Attosecond streaking enables the measurement of quantum phase

Self-Referenced Spectral Interferometry for Single-Shot Characterization of Ultrashort Free-Electron Laser Pulses

An attosecond x-ray pulse with known spectrotemporal information is an essential tool for the investigation of ultrafast electron dynamics in quantum systems. Ultrafast free-electron lasers (FELs) have the unique advantage on unprecedented high intensity at x-ray wavelengths. However, no suitable method has been established so far for the spectrotemporal characterization of these ultrashort x-ray pulses. In this Letter, a simple method has been proposed based on self-referenced spectral interferometry for reconstructing the temporal profile and phase of ultrashort FEL pulses. We have demonstrated that the proposed method is reliable to completely characterize the attosecond x-ray FEL pulses with an error at the level of a few percent. Moreover, the first proof-of-principle experiment has been performed to achieve the single-shot spectrotemporal characterization of ultrashort pulses from a high-gain FEL. The precision of the proposed method will be enhanced with the decrease of the pulse duration, paving a new way for complete attosecond pulse characterization at x-ray FELs.

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.

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.

Time Dependence of Ultra-Short Laser Pulses Scattering by Atom in High Frequency Limit

We investigated theoretically the time dependence of ultra-short laser pulse scattering by an atom at the high-frequency limit for the spectral and total probability of the process using new expression which we derived in this paper. We established that the time dependence of spectral scattering is presented by the curve with the maximum for sufficiently large detuning of scattering frequency from the carrier frequency of the pulse, while the total scattering probability is always the monotonically increasing function of time. We also studied the dependence of scattering probability on pulse duration at the long-time limit. It was shown that, at the long-pulse limit, the scattering probability is a linear function of pulse duration, while in the opposite case, it is a function with maximum. The position of this maximum is determined by the detuning of the scattering frequency from the carrier frequency of the pulse.

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.

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.

Holographic imaging of electromagnetic fields via electron-light quantum interference

Holography relies on the interference between a known reference and a signal of interest to reconstruct both the amplitude and the phase of that signal. With electrons, the extension of holography to the ultrafast time domain remains a challenge, although it would yield the highest possible combined spatiotemporal resolution. Here, we show that holograms of local electromagnetic fields can be obtained with combined attosecond/nanometer resolution in an ultrafast transmission electron microscope (UEM). Unlike conventional holography, where signal and reference are spatially separated and then recombined to interfere, our method relies on electromagnetic fields to split an electron wave function in a quantum coherent superposition of different energy states. In the image plane, spatial modulation of the electron energy distribution reflects the phase relation between reference and signal fields. Beyond imaging applications, this approach allows implementing quantum measurements in parallel, providing an efficient and versatile tool for electron quantum optics.

Investigation of valence band reconstruction methods for attosecond streaking data from surfaces

We analyze simulated streaked valence band photoemission with atomic streaking theory-based reconstruction methods to investigate the differences between atomic gas-phase streaking and valence band surface streaking. The careful distinction between atomic and surface streaking is a prerequisite to justify the application of atomic streaking theory-based reconstruction methods to surface streaking measurements. We show that neglecting the band structure underestimates the width of reconstructed photoelectron wavepackets, consistent with the Fourier transform limit of the band spectrum. We find that a fit of Gaussian wavepackets within the description of atomic streaking is adequate to a limited extent. Systematic errors that depend on the near-infrared skin depth, an inherently surface-specific property, are present in temporal widths of wavepackets reconstructed with atomic streaking theory-based methods.

100% reliable algorithm for second-harmonic-generation frequency-resolved optical gating

We demonstrate a novel algorithmic approach for the second-harmonic-generation (SHG) frequency-resolved optical gating (FROG) ultrashort-pulse-measurement technique that always converges and, for complex pulses, is also much faster. It takes advantage of the Paley-Wiener Theorem to retrieve the precise pulse spectrum-half the desired information-directly from the measured trace. It also uses a multi-grid approach, permitting the algorithm to operate on smaller arrays for early iterations and on the complete array for only the final few iterations. We tested this approach on more than 25,000 randomly generated complex pulses with time-bandwidth products up to 100, yielding SHG FROG traces to which noise was added, and have achieved convergence to the correct pulse in all cases. Moreover, convergence occurs in less than half the time for extremely large traces corresponding to extremely complex pulses.

Absolute timing of the photoelectric effect

Photoemission spectroscopy is central to understanding the inner workings of condensed matter, from simple metals and semiconductors to complex materials such as Mott insulators and superconductors¹. Most state-of-the-art knowledge about such solids stems from spectroscopic investigations, and use of subfemtosecond light pulses can provide a time-domain perspective. For example, attosecond (10^-18 seconds) metrology allows electron wave packet creation, transport and scattering to be followed on atomic length scales and on attosecond timescales^2-7. However, previous studies could not disclose the duration of these processes, because the arrival time of the photons was not known with attosecond precision. Here we show that this main source of ambiguity can be overcome by introducing the atomic chronoscope method, which references all measured timings to the moment of light-pulse arrival and therefore provides absolute timing of the processes under scrutiny. Our proof-of-principle experiment reveals that photoemission from the tungsten conduction band can proceed faster than previously anticipated. By contrast, the duration of electron emanation from core states is correctly described by semiclassical modelling. These findings highlight the necessity of treating the origin, initial excitation and transport of electrons in advanced modelling of the attosecond response of solids, and our absolute data provide a benchmark. Starting from a robustly characterized surface, we then extend attosecond spectroscopy towards isolating the emission properties of atomic adsorbates on surfaces and demonstrate that these act as photoemitters with instantaneous response. We also find that the tungsten core-electron timing remains unchanged by the adsorption of less than one monolayer of dielectric atoms, providing a starting point for the exploration of excitation and charge migration in technologically and biologically relevant adsorbate systems.

Ultrafast quantum control of ionization dynamics in krypton

Ultrafast spectroscopy with attosecond resolution has enabled the real time observation of ultrafast electron dynamics in atoms, molecules and solids. These experiments employ attosecond pulses or pulse trains and explore dynamical processes in a pump–probe scheme that is selectively sensitive to electronic state of matter via photoelectron or XUV absorption spectroscopy or that includes changes of the ionic state detected via photo-ion mass spectrometry. Here, we demonstrate how the implementation of combined photo-ion and absorption spectroscopy with attosecond resolution enables tracking the complex multidimensional excitation and decay cascade of an Auger auto-ionization process of a few femtoseconds in highly excited krypton. In tandem with theory, our study reveals the role of intermediate electronic states in the formation of multiply charged ions. Amplitude tuning of a dressing laser field addresses different groups of decay channels and allows exerting temporal and quantitative control over the ionization dynamics in rare gas atoms.

Photoionization of atoms and molecules is a complex process and requires sensitive probes to explore the ultrafast dynamics. Here the authors combine transient absorption and photo-ion spectroscopy methods to explore and control the attosecond pulse initiated excitation, ionization and Auger decay in Kr atoms.

Comparison of attosecond streaking and RABBITT

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

Monitoring Nonadiabatic Electron-Nuclear Dynamics in Molecules by Attosecond Streaking of Photoelectrons

Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences. We demonstrate how streaked photoelectrons offer a novel tool for monitoring nonadiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can provide high time resolution direct signatures of electronic coherences, which affect many primary photochemical and biological events.

Attosecond pulse shaping around a Cooper minimum

High harmonic generation (HHG) is used to measure the spectral phase of the recombination dipole matrix element (RDM) in argon over a broad frequency range that includes the 3p Cooper minimum (CM). The measured RDM phase agrees well with predictions based on the scattering phases and amplitudes of the interfering s- and d-channel contributions to the complementary photoionization process. The reconstructed attosecond bursts that underlie the HHG process show that the derivative of the RDM spectral phase, the group delay, does not have a straightforward interpretation as an emission time, in contrast to the usual attochirp group delay. Instead, the rapid RDM phase variation caused by the CM reshapes the attosecond bursts.

Time delay in the recoiling valence photoemission of ar endohedrally confined in C60

The effects of confinement and electron correlations on the relative time delay between the 3s and 3p photoemissions of Ar confined endohedrally in C60 are investigated using the time-dependent local density approximation--a method that is also found to mostly agree with recent time delay measurements between the 3s and 3p subshells in atomic Ar. At energies in the neighborhood of 3p Cooper minimum, correlations with C60 electrons are found to induce opposite temporal effects in the emission of Ar 3p hybridized symmetrically versus that of Ar 3p hybridized antisymmetrically with C60. A recoil-type interaction model mediated by the confinement is found to best describe the phenomenon.

Attosecond streaking of correlated two-electron transitions in helium

We present fully ab initio simulations of attosecond streaking for ionization of helium accompanied by shakeup of the second electron. This process represents a prototypical case for strongly correlated electron dynamics on the attosecond time scale. We show that streaking spectroscopy can provide detailed information on the Eisenbud-Wigner-Smith time delay as well as on the infrared-field dressing of both bound and continuum states. We find a novel contribution to the streaking delay that stems from the interplay of electron-electron and infrared-field interactions in the exit channel. We quantify all the contributions with attosecond precision and provide a benchmark for future experiments.

Amplitude and phase reconstruction of electron wave packets for probing ultrafast photoionization dynamics

Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the 1s3p state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.

How accurate is the attosecond streak camera?

An attosecond streak camera holds the promise of time resolving the dynamics of photoionization with a few-attosecond accuracy. But can the attosecond measurement be disentangled from the process it measures? We address this question by deriving simple closed-form analytical expressions for the measurement-related apparent time delays in photoionization, associated with the application of the attosecond streak camera and/or resolution of attosecond beating by interference of two-photon transitions techniques. Our analytical results are accurate on about the 1 asec level and show that both intrinsic and measurement-induced delays depend on the same scattering phase and are, therefore, not independent. We also suggest a procedure for extracting intrinsic time delays from the measurement and a possible resolution of the controversy caused by the experiments of Schultze et al. [Science 328, 1658 (2010)].

Probing single-photon ionization on the attosecond time scale

We study photoionization of argon atoms excited by attosecond pulses using an interferometric measurement technique. We measure the difference in time delays between electrons emitted from the 3s(2) and from the 3p(6) shell, at different excitation energies ranging from 32 to 42 eV. The determination of photoemission time delays requires taking into account the measurement process, involving the interaction with a probing infrared field. This contribution can be estimated using a universal formula and is found to account for a substantial fraction of the measured delay.

Attosecond resolved electron release in two-color near-threshold photoionization of N2

We have simulated two-color photoionization of N(2) by solving the time-dependent Schrödinger equation with a simple model accounting for the correlated vibronic dynamics of the molecule and of the ion N(2)(+). Our results, in very good agreement with recent experiments [Haessler et al., Phys. Rev. A 80, 011404 (2009)], show how a resonance embedded in the molecular continuum dramatically affects the phases of the two-photon transition amplitudes. In addition, we introduce a formal relation between these measurable phases and the photoelectron release time, opening the way to attosecond time-resolved measurements, equivalent to double-slit experiments in the time domain.

Attosecond dispersion control by extreme ultraviolet multilayer mirrors

We report the first experimental demonstration of a-periodic multilayer mirrors controlling the frequency sweep (chirp) of isolated attosecond XUV pulses. The concept was proven with about 200-attosecond pulses in the photon energy range of 100-130 eV measured via photoelectron streaking in neon. The demonstrated attosecond dispersion control is engineerable in a wide range of XUV photon energies and bandwidths. The resultant tailor-made attosecond pulses with highly enhanced photon flux are expected to significantly advance attosecond metrology and spectroscopy and broaden their range of applications.

Delay in atomic photoionization

We analyze the time delay between emission of photoelectrons from the outer valence ns and np subshells in noble gas atoms following absorption of an attosecond extreme ultraviolet pulse. Various processes such as elastic scattering of the photoelectron on the parent ion and many-electron correlation affect the apparent "time zero" when the photoelectron leaves the atom. This qualitatively explains the time delay between photoemission from the 2s and 2p subshells of Ne as determined experimentally by attosecond streaking [Science 328, 1658 (2010)]. However, with our extensive numerical modeling, we were only able to account for less than half of the measured time delay of 21 ± 5 as. We argue that the extreme ultraviolet pulse alone cannot produce such a large time delay and it is the streaking IR field that is most likely responsible for this effect.