Imaging the Renner-Teller effect using laser-induced electron diffraction

Directly imaging excited state-resolved transient structures of water induced by valence and inner-shell ionisation

Real-time imaging of transient structure of the electronic excited state is fundamentally critical to understand and control ultrafast molecular dynamics. The ejection of electrons from the inner-shell and valence level can lead to the population of different excited states, which trigger manifold ultrafast relaxation processes, however, the accurate imaging of such electronic state-dependent structural evolutions is still lacking. Here, by developing the laser-induced electron recollision-assisted Coulomb explosion imaging approach and molecular dynamics simulations, snapshots of the vibrational wave-packets of the excited (A) and ground states (X) of D2O+ are captured simultaneously with sub-10 picometre and few-femtosecond precision. We visualise that θDOD and ROD are significantly increased by around 50∘ and 10 pm, respectively, within approximately 8 fs after initial ionisation for the A state, and the ROD further extends 9 pm within 2 fs along the ground state of the dication in the present condition. Moreover, the ROD can stretch more than 50 pm within 5 fs along autoionisation state of dication. The accuracies of the results are limited by the simulations. These results provide comprehensive structural information for studying the fascinating molecular dynamics of water, and pave the way towards to make a movie of excited state-resolved ultrafast molecular dynamics and light-induced chemical reaction.

Filming movies of attosecond charge migration in single molecules with high harmonic spectroscopy

Electron migration in molecules is the progenitor of chemical reactions and biological functions after light-matter interaction. Following this ultrafast dynamics, however, has been an enduring endeavor. Here we demonstrate that, by using machine learning algorithm to analyze high-order harmonics generated by two-color laser pulses, we are able to retrieve the complex amplitudes and phases of harmonics of single fixed-in-space molecules. These complex dipoles enable us to construct movies of laser-driven electron migration after tunnel ionization of N₂ and CO₂ molecules at time steps of 50 attoseconds. Moreover, the angular dependence of the migration dynamics is fully resolved. By examining the movies, we observe that electron holes do not just migrate along the laser polarization direction, but may swirl around the atom centers. Our result establishes a general scheme for studying ultrafast electron dynamics in molecules, paving a way for further advance in tracing and controlling photochemical reactions by femtosecond lasers.

Trends in angle-resolved molecular photoelectron spectroscopy

In this perspective article, main trends of angle-resolved molecular photoelectron spectroscopy in the laboratory up to the molecular frame, in different regimes of light-matter interactions, are highlighted with emphasis on foundations and most recent applications.

Machine learning for laser-induced electron diffraction imaging of molecular structures

Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult with increasing structural complexity, given that a global extremum must be found in a multi-dimensional solution space. Worse, pre-calculating many thousands of molecular configurations for all orientations becomes simply intractable. As a remedy, here, we propose a machine learning algorithm with a convolutional neural network which can be trained with a limited set of molecular configurations. We demonstrate structural retrieval of a complex and large molecule, Fenchone (C₁₀H₁₆O), from laser-induced electron diffraction (LIED) data without fitting algorithms or ab initio calculations. Retrieval of such a large molecular structure is not possible with other variants of LIED or ultrafast electron diffraction. Combining electron diffraction with machine learning presents new opportunities to image complex and larger molecules in static and time-resolved studies.

Two-dimensional retrieval methods for ultrafast imaging of molecular structure using laser-induced electron diffraction

Molecular structural retrieval based on electron diffraction has been proposed to determine the atomic positions of molecules with sub-angstrom spatial and femtosecond temporal resolutions. Given its success on small molecular systems, in this work, we point out that the accuracy of structure retrieval is constrained by the availability of a wide range of experimental data in the momentum space in all molecular systems. To mitigate the limitations, for laser-induced electron diffraction, here we retrieve molecular structures using two-dimensional (energy and angle) electron momentum spectra in the laboratory frame for a number of small molecular systems, which have previously been studied with 1D methods. Compared to the conventional single-energy or single-angle analysis, our 2D methods effectively expand the momentum range of the measured data. Besides utilization of the 2D data, two complementary methods are developed for consistency check on the retrieved results. The 2D nature of our methods also offers a way of estimating the error from retrieval, which has never been explored before. Comparing with results from prior experiments, our findings show evidence that our 2D methods outperform the conventional 1D methods. Paving the way to the retrieval of large molecular systems, in which their tunneling ionization rates are challenging to obtain, we estimate the error of using the isotropic model in place of including the orientation-dependent ionization rate.

Optical Excitations with Electron Beams: Challenges and Opportunities

Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral precision through the analysis of electron energy losses and cathodoluminescence light emission. In combination with ultrafast optics, the emerging field of ultrafast electron microscopy utilizes synchronized femtosecond electron and light pulses that are aimed at the sampled structures, holding the promise to bring simultaneous sub-Å-sub-fs-sub-meV space-time-energy resolution to the study of material and optical-field dynamics. In addition, these advances enable the manipulation of the wave function of individual free electrons in unprecedented ways, opening sound prospects to probe and control quantum excitations at the nanoscale. Here, we provide an overview of photonics research based on free electrons, supplemented by original theoretical insights and discussion of several stimulating challenges and opportunities. In particular, we show that the excitation probability by a single electron is independent of its wave function, apart from a classical average over the transverse beam density profile, whereas the probability for two or more modulated electrons depends on their relative spatial arrangement, thus reflecting the quantum nature of their interactions. We derive first-principles analytical expressions that embody these results and have general validity for arbitrarily shaped electrons and any type of electron-sample interaction. We conclude with some perspectives on various exciting directions that include disruptive approaches to noninvasive spectroscopy and microscopy, the possibility of sampling the nonlinear optical response at the nanoscale, the manipulation of the density matrices associated with free electrons and optical sample modes, and appealing applications in optical modulation of electron beams, all of which could potentially revolutionize the use of free electrons in photonics.

Imaging of electron transition and bond breaking in the photodissociation of H2+ via ultrafast X-ray photoelectron diffraction

We theoretically investigate the photodissociation dynamics of H2+ using the methodology of ultrafast X-ray photoelectron diffraction (UXPD). We use a femtosecond infrared pulse to prompt a coherent excitation from the molecular vibrational state (v = 9) of the electronic ground state (1sσ_g) and then adopt another time-delayed attosecond X-ray pulse to probe the dynamical properties. We have calculated photoionization momentum distributions by solving the non-Born-Oppenheimer time-dependent Schrödinger equation (TDSE). We unambiguously identify the phenomena associated with the g - u symmetry breakdown in the time-resolved photoelectron diffraction spectra. Using the two-center interference model, we can determine the variation in nuclear spacing with high accuracy. In addition, we use a strong field approximation (SFA) model to interpret the UXPD profile, and the SFA simulations can reproduce the TDSE results in a quantitative way.

Molecular structure retrieval directly from laboratory-frame photoelectron spectra in laser-induced electron diffraction

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 method, which is based only on the identification of critical points in the oscillating molecular interference scattering signal that is extracted directly from the laboratory-frame photoelectron spectrum. The method is compared with a Fourier-based retrieval method, and we show that both methods correctly retrieve the asymmetrically stretched and bent field-dressed configuration of the asymmetric top molecule carbonyl sulfide (OCS), which is confirmed by our quantum-classical calculations.

Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia

Visualizing molecular transformations in real-time requires a structural retrieval method with Ångström spatial and femtosecond temporal atomic resolution. Imaging of hydrogen-containing molecules additionally requires an imaging method sensitive to the atomic positions of hydrogen nuclei, with most methods possessing relatively low sensitivity to hydrogen scattering. Laser-induced electron diffraction (LIED) is a table-top technique that can image ultrafast structural changes of gas-phase polyatomic molecules with sub-Ångström and femtosecond spatiotemporal resolution together with relatively high sensitivity to hydrogen scattering. Here, we image the umbrella motion of an isolated ammonia molecule (NH₃) following its strong-field ionization. Upon ionization of a neutral ammonia molecule, the ammonia cation (NH₃ ⁺) undergoes an ultrafast geometrical transformation from a pyramidal ( Φ HNH = 107 ° ) to planar ( Φ HNH = 120 ° ) structure in approximately 8 femtoseconds. Using LIED, we retrieve a near-planar ( Φ HNH = 117   ±   5 ° ) field-dressed NH₃ ⁺ molecular structure 7.8 - 9.8 femtoseconds after ionization. Our measured field-dressed NH₃ ⁺ structure is in excellent agreement with our calculated equilibrium field-dressed structure using quantum chemical ab initio calculations.

Setting the photoelectron clock through molecular alignment

The interaction of strong laser fields with matter intrinsically provides a powerful tool for imaging transient dynamics with an extremely high spatiotemporal resolution. Here, we study strong-field ionisation of laser-aligned molecules, and show a full real-time picture of the photoelectron dynamics in the combined action of the laser field and the molecular interaction. We demonstrate that the molecule has a dramatic impact on the overall strong-field dynamics: it sets the clock for the emission of electrons with a given rescattering kinetic energy. This result represents a benchmark for the seminal statements of molecular-frame strong-field physics and has strong impact on the interpretation of self-diffraction experiments. Furthermore, the resulting encoding of the time-energy relation in molecular-frame photoelectron momentum distributions shows the way of probing the molecular potential in real-time, and accessing a deeper understanding of electron transport during strong-field interactions.

Interaction of strong laser fields with matter provides powerful tools to image transient dynamics with high spatiotemporal resolution. The authors investigate strong-field ionisation of laser-aligned molecules showing the effect of molecular alignment on the photoelectron dynamics and the resulting influence of the molecular frame in imaging experiments.

Ultrafast X-ray photoelectron diffraction in triatomic molecules by circularly polarized attosecond light pulses

We theoretically study ultrafast photoelectron diffraction in triatomic molecules with cyclic geometry by ultrafast circular soft X-ray attosecond pulses.

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.

Femtosecond Laser-Assisted Electron Scattering for Ultrafast Dynamics of Atoms and Molecules

The recent progress in experimental studies of laser-assisted electron scattering (LAES) induced by ultrashort intense laser fields is reviewed. After a brief survey of the theoretical backgrounds of the LAES process and earlier LAES experiments started in the 1970s, new concepts of optical gating and optical streaking for the LAES processes, which can be realized by LAES experiments using ultrashort intense laser pulses, are discussed. A new experimental setup designed for measurements of LAES induced by ultrashort intense laser fields is described. The experimental results of the energy spectra, angular distributions, and laser polarization dependence of the LAES signals are presented with the results of the numerical simulations. A light-dressing effect that appeared in the recorded LAES signals is also shown with the results of the numerical calculations. In addition, as applications of the LAES process, laser-assisted electron diffraction and THz-wave-assisted electron diffraction, both of which have been developed for the determination of instantaneous geometrical structure of molecules, are introduced.

Grid-Based Ehrenfest Model To Study Electron-Nuclear Processes

The two-dimensional electron-nuclear Schrödinger equation using soft-core Coulomb potentials has been a cornerstone for modeling and predicting the behavior of one-active-electron diatomic molecules, particularly for processes where both bound and continuum states are important. The model, however, is computationally expensive to extend to more electron or nuclear coordinates. Here we propose use of the Ehrenfest approach to treat the nuclear motion, while the electronic motion is still solved by quantum propagation on a grid. In this work, we present results for a one-dimensional treatment of H₂⁺, where the quantum and semiclassical dynamics can be directly compared, showing remarkably good agreement for a variety of situations. The advantage of the Ehrenfest approach is that it can be easily extended to treat as many nuclear degrees of freedom as needed.

Imaging an isolated water molecule using a single electron wave packet

Observing changes in molecular structure requires atomic-scale Ångstrom and femtosecond spatio-temporal resolution. We use the Fourier transform (FT) variant of laser-induced electron diffraction (LIED), FT-LIED, to directly retrieve the molecular structure of H₂O⁺ with picometer and femtosecond resolution without a priori knowledge of the molecular structure nor the use of retrieval algorithms or ab initio calculations. We identify a symmetrically stretched H₂O⁺ field-dressed structure that is most likely in the ground electronic state. We subsequently study the nuclear response of an isolated water molecule to an external laser field at four different field strengths. We show that upon increasing the laser field strength from 2.5 to 3.8 V/Å, the O-H bond is further stretched and the molecule slightly bends. The observed ultrafast structural changes lead to an increase in the dipole moment of water and, in turn, a stronger dipole interaction between the nuclear framework of the molecule and the intense laser field. Our results provide important insights into the coupling of the nuclear framework to a laser field as the molecular geometry of H₂O⁺ is altered in the presence of an external field.