Diffraction using laser-driven broadband electron wave packets

Ultrafast Picometer-Resolved Molecular Structure Imaging by Laser-Induced High-Order Harmonics

Real-time visualization of molecular transformations is a captivating yet challenging frontier of ultrafast optical science and physical chemistry. While ultrafast x-ray and electron diffraction methods can achieve the needed subangstrom spatial resolution, their temporal resolution is still limited to hundreds of femtoseconds, much longer than the few femtoseconds required to probe real-time molecular dynamics. Here, we show that high-order harmonics generated by intense femtosecond lasers can be used to image molecules with few-ten-attosecond temporal resolution and few-picometer spatial resolution. This is achieved by exploiting the sensitive dependence of molecular recombination dipole moment to the geometry of the molecule at the time of harmonic emission. In a proof-of-principle experiment, we have applied this high-harmonic structure imaging (HHSI) method to monitor the structural rearrangement in NH_{3}, ND_{3}, and N_{2} from one to a few femtoseconds after the molecule is ionized by an intense laser. Our findings establish HHSI as an effective approach to resolve molecular dynamics with unprecedented spatiotemporal resolution, which can be extended to trace photochemical reactions in the future.

Laser-induced electron diffraction: Imaging of a single gas-phase molecular structure with one of its own electrons

Among the many methods to image molecular structure, laser-induced electron diffraction (LIED) can image a single gas-phase molecule by locating all of a molecule's atoms in space and time. The method is based on attosecond electron recollision driven by a laser field and can reach attosecond temporal resolution. Implementation with a mid-IR laser and cold-target recoil ion-momentum spectroscopy, single molecules are measured with picometer resolution due to the keV electron impact energy without ensemble averaging or the need for molecular orientation. Nowadays, the method has evolved to detect single complex and chiral molecular structures in 3D. The review will touch on the various methods to discuss the implementations of LIED toward single-molecule imaging and complement the discussions with noteworthy experimental findings in the field.

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.

Simulation of photo-electron spectrum and electron scattering by dual time propagation

A dual time propagation approach is introduced to describe electron scattering and ionization. The space is divided into two regions, a central region with a full time-dependent Hamiltonian and an outer region where the kinetic operator and the laser field dominate. The two regions are connected by a source term. Time-dependent density functional theory calculations of wave packet scattering on molecules and photoelectron spectrum due to circularly polarized laser are presented to illustrate the efficiency and applicability of the approach.

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.

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.

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.

Atomic-resolution imaging of carbonyl sulfide by laser-induced electron diffraction

Measurements on the strong-field ionization of carbonyl sulfide molecules by short, intense, 2 µm wavelength laser pulses are presented from experiments where angle-resolved photoelectron distributions were recorded with a high-energy velocity map imaging spectrometer, designed to reach a maximum kinetic energy of 500 eV. The laser-field-free elastic-scattering cross section of carbonyl sulfide was extracted from the measurements and is found in good agreement with previous experiments, performed using conventional electron diffraction. By comparing our measurements to the results of calculations, based on the quantitative rescattering theory, the bond lengths and molecular geometry were extracted from the experimental differential cross sections to a precision better than ±5 pm and in agreement with the known values.

Tomographic Extraction of the Internuclear Separation Based on Two-Center Interference with Aligned Diatomic Molecules

We experimentally investigate the two-dimensional photoelectron momentum spectra of aligned diatomic molecules in an intense laser field. Our results reveal a novel prominent valley structure in the molecular alignment dependence of the high-energy photoelectron spectra along the laser polarization. Resorting to the molecular strong-field approximation and a simple semiclassical analysis, we show that this valley structure stems from the destructive two-center interference of the laser-driven rescattered electrons in diatomic molecules. Based on this two-center interference with aligned diatomic molecules, we demonstrate for the first time a tomographic method to extract the molecular internuclear separation, providing a more straightforward approach of molecular imaging, in comparison with, e.g., laser-induced electron diffraction and fixed-angle broadband laser-driven electron scattering.

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

Structural information on electronically excited neutral molecules can be indirectly retrieved, largely through pump-probe and rotational spectroscopy measurements with the aid of calculations. Here, we demonstrate the direct structural retrieval of neutral carbonyl disulfide (CS₂) in the [Formula: see text] excited electronic state using laser-induced electron diffraction (LIED). We unambiguously identify the ultrafast symmetric stretching and bending of the field-dressed neutral CS₂ molecule with combined picometer and attosecond resolution using intrapulse pump-probe excitation and measurement. We invoke the Renner-Teller effect to populate the [Formula: see text] excited state in neutral CS₂, leading to bending and stretching of the molecule. Our results demonstrate the sensitivity of LIED in retrieving the geometric structure of CS₂, which is known to appear as a two-center scatterer.

Diffractive Imaging of C_{60} Structural Deformations Induced by Intense Femtosecond Midinfrared Laser Fields

Theoretical studies indicated that C_{60} exposed to linearly polarized intense infrared pulses undergoes periodic cage structural distortions with typical periods around 100 fs (1  fs=10^{-15}  s). Here, we use the laser-driven self-imaging electron diffraction technique, previously developed for atoms and small molecules, to measure laser-induced deformation of C_{60} in an intense 3.6  μm laser field. A prolate molecular elongation along the laser polarization axis is determined to be (6.1±1.4)% via both angular- and energy-resolved measurements of electrons that are released, driven back, and diffracted from the molecule within the same laser field. The observed deformation is confirmed by density functional theory simulations of nuclear dynamics on time-dependent adiabatic states and indicates a nonadiabatic excitation of the h_{g}(1) prolate-oblate mode. The results demonstrate the applicability of laser-driven electron diffraction methods for studying macromolecular structural dynamics in four dimensions with atomic time and spatial resolutions.

Static Coherent States Method: One- and Two-Electron Laser-Induced Systems with Classical Nuclear Dynamics

In this report, we introduce the static coherent states (SCS) method for investigating quantum electron dynamics in a one- or two-electron laser-induced system. The SCS method solves the time-dependent Schrödinger equation (TDSE) both in imaginary and real times on the basis of a static grid of coherent states (CSs). Moreover, we consider classical dynamics for the nuclei by solving their Newtonian equations of motion. By implementing classical nuclear dynamics, we compute the electronic-state potential energy curves of H2+ in the absence and presence of an ultra-short intense laser field. We used this method to investigate charge migration in H2+. In particular, we found that the charge migration time increased exponentially with inter-nuclear distance. We also observed substantial charge localization for sufficiently long molecular bonds.

Molecular orbital imprint in laser-driven electron recollision

Electrons released by strong-field ionization from atoms and molecules or in solids can be accelerated in the oscillating laser field and driven back to their ion core. The ensuing interaction, phase-locked to the optical cycle, initiates the central processes underlying attosecond science. A common assumption assigns a single, well-defined return direction to the recolliding electron. We study laser-induced electron rescattering associated with two different ionization continua in the same, spatially aligned, polyatomic molecule. We show by experiment and theory that the electron return probability is molecular frame-dependent and carries structural information on the ionized orbital. The returning wave packet structure has to be accounted for in analyzing strong-field spectroscopy experiments that critically depend on the interaction of the laser-driven continuum electron, such as laser-induced electron diffraction.

Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering

Strong-field photoelectron holography and laser-induced electron diffraction (LIED) are two powerful emerging methods for probing the ultrafast dynamics of molecules. However, both of them have remained restricted to static systems and to nuclear dynamics induced by strong-field ionization. Here we extend these promising methods to image purely electronic valence-shell dynamics in molecules using photoelectron holography. In the same experiment, we use LIED and photoelectron holography simultaneously, to observe coupled electronic-rotational dynamics taking place on similar timescales. These results offer perspectives for imaging ultrafast dynamics of molecules on femtosecond to attosecond timescales.

Capturing ultrafast molecular dynamics is difficult as the process involves coupled and very fast motions of electrons and nuclei. Here the authors study non-adiabatic dynamics in the NO molecule using strong-field photoelectron holography to shed light on the valence-shell electron dynamics.

Attosecond physics at the nanoscale

Recently two emerging areas of research, attosecond and nanoscale physics, have started to come together. Attosecond physics deals with phenomena occurring when ultrashort laser pulses, with duration on the femto- and sub-femtosecond time scales, interact with atoms, molecules or solids. The laser-induced electron dynamics occurs natively on a timescale down to a few hundred or even tens of attoseconds (1 attosecond  =  1 as  =  10^-18 s), which is comparable with the optical field. For comparison, the revolution of an electron on a 1s orbital of a hydrogen atom is  ∼152 as. On the other hand, the second branch involves the manipulation and engineering of mesoscopic systems, such as solids, metals and dielectrics, with nanometric precision. Although nano-engineering is a vast and well-established research field on its own, the merger with intense laser physics is relatively recent. In this report on progress we present a comprehensive experimental and theoretical overview of physics that takes place when short and intense laser pulses interact with nanosystems, such as metallic and dielectric nanostructures. In particular we elucidate how the spatially inhomogeneous laser induced fields at a nanometer scale modify the laser-driven electron dynamics. Consequently, this has important impact on pivotal processes such as above-threshold ionization and high-order harmonic generation. The deep understanding of the coupled dynamics between these spatially inhomogeneous fields and matter configures a promising way to new avenues of research and applications. Thanks to the maturity that attosecond physics has reached, together with the tremendous advance in material engineering and manipulation techniques, the age of atto-nanophysics has begun, but it is in the initial stage. We present thus some of the open questions, challenges and prospects for experimental confirmation of theoretical predictions, as well as experiments aimed at characterizing the induced fields and the unique electron dynamics initiated by them with high temporal and spatial resolution.

Imaging molecular geometry with electron momentum spectroscopy

Electron momentum spectroscopy is a unique tool for imaging orbital-specific electron density of molecule in momentum space. However, the molecular geometry information is usually veiled due to the single-centered character of momentum space wavefunction of molecular orbital (MO). Here we demonstrate the retrieval of interatomic distances from the multicenter interference effect revealed in the ratios of electron momentum profiles between two MOs with symmetric and anti-symmetric characters. A very sensitive dependence of the oscillation period on interatomic distance is observed, which is used to determine F-F distance in CF₄ and O-O distance in CO₂ with sub-Ångström precision. Thus, using one spectrometer, and in one measurement, the electron density distributions of MOs and the molecular geometry information can be obtained simultaneously. Our approach provides a new robust tool for imaging molecules with high precision and has potential to apply to ultrafast imaging of molecular dynamics if combined with ultrashort electron pulses in the future.

High-energy electron emission from metallic nano-tips driven by intense single-cycle terahertz pulses

Electrons ejected from atoms and subsequently driven to high energies in strong laser fields enable techniques from attosecond pulse generation to imaging with rescattered electrons. Analogous processes govern strong-field electron emission from nanostructures, where long wavelength radiation and large local field enhancements hold the promise for producing electrons with substantially higher energies, allowing for higher resolution time-resolved imaging. Here we report on the use of single-cycle terahertz pulses to drive electron emission from unbiased nano-tips. Energies exceeding 5 keV are observed, substantially greater than previously attained at higher drive frequencies. Despite large differences in the magnitude of the respective local fields, we find that the maximum electron energies are only weakly dependent on the tip radius, for 10 nm<R<1,000 nm. Due to the single-cycle nature of the field, the high-energy electron emission is predicted to be confined to a single burst, potentially enabling a variety of applications.

High-energy electron sources are powerful tools for investigating dynamics at atomic and subatomic scales. Here, Li and Jones demonstrate the terahertz-driven emission of electrons with energies exceeding five kiloelectronvolts from nano-tips and study its dependence on the tip radius.

Controlling Nonsequential Double Ionization in Two-Color Circularly Polarized Femtosecond Laser Fields

Atoms undergoing strong-field ionization in two-color circularly polarized femtosecond laser fields exhibit unique two-dimensional photoelectron trajectories and can emit bright circularly polarized extreme ultraviolet and soft-x-ray beams. In this Letter, we present the first experimental observation of nonsequential double ionization in these tailored laser fields. Moreover, we can enhance or suppress nonsequential double ionization by changing the intensity ratio and helicity of the two driving laser fields to maximize or minimize high-energy electron-ion rescattering. Our experimental results are explained through classical simulations, which also provide insight into how to optimize the generation of circularly polarized high harmonic beams.

High power multi-color OPCPA source with simultaneous femtosecond deep-UV to mid-IR outputs

Many experimental investigations demand synchronized pulses at various wavelengths, ideally with very short pulse duration and high repetition rate. Here we describe a femtosecond multi-color optical parametric chirped pulse amplifier (OPCPA) with simultaneous outputs from the deep-UV to the mid-IR with optical synchronization. The high repetition rate of 160 kHz is well suited to compensate for low interaction probability or low cross section in strong-field interactions. Our source features high peak powers in the tens to hundreds of MW regime with pulse durations below 110 fs, which is ideal for pump-probe experiments of nonlinear and strong-field physics. We demonstrate its utility by strong-field ionization experiments of xenon in the near- to mid-IR.

Influence of orbital symmetry on diffraction imaging with rescattering electron wave packets

The ability to directly follow and time-resolve the rearrangement of the nuclei within molecules is a frontier of science that requires atomic spatial and few-femtosecond temporal resolutions. While laser-induced electron diffraction can meet these requirements, it was recently concluded that molecules with particular orbital symmetries (such as πg) cannot be imaged using purely backscattering electron wave packets without molecular alignment. Here, we demonstrate, in direct contradiction to these findings, that the orientation and shape of molecular orbitals presents no impediment for retrieving molecular structure with adequate sampling of the momentum transfer space. We overcome previous issues by showcasing retrieval of the structure of randomly oriented O2 and C2H2 molecules, with πg and πu symmetries, respectively, and where their ionization probabilities do not maximize along their molecular axes. While this removes a serious bottleneck for laser-induced diffraction imaging, we find unexpectedly strong backscattering contributions from low-Z atoms.

Dynamics of Strong-Field Double Ionization in Two-Color Counterrotating Fields

The double ionization of helium in bichromatic, circularly polarized intense laser fields is analyzed with a classical ensemble approach. It is found that counterrotating fields produce significant nonsequential double-ion yield and drive novel ionization dynamics. It is shown that distinct pathways to ionization can be modified by altering the relative intensities of the two colors, allowing for unique control of strong-field processes. Electrons are observed to return to the ion at different angles from the angle of ionization, opening new possibilities for probing electronic and molecular structure on the ultrafast time scale.

Reconstruction of two-dimensional molecular structure with laser-induced electron diffraction from laser-aligned polyatomic molecules

Imaging the transient process of molecules has been a basic way to investigate photochemical reactions and dynamics. Based on laser-induced electron diffraction and partial one-dimensional molecular alignment, here we provide two effective methods for reconstructing two-dimensional structure of polyatomic molecules. We demonstrate that electron diffraction images in both scattering angles and broadband energy can be utilized to retrieve complementary structure information, including positions of light atoms. With picometre spatial resolution and the inherent femtosecond temporal resolution of lasers, laser-induced electron diffraction method offers significant opportunities for probing atomic motion in a large molecule in a typical pump-probe measurement.

Dynamic Exchange in the Strong Field Ionization of Molecules

We show that dynamic exchange is a dominant effect in strong field ionization of molecules. In CO(2) it fixes the peak ionization yield at the experimentally observed angle of 45° between polarization direction and the molecular axis. For O(2) it changes the angle of peak emission and for N(2) the alignment dependence of yields is modified by up to a factor of 2. The effect appears on the Hartree-Fock level as well as in full ab initio solutions of the Schrödinger equation.

Imaging an aligned polyatomic molecule with laser-induced electron diffraction

Laser-induced electron diffraction is an evolving tabletop method that aims to image ultrafast structural changes in gas-phase polyatomic molecules with sub-Ångström spatial and femtosecond temporal resolutions. Here we demonstrate the retrieval of multiple bond lengths from a polyatomic molecule by simultaneously measuring the C–C and C–H bond lengths in aligned acetylene. Our approach takes the method beyond the hitherto achieved imaging of simple diatomic molecules and is based on the combination of a 160 kHz mid-infrared few-cycle laser source with full three-dimensional electron–ion coincidence detection. Our technique provides an accessible and robust route towards imaging ultrafast processes in complex gas-phase molecules with atto- to femto-second temporal resolution.

Laser-induced electron diffraction can provide structural information on gas-phase molecules with high spatial and temporal resolution. Going beyond previous diatomic cases, Pullen et al. apply this approach to acetylene and show that it can be used to measure bond lengths for polyatomic molecules.