Coherent, broadband pulses of extreme ultraviolet (XUV) light provide a new and exciting tool for exploring attosecond electron dynamics. Using photoelectron streaking, interferometric spectrograms can be generated that contain a wealth of information about the phase properties of the photoionization process. If properly retrieved, this phase information reveals attosecond dynamics during photoelectron emission such as multielectron dynamics and resonance processes. However, until now, the full retrieval of the continuous electron wavepacket phase from isolated attosecond pulses has remained challenging. Here, after elucidating key approximations and limitations that hinder one from extracting the coherent electron wavepacket dynamics using available retrieval algorithms, we present a new method called Absolute Complex Dipole transmission matrix element reConstruction (ACDC). We apply the ACDC method to experimental spectrograms to resolve the phase and group delay difference between photoelectrons emitted from Ne and Ar. Our results reveal subtle dynamics in this group delay difference of photoelectrons emitted form Ar. These group delay dynamics were not resolvable with prior methods that were only able to extract phase information at discrete energy levels, emphasizing the importance of a complete and continuous phase retrieval technique such as ACDC. Here we also make this new ACDC retrieval algorithm available with appropriate citation in return.
Initial-state symmetry has been underappreciated in strong-field spectroscopies, where laser fields dominate the dynamics. We demonstrate numerically that the transverse photoelectron phase structure, arising from this symmetry, is robust in strong-field rescattering, and manifests in strong-field photoelectron spectra. Interpretation of rescattering experiments need to take these symmetry effects into account. In turn, transverse photoelectron phase structures may enable attosecond super-resolution imaging with structured electron beams.
Numerical simulations are presented to validate the possible use of cutting-edge attosecond time- resolved photoelectron spectroscopy to observe in real time the creation of an electronic wavepacket and subsequent electronic motion in a neutral molecule photoexcited by a UV pump pulse within a few femtoseconds.
Coherent control over photoelectron wavepackets, via the use of polarization-shaped laser pulses, can be understood as a time and polarization-multiplexed process. In this work, we investigate this multiplexing via computation of the observable photoelectron angular interferograms resulting from multi-photon atomic ionization with polarization-shaped laser pulses. We consider the polarization sensitivity of both the instantaneous and cumulative continuum wavefunction; the nature of the coherent control over the resultant photoelectron interferogram is thus explored in detail. Based on this und…
Amplitude and phase of wavepackets encode the dynamics of quantum systems. However, the rapidity of electron dynamics on the attosecond timescale has precluded their complete measurement in the time domain. Here, we demonstrate that spectrally-resolved electron interferometry reveals the amplitude and phase of a photoelectron wavepacket created through a Fano autoionizing resonance in helium. Replicas obtained by two-photon transitions interfere with reference wavepackets formed through smooth continua, allowing the full temporal reconstruction, purely from experimental data, of the resonant w…
The application of a matrix-based reconstruction protocol for obtaining Molecular Frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is explored. Similarly to other recent works on the topic of MF reconstruction, this protocol makes use of time-resolved LF measurements, in which a rotational wavepacket is prepared and probed via photoionization, followed by a numerical reconstruction routine; however, in contrast to other methodologies, the protocol developed herein does not require determination of photoionization matrix elements, and cons…
We present the extension of the time-dependent configuration interaction singles (TDCIS) method to the computation of the electron kinetic-energy spectrum in photoionization processes. Especially for strong and long ionizing light pulses the detection of the photoelectron poses a computational challenge because propagating the outgoing photoelectron wavepacket requires large grid sizes. Two different methods which allow for the extraction of the asymptotic photoelectron momentum are compared regarding their methodological and computational performance. The first method follows the scheme of To…
We propose a new technique to fully characterize the temporal structure of extreme ultraviolet pulses by ionizing a bound coherent electronic wavepacket. The populated energy levels make it possible to interfere different spectral components leading to quantum beats in the photoelectron spectrum as a function of the delay between ionization and initiation of the wavepacket. The influence of the dipole phase, which is the main obstacle for state-of-the-art pulse characterization schemes, can be eliminated by angle integration of the photoelectron spectrum. We show that particularly atomic Rydbe…
Photoelectron interferometry with femto- and atto-second light pulses is a powerful probe of the fast electron wavepacket dynamics, albeit it has practical limitations on the energy resolution. We show that one can simultaneously obtain both high temporal and spectral resolution by stimulating Raman interferences with one light pulse and monitoring the differential changes in the electron yield in a separate step. Applying this spectroscopic approach to the autoionizing states of argon, we experimentally resolved its electronic composition and time-evolution in exquisite detail. Theoretical ca…
We use a convolutional neural network to retrieve the internuclear distance in the two-dimensional H$_2^{+}$ molecule ionized by a strong few-cycle laser pulse based on the photoelectron momentum distribution. We show that a neural network trained on a relatively small dataset consisting of a few thousand of images can predict the internuclear distance with an absolute error less than 0.1 a.u. We study the effect of focal averaging, and we find that the convolutional neural network trained using the focal averaged electron momentum distributions also shows a good performance in reconstructing …
We investigate the application of deep learning to the retrieval of the internuclear distance in the two-dimensional H$_2^{+}$ molecule from the momentum distribution of photoelectrons produced by strong-field ionization. We study the effect of the carrier-envelope phase on the prediction of the internuclear distance with a convolutional neural network. We apply the transfer learning technique to make our convolutional neural network applicable to distributions obtained for parameters outside the ranges of the training data. The convolutional neural network is compared with alternative approac…
Attosecond photoelectron spectroscopy is often performed with interferometric experimental setups that require outstanding stability. We demonstrate and characterize in detail an actively stabilized, versatile, high spectral resolution attosecond beamline. The active-stabilization system can remain ultra-stable for several hours with an RMS stability of 13 as and a total pump-probe delay scanning range of \sim 400 fs. A tunable femtosecond laser source to drive high-order harmonic generation allows for precisely addressing atomic and molecular resonances. Furthermore, the interferometer includ…
By analyzing ``exact'' theoretical results from solving the time-dependent Schrödinger equation of atoms in few-cycle laser pulses, we established the general conclusion that differential elastic scattering and photo-recombination cross sections of the target ion with {\em free} electrons can be extracted accurately from laser-generated high-energy electron momentum spectra and high-order harmonic spectra, respectively. Since both electron scattering and photoionization (the inverse of photo-recombination) are the conventional means for interrogating the structure of atoms and molecules, this …
The evolution of electron wavepackets determines the course of many physical and chemical phenomena and attosecond spectroscopy aims to measure and control such dynamics in real-time. Here, we investigate radial electron wavepacket motion in Helium by using an XUV attosecond pulse train to prepare a coherent superposition of excited states and a delayed femtosecond IR pulse to ionize them. Quantum beat signals observed in the high resolution photoelectron spectrogram allow us to follow the field-free evolution of the bound electron wavepacket and determine the time-dependent ionization dynamic…
We investigate the photoionization spectrum of helium by attosecond XUV pulses both in the spectral region of doubly excited resonances as well as above the double ionization threshold. In order to probe for convergence, we compare three techniques to extract photoelectron spectra from the wavepacket resulting from the integration of the time-dependent Schroedinger equation in a finite-element discrete variable representation basis. These techniques are: projection on products of hydrogenic bound and continuum states, projection onto multi-channel scattering states computed in a B-spline clos…
Chiral light-matter interactions have been investigated for two centuries, leading to the discovery of many chiroptical processes used for discrimination of enantiomers. Whereas most chiroptical effects result from a response of bound electrons, photoionization can produce much stronger chiral signals that manifest as asymmetries in the angular distribution of the photoelectrons along the light propagation axis. Here we implement a self-referenced attosecond photoelectron interferometry to measure the temporal profile of the forward and backward electron wavepackets emitted upon photoionizatio…
We investigated the two-dimensional electron momentum distributions of atomic negative ions in an intense laser field by solving the time-dependent Schrodinger equation (TDSE) and using the first- and 2nd-order strong-field approximations (SFA). We showed that photoelectron energy distributions and low-energy photoelectron momentum spectra predicted from SFA are in reasonable agreement with the solutions from the TDSE. More importantly, we showed that accurate electron-atom elastic scattering cross sections can be retrieved directly from high-energy electron momentum spectra of atomic negative…
Ubiquitous to most molecular scattering methods is the challenge to retrieve bond distance and angle from the scattering signals since this requires convergence of pattern matching algorithms or fitting methods. This problem is typically exacerbated when imaging larger molecules or for dynamic systems with little a priori knowledge. Here, we employ laser-induced electron diffraction (LIED) which is a powerful means to determine the precise atomic configuration of an isolated gas-phase molecule with picometre spatial and attosecond temporal precision. We introduce a simple molecular retrieval m…
Attosecond photoionisation time delays reveal information about the potential energy landscape an outgoing electron wavepacket probes upon ionisation. In this study we experimentally quantify, for the first time, the dependence of the time delay on the angular momentum of the liberated photoelectrons. For this purpose, electron quantum-path interference spectra have been resolved in energy and angle using a two-color attosecond pump-probe photoionisation experiment in helium. A fitting procedure of the angle-dependent interference pattern allows us to disentangle the relative phase of all four…
We describe a numerical method that simulates the interaction of the helium atom with sequences of femtosecond and attosecond light pulses. The method, which is based on the close-coupling expansion of the electronic configuration space in a B-spline bipolar spherical harmonic basis, can accurately reproduce the excitation and single ionization of the atom, within the electrostatic approximation. The time dependent Schrödinger equation is integrated with a sequence of second-order split-exponential unitary propagators. The asymptotic channel-, energy- and angularly-resolved photoelectron distr…
Imaging in real time the complete dynamics of a process as fundamental as photoemission has long been out of reach due to the difficulty of combining attosecond temporal resolution with fine spectral and angular resolutions. Here, we achieve full decoding of the intricate angle-dependent dynamics of a photoemission process in helium, spectrally and anisotropically structured by twophoton transitions through intermediate bound states. Using spectrally- and angularly-resolved attosecond electron interferometry, we characterize the complex-valued transition probability amplitude towards the photo…
We study resonant two-photon ionization of helium atoms via the $1s3p$, $1s4p$ and $1s5p^1$P$_1$ states using the 15$^\mathrm{th}$ harmonic of a titanium-sapphire laser for the excitation and a weak fraction of the laser field for the ionization. The phase of the photoelectron wavepackets is measured by an attosecond interferometric technique, using the 17$^\mathrm{th}$ harmonic. We perform experiments with angular resolution using a velocity map imaging spectrometer and with high energy resolution using a magnetic bottle electron spectrometer. Our results are compared to calculations using th…
A new scheme based on (i) upcoming brilliant X-ray Free Electron Laser (FEL) sources, (ii) novel energy and angular dispersive, large-area electron imagers and (iii) the well-known photoelectron holography is elaborated that provides time-dependent three-dimensional structure determination of small to medium sized molecules with Ångström spatial and femtosecond time resolution. Inducing molecular dynamics, wave-packet motion, dissociation, passage through conical intersections or isomerization by a pump pulse this motion is visualized by the X-ray FEL probe pulse launching keV photoelectrons w…
Photoelectron spectroscopy is a powerful method that provides insight into the quantum mechanical properties of a wide range of systems. The ionized electron wavefunction carries information on the structure of the bound orbital, the ionic potential as well as the photo-ionization dynamics itself. While photoelectron spectroscopy resolves the absolute amplitude of the wavefunction, retrieving the spectral phase information has been a long-standing challenge. Here, we transfer the electron phase retrieval problem into an optical one by measuring the time-reversed process of photo-ionization -- …
