Attosecond Streaking Research Articles

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.

Absolute delay calibration by analytical fitting of attosecond streaking measurements

An accurate temporal characterization of both pump and probe pulses is essential for the correct interpretation of any pump-probe experiment. This is particularly true for attosecond spectroscopy, where the pulses are too short to be directly measured with electronic devices. However, when measuring the absolute timing between a light waveform and the related photoinduced physical phenomenon, such characterization does not suffice. Here, we introduce a new method called rACE (refined Analytical Chirp Evaluation), which retrieves both pump and probe pulses while establishing a direct relation between the reconstructed time axis and the experimental delay. This feature is particularly relevant for the extraction of absolute time delays, a growing field in attosecond spectroscopy. In this work, we prove the robustness of rACE with simulated datasets involving the effect of pulse chirp, distinctive target attributes, and non-isolated attosecond pulses, which normally constitute challenging situations for standard methods. For all the cases reported here, rACE achieves a precise absolute delay calibration with an accuracy better than the atomic unit of time. Its successful application to attosecond experimental measurements makes it a fundamental tool for attaining sub-cycle absolute temporal resolution, enabling new investigations of lightwave-driven ultrafast phenomena.

Comparative study on generation of attosecond pulse train and phase information reconstruction

<sec>Attosecond pulses provide higher measurement precision for analyzing ultrafast dynamics in atoms, molecules, and electrons, laying the foundation for studying electronic motion in atomic and molecular systems. The most important method currently is to generate attosecond pulse trains and isolated attosecond pulses through the interaction of femtosecond lasers with gases. The temporal information of attosecond pulses and the dynamic information of electrons can be extracted from spectrograms by using attosecond streak camera or the reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) method based on two-photon transition interference. Although the differences in phase among different high-order harmonics can be directly extracted from the oscillation frequencies of sidebands, the iterative algorithm of attosecond streak camera can provide complete phase information of attosecond pulse trains to better support the study of electron dynamics in atoms.</sec> <sec> <b>Research purpose</b> This work is dedicated to the investigation of the generation, measurement, and characterization of attosecond pulse train (APT), which are essential for probing ultrafast dynamics in atomic, molecular, and electronic systems. The focus is on the generation of APTs through interactions between femtosecond lasers and gases, as well as the extraction of temporal and dynamic information from these pulses by using advanced spectroscopic techniques such as the RABITT method.</sec> <sec> <b>Methods</b> The experimental approach involves the use of a homebuilt femtosecond titanium sapphire regenerative amplifier to produce high-order harmonics, leading to the generation of APTs. The setup includes the homebuilt titanium sapphire chirped pulse amplifier and a collinear attosecond pulse generation and measurement beamline, which are used to conduct RABITT experiments. The process requires the interaction of femtosecond lasers with gas targets to generate high-energy photons in the extreme ultraviolet and soft X-ray spectral ranges. By optimizing the phase-matching conditions within the gas target, strong high-order harmonic signals are observed on an XUV spectrometer. The temporal information of the attosecond pulses is indirectly measured through the photoelectron spectrum produced by the interaction of attosecond pulses with femtosecond lasers. The research also employs the FROG-CRAB algorithm and the extended phase retrieval and iterative engine (ePIE) algorithm for temporally reconstructing APTs and attempts to use a genetic algorithm to extract phase information.</sec> <sec> <b>Results</b> The study yields three sets of RABITT spectrograms, which are analyzed by using the RABITT sideband phase method to directly reconstruct APTs. Fourier transform analysis is used to extract phase differences between sidebands, offering insights into the phase differences between corresponding high-order harmonics. This method, however, provides an estimation of the phase in the center of each harmonic order, which does not fully represent the actual pulse shape. The FROG-CRAB algorithm and ePIE algorithm successfully reconstructs the attosecond pulse trains from the RABITT spectrograms, revealing similar temporal pulse train morphologies. In contrast, the genetic algorithm, despite its potential for high constraint optimization, does not yield satisfactory results, possibly due to the sensitivity of the algorithm to discrepancies between theoretical simulations and experimental data.</sec> <sec> <b>Conclusions</b> The research concludes that achieving ideal inversion results for APTs necessitates small time delay steps and a wide scanning range in the experimental data collection process to ensure a rich dataset for inversion. The FROG-CRAB algorithm and ePIE algorithm demonstrate their effective performance in reconstructing APTs, with ePIE showing higher computational efficiency. The genetic algorithm, while offering a high degree of constraint, faces challenges and requires to be further refined. The study underscores the importance of the signal-to-noise ratio in experimental data for the accuracy of inversion results. This work provides significant guidance for future measuring electron dynamics and explaining their evolution patterns, contributing valuable experimental methods and data analysis techniques to the field of attosecond science.</sec>

Rapid retrieval of femtosecond and attosecond pulses from streaking traces using convolutional neural networks

Attosecond streaking is a powerful and versatile technique that allows the full-field characterisation of femtosecond to attosecond optical pulses. It has been instrumental in the verification of attosecond pulse generation and probing of ultrafast dynamics in matter. Recently, machine learning (ML) has been applied to retrieve the fields from streaking data (White and Chang 2019 Opt. Express 27 4799; Zhu et al 2020 Sci. Rep. 10 5782; Brunner et al 2022 Opt. Express 30 15669–84). This offers a number of advantages compared with traditional iterative algorithms, including faster processing and better resilience to noise. Here, we implement a ML approach based on convolutional neural networks and limit the search to physically realistic pulses that can be specified with a small number of parameters. This leads to substantial reductions in both training and retrieval times, enabling near kHz retrieval rates. We examine how the retrieval performance is affected by noise, and for the first time in this context, study the effect of missing data. We show that satisfactory retrievals are still possible with signal to noise ratios as low as 10, and with up to of data missing.

High-harmonic generation from a flat liquid-sheet plasma mirror

High-harmonic radiation can be generated when an ultra-intense laser beam is reflected from an over-dense plasma, known as a plasma mirror. It is considered a promising technique for generating intense attosecond pulses in the extreme ultraviolet and X-ray wavelength ranges. However, a solid target used for the formation of the over-dense plasma is completely damaged by the interaction. Thus, it is challenging to use a solid target for applications such as time-resolved studies and attosecond streaking experiments that require a large amount of data. Here we demonstrate that high-harmonic radiation can be continuously generated from a liquid plasma mirror in both the coherent wake emission and relativistic oscillating mirror regimes. These results will pave the way for the development of bright, stable, and high-repetition-rate attosecond light sources, which can greatly benefit the study of ultrafast laser-matter interactions.

Non-Collinear Attosecond Streaking without the Time Delay Scan

Attosecond streaking provides an extremely high temporal resolution for characterizing light pulses and photoionization processes with attosecond (10−18 s) accuracy, which employs a laser as a streaking field to deflect electrons generated by photoionization. The current attosecond streaking requires a time delay scan between the attosecond pulses and streaking field with attosecond accuracy and a femtosecond range, which is difficult to realize real-time measurement. In this study, we theoretically propose a non-collinear attosecond streaking scheme without the time delay scan, enabling real-time and even the potential to perform single-shot attosecond pulse measurement. In the proposal, time-delay information is projected into longitudinal space, both horizontally and vertically, enabling attosecond pulse characterization with temporal-spatial coupling. From our calculation, down to 70 as pulses with pulse front and wavefront tilt are characterized with high accuracy. Our study not only provides a method toward real-time attosecond pulse measurement, but also an approach for attosecond pump-probe experiments without time delay scan.

Attosecond streaking of sub-cycle electron wave packets for probing rescattering dynamics in an intense laser field

Attosecond streaking of sub-cycle electron wave packets for probing rescattering dynamics in an intense laser field

Hearing the Heartbeat of Atoms: Unveiling Attosecond Horizons

The 2023 Nobel Prize in Physics spotlights the techniques to generate attosecond light pulses. The generation of attosecond pulses heralds a new era in understanding electron dynamics. This perspective traces the evolution of ultrafast science, from early microwave electronics to the recent breakthroughs in attosecond pulse generation and measurement. Key milestones, such as high harmonic generation, the RABBITT method, attosecond streaking camera, etc, illuminate our journey toward capturing the transient electron motions in atoms. Recent discoveries, including zeptosecond delays in H 2 single-photon double ionization and the potential of attosecond “electron” pulses despite challenges, etc., hint at an exciting future for ultrafast studies.

All-optical spatio-temporal metrology for isolated attosecond pulses

Characterizing an isolated attosecond pulse (IAP) is essential for its potential applications. A complete characterization of an IAP ultimately requires the determination of its electric field in both time and space domains. However, previous methods, like the widely-used RABBITT and attosecond streaking, only measure the temporal profile of the attosecond pulse. Here we demonstrate an all-optical method for the measurement of the space-time properties of an IAP. By introducing a non-collinear perturbing pulse to the driving field, the process of IAP generation is modified both spatially and temporally, manifesting as a spatial and a frequency modulation in the harmonic spectrum. By using a FROG-like retrieval method, the spatio-spectral phases of the harmonic spectrum are faithfully extracted from the induced spatio-spectral modulations, which allows a thorough characterization of the IAP in both time and space. With this method, the spatio-temporal structures of the IAP generated in a two-color driving field in both the near- and far-field are fully reconstructed, from which a weak spatio-temporal coupling in the IAP generation is revealed. Our approach overcomes the limitation in the temporal measurement in conventional in situ scheme, providing a reliable and holistic metrology for IAP characterization.

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.

Gigawatt-class, tabletop, isolated-attosecond-pulse light source

Powerful and stable attosecond pulse sources have the potential for wide application in ultrafast science. For this purpose, we have produced a soft X-ray supercontinuum with a pulse energy of 0.24 µJ using high-order harmonics from a multi-terawatt, 10 Hz, three-channel waveform synthesizer [Sci. Adv. 6, eaay2802 (2020)STAMCV1468-699610.1126/sciadv.aay2802]. Here, we report an attosecond streaking scheme that is designed to measure this isolated attosecond pulse at a low-repetition rate. We retrieved a pulse duration of 226 attoseconds (as), demonstrating the realization of 1.1 gigawatt isolated as pulses on a tabletop, which compares favorably to an X-ray free-electron laser in a large facility.

Isolating Attosecond Electron Dynamics in Molecules where Nuclei Move Fast.

Capturing electronic dynamics in real time has been the ultimate goal of attosecond science since its beginning. While for atomic targets the existing measurement techniques have been thoroughly validated, in molecules there are open questions due to the inevitable copresence of moving nuclei, which are not always mere spectators of the phototriggered electron dynamics. Previous work has shown that not only can nuclear motion affect the way electrons move in a molecule, but it can also lead to contradictory interpretations depending on the chosen experimental approach. In this Letter we investigate how nuclear motion affects and eventually distorts the electronic dynamics measured by using two of the most popular attosecond techniques, reconstruction of attosecond beating by interference of two-photon transitions and attosecond streaking. Both methods are employed, in combination with abinitio theoretical calculations, to retrieve photoionization delays in the dissociative ionization of H_{2}, H_{2}→H^{+}+H+e^{-}, in the region of the Q_{1} series of autoionizing states, where nuclear motion plays a prominent role. We find that the experimental reconstruction of attosecond beating by interference of two-photon transitions results are very sensitive to bond softening around the Q_{1} threshold (27.8eV), even at relatively low infrared (IR) intensity (I_{0}∼1.4×10^{11} W/cm^{2}), due to the long duration of the probe pulse that is inherent to this technique. Streaking, on the other hand, seems to be a better choice to isolate attosecond electron dynamics, since shorter pulses can be used, thus reducing the role of bond softening. This conclusion is supported by very good agreement between our streaking measurements and the results of accurate theoretical calculations. Additionally, the streaking technique offers the necessary energy resolution to accurately retrieve the fast-oscillating phase of the photoionization matrix elements, an essential requirement for extending this technique to even more complicated molecular targets.

Generation and characterization of isolated attosecond pulses at 100 kHz repetition rate

The generation of coherent light pulses in the extreme ultraviolet (XUV) spectral region with attosecond pulse durations constitutes the foundation of the field of attosecond science. Twenty years after the first demonstration of isolated attosecond pulses, they continue to be a unique tool enabling the observation and control of electron dynamics in atoms, molecules, and solids. It has long been identified that an increase in the repetition rate of attosecond light sources is necessary for many applications in atomic and molecular physics, surface science, and imaging. Although high harmonic generation (HHG) at repetition rates exceeding 100 kHz, showing a continuum in the cutoff region of the XUV spectrum, was already demonstrated in 2013, the number of photons per pulse was insufficient to perform pulse characterization via attosecond streaking, let alone to perform a pump-probe experiment. Here we report on the generation and full characterization of XUV attosecond pulses via HHG driven by near-single-cycle pulses at a repetition rate of 100 kHz. The high number of 10 6 XUV photons per pulse on target enables attosecond electron streaking experiments through which the XUV pulses are determined to consist of a dominant single attosecond pulse. These results open the door for attosecond pump-probe spectroscopy studies at a repetition rate 1 or 2 orders of magnitude above current implementations.

Characterization of single-shot attosecond pulses with angular streaking photoelectron spectra

Most of the traditional attosecond pulse retrieval algorithms are based on a so-called attosecond streak camera technique, in which the momentum of the electron is shifted by an amount depending on the relative time delay between the attosecond pulse and the streaking infrared pulse. Thus, temporal information of the attosecond pulse is encoded in the amount of momentum shift in the streaked photoelectron momentum spectrogram $S(p,\ensuremath{\tau})$, where $p$ is the momentum of the electron along the polarization direction and $\ensuremath{\tau}$ is the time delay. An iterative algorithm is then employed to reconstruct the attosecond pulse from the streaking spectrogram. This method, however, cannot be applied to attosecond pulses generated from free-electron x-ray lasers where each single shot is different and stochastic in time. However, using a circularly polarized infrared laser as the streaking field, a two (or three)-dimensional angular streaking electron spectrum can be used to retrieve attosecond pulses for each shot, as well as the time delay with respect to the circularly polarized IR field. Here we show that a retrieval algorithm previously developed for the traditional streaking spectrogram can be modified to efficiently characterize single-shot attosecond pulses. The methods have been applied to retrieve 188 single shots from recent experiments. We analyze the statistical behavior of these 188 pulses in terms of pulse duration, bandwidth, pulse peak energy, and time delay with respect to the IR field. The retrieval algorithm is efficient and can be easily used to characterize a large number of shots in future experiments for attosecond pulses at free-electron x-ray laser facilities.

A Composite Velocity Map Imaging Spectrometer for Ions and 1 keV Electrons at the Shanghai Soft X-ray Free-Electron Laser

Velocity map imaging (VMI) spectrometry is widely used to measure the momentum distribution of charged particles with the kinetic energy of a few tens of electronVolts. With the progress of femtosecond laser and X-ray free-electron laser, it becomes increasingly important to extend the electron kinetic energy to 1 keV. Here, we report on a recently built composite VMI spectrometer at the Shanghai soft X-ray free-electron laser, which can measure ion images and high-energy electron images simultaneously. In the SIMION simulation, we extended the electron kinetic energy to 1 keV with a resolution <2% while measuring the ions with the kinetic energy of 20 eV. The experimental performance is tested by measuring Ar 2p photoelectron spectra at Shanghai Synchrotron Radiation Facility, and O+ kinetic energy spectrum from dissociative ionization of O2 by 800 nm femtosecond laser. We reached a resolution of 1.5% at the electron kinetic energy of 500 eV. When the electron arm is set for 100 eV, a resolution of 4% is reached at the ion kinetic energy of 5.6 eV. This composite VMI spectrometer will support the experiment, such as X-ray multi-photon excitation/ionization, Auger electrons emission, attosecond streaking.

Eisenbud–Wigner–Smith time delay in atom–laser interactions

Recent development of ultrafast measurement techniques on the sub-femtosecond time scale has enabled us to see the atom–laser interaction in real time. One of the important observables to study the temporally resolved dynamics is the various time delay in the process. Time delays is an experimentally measurable quantity, where the time is not. Time delays in quantum collisions and in photoionization/photodetachment of atomic and molecular systems is reviewed. The formalisms of time delay in the context of quantum collisions by Eisenbud and Wigner that by Smith and their equivalence is discussed. The time-reversal symmetry between solutions with outgoing and ingoing wave boundary conditions allow us to interpret photoionization/photodetachment as half-scattering. Subsequently, the formalism of Eisenbud–Wigner–Smith time delay is extended in photoionization/photodetachment from collisions. We discuss that the time delay can be written as a self-adjoint quantum operator which depicts its measurability. On the experimental side, the measurement protocols are reviewed for attosecond streaking and RABBITT. Along with the EWS time delay, the measurement introduces an additional (which is negative) time delay. From the measurement of total delay and an analytical/numerical estimate of the measurement induced part, one gets the EWS time delay in the process. A few illustrative examples of studies on time delay are given to get a flavour of the outstanding advances made in this field in the last two decades.

Anisotropic photoelectron emission delay in two-dimensional atomic arrangements

In two-dimensional semiconductors, the density fluctuation potential created by a screening of the photohole is intrinsically anisotropic because of the infinitely periodic planar arrangements of atoms. Modeling the anisotropic-localized screening with the cylindrical geometry, we investigate the emission delay of the photoelectron from $2s$ and $2{p}_{z}$ states of graphene in an angle-resolved mode of the attosecond streaking by solving the time-dependent Schr\"odinger equation. Strong angle dependencies in absolute emission delays of $2s$ and $2{p}_{z}$ states are obtained, from which the effects of the infrared-induced continuum transition are ruled out and those of the anisotropic screening could be solely extracted. Consequently, the anisotropic scattering induces photoelectrons to be emitted with substantial negative delays within small angles (i.e., $\ensuremath{\theta}\ensuremath{\lesssim}{\ensuremath{\theta}}_{c}$) from the normal direction to the atomic arrangement, that is, a conical electron emission in a very early stage of the photoemission.

Spatiotemporal delay in photoionization by polarization-structured laser fields

Focused laser fields with textured polarization on a subwavelength scale allow extracting information on electronic processes which are not directly accessible by homogeneous fields. Here we consider photoionization in radially and azimuthally polarized laser fields and show that, due to the local polarizations of the transversal and the longitudinal laser electric field components, the detected photoelectron spectra depend on the atom position from which the electron originates. The calculation results show the angular dependence of the photoionization amplitude, the quantum phase, and the time delay of the valence shell electrons as the parent atom's position varies across the laser spot. We discuss the possibility of using the photoelectron spectra to identify the position of the ionized atom within the laser spot on the subwavelength scale. The proposal and its illustrations underline the potential for the detection of the atomic position based on attosecond streaking methods.

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.

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

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