited atom or molecule leads to ionization of a neighboring one via Coulombic electron interactions. ICD has been predicted theoretically in the mid nineties of the last century, and its existence has been confirmed experimentally approximately ten years later. Since then, a number of fundamental and applied aspects have been studied in this quickly growing field of research. This review provides an introduction to ICD and draws the connection to related energy transfer and ionization processes. The theoretical approaches for the description of ICD as well as the experimental techniques developed and employed for its investigation are described. The existing body of literature on experimental and theoretical studies of ICD processes in different atomic and molecular systems is reviewed.

Proper Time Delays Measured by Optical Streaking

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

Generation and measurement of isolated attosecond pulses with enhanced flux using a two colour synthesized laser field

We have generated isolated attosecond pulses and performed attosecond streaking measurements using a two-colour synthesized laser field consisting of a strong near-infrared few-cycle pulse and a weaker multi-cycle pulse centred at 400 nm. An actively stabilized interferometer was used to coherently combine the two pulses. Using attosecond streaking we characterised the electric fields of the two pulses and accurately retrieved the spectrum of the multi-cycle pulse. We demonstrated a two-fold increase in the flux of isolated attosecond pulses produced and show that their duration was minimally affected by the presence of the weaker field due to spectral filtering by a multilayer mirror.

The Photoionization Time in π-Conjugated Molecular Systems

The photoionization time of C₂H₄ is calculated as a model for π-conjugated molecular systems. Analytical results are obtained using the Wigner phase delay, which is compared with energy-streaking measurements. We find that, although the ionization time averaged over nuclear configurations compares well in the two measures, the dependence on the nuclear configuration is different. Interference between different ionization pathways depends significantly on the molecular geometry and the ionizing electron energy and may lead to qualitative changes in the ionization time.

Energy, Particle, and Photon Fluxes in Molecular Junctions

Electroluminescence from a current-carrying molecular junction at steady state is simulated. (Charge) particle conservation and energy conservation are satisfied by a perturbative expansion in the radiation/matter coupling. Our approach makes it possible to adopt standard tools of traditional (equilibrium) spectroscopy to study signals from open systems such as molecular junctions. The nonperturbative analysis of spontaneous light emission signals coincides with the perturbative approach for weak molecule-field coupling.

Noise effects and the impact of detector responses on the characterization of extreme ultraviolet attosecond pulses

We employ numerical simulations to study the effects of noise on the reconstruction of the duration and satellite intensity ratio for transform-limited single and double pulses of 200 as duration. The forms of noise we implement are delay jitters between the attosecond pulse and the near-IR laser field, energy resolution of the photoelectron detector, and Poisson noise in streaking spectrograms with different count levels. We use the streaking method to characterize the pulse and the extended ptychographic iterative engine retrieval algorithm to reconstruct the pulse from the simulated streaking spectrogram. We found that, for practical purposes, when implementing a combination of all three mentioned noise contributions, the attosecond pulse duration will be overestimated when the photoelectron count level is low. Furthermore, the satellite pulse amplitude of the attosecond double pulse can be retrieved within 10% accuracy.

Attosecond optoelectronic field measurement in solids

The sub-cycle interaction of light and matter is one of the key frontiers of inquiry made accessible by attosecond science. Here, we show that when light excites a pair of charge carriers inside of a solid, the transition probability is strongly localized to instants slightly after the extrema of the electric field. The extreme temporal localization is utilized in a simple electronic circuit to record the waveforms of infrared to ultraviolet light fields. This form of petahertz-bandwidth field metrology gives access to both the modulated transition probability and its temporal offset from the laser field, providing sub-fs temporal precision in reconstructing the sub-cycle electronic response of a solid state structure.

Characterization of light pulses is important in order to understand their interaction with matter. Here the authors demonstrate a nonlinear photoconductive sampling method to measure electric field wave-forms in the infrared, visible and ultraviolet spectral ranges.

Low-energy photoelectron interference structure in attosecond streaking

By numerically solving the time-dependent Schrödinger equation, we theoretically investigate the dynamics of the low-energy photoelectrons ionized by a single attosecond pulse in the presence of an infrared laser field. The obtained photoelectron momentum distributions exhibit complicated interference structures. With the semiclassical model, the originations for the different types of the interference structures are unambiguously identified. Moreover, by changing the time delay between the attosecond pulse and the infrared laser field, these interferences could be selectively enhanced or suppressed. This enables us to extract information about the ionization dynamics encoded in the interference structures. As an example, we show that the phase of the electron wave-packets ionized by the linearly and circularly polarized attosecond pulses can be extracted from the interference structures of the direct and the near-forward rescattering electrons.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

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.

Circular Holographic Ionization-Phase Meter

We propose an attosecond extreme ultraviolet pump IR-probe photoionization protocol that employs pairs of counterrotating consecutive harmonics and angularly resolved photoelectron detection, thereby providing a direct measurement of ionization phases. The present method, which we call circular holographic ionization-phase meter, gives also access to the phase of photoemission amplitudes of even-parity continuum states from a single time-delay measurement since the relative phase of one- and two-photon ionization pathways is imprinted in the photoemission anisotropy. The method is illustrated with ab initio simulations of photoionization via autoionizing resonances in helium. The rapid phase excursion in the transition amplitude to both the dipole-allowed (2s2p)^{1}P^{o} and the dipole-forbidden (2p^{2})^{1}D^{e} states are faithfully reproduced.

Self referencing attosecond interferometer with zeptosecond precision

In this work we demonstrate the generation of two intense, ultrafast laser pulses that allow a controlled interferometric measurement of higher harmonic generation pulses with 12.8 attoseconds in resolution (half the atomic unit of time) and a precision as low as 680 zeptoseconds (10^-21 seconds). We create two replicas of a driving femtosecond pulse which share the same optical path except at the focus where they converge to two foci. An attosecond pulse train emerges from each focus through the process of high harmonic generation. The two attosecond pulse trains from each focus interfere in the far field producing a clear interference pattern in the extreme ultraviolet region. By controlling the relative optical phase (carrier envelope phase for pulsed fields) between the two driving laser pulses we are able to actively influence the delay between the pulses and are able to perform very stable and precise pump-probe experiments. Because of the phase shaping operation occurs homogeneously across the entire spatial profile, we effectively create two indistinguishable intense laser pulses or a common path interferometer for attosecond pulses. Commonality across the two beams means that they are extremely stable to environmental and mechanical fluctuations up to a Rayleigh range from the focus. In our opinion this represents an ideal source for homodyne and heterodyne spectroscopic measurements with sub-attosecond precision.