The Role of Momentum Partitioning in Covariance Ion Imaging Analysis

We present results from a covariance ion imaging study, which employs extensive filtering, on the relationship between fragment momenta to gain deeper insight into photofragmentation dynamics. A new data analysis approach is introduced that considers the momentum partitioning between the fragments of the breakup of a molecular polycation to disentangle concurrent fragmentation channels, which yield the same ion species. We exploit this approach to examine the momentum exchange relationship between the products, which provides direct insight into the dynamics of molecular fragmentation. We apply these techniques to extensively characterize the dissociation of 1-iodopropane and 2-iodopropane dications prepared by site-selective ionization of the iodine atom using extreme ultraviolet intense femtosecond laser pulses with a photon energy of 95 eV. Our assignments are supported by classical simulations, using parameters largely obtained directly from the experimental data.

Exploring the ultrafast and isomer-dependent photodissociation of iodothiophenes via site-selective ionization

C-I bond extension and fission following ultraviolet (UV, 262 nm) photoexcitation of 2- and 3-iodothiophene is studied using ultrafast time-resolved extreme ultraviolet (XUV) ionization in conjunction with velocity map ion imaging. The photoexcited molecules and eventual I atom products are probed by site-selective ionization at the I 4d edge using intense XUV pulses, which induce multiple charges initially localized to the iodine atom. At C-I separations below the critical distance for charge transfer (CT), charge can redistribute around the molecule leading to Coulomb explosion and charged fragments with high kinetic energy. At greater C-I separations, beyond the critical distance, CT is no longer possible and the measured kinetic energies of the charged iodine atoms report on the neutral dissociation process. The time and momentum resolved measurements allow determination of the timescales and the respective product momentum and kinetic energy distributions for both isomers, which are interpreted in terms of rival 'direct' and 'indirect' dissociation pathways. The measurements are compared with a classical over the barrier model, which reveals that the onset of the indirect dissociation process is delayed by ∼1 ps relative to the direct process. The kinetics of the two processes show no discernible difference between the two parent isomers, but the branching between the direct and indirect dissociation channels and the respective product momentum distributions show isomer dependencies. The greater relative yield of indirect dissociation products from 262 nm photolysis of 3-iodothiophene (cf. 2-iodothiophene) is attributed to the different partial cross-sections for (ring-centred) π∗ ← π and (C-I bond localized) σ∗ ← (n/π) excitation in the respective parent isomers.

Femtosecond Electronic and Hydrogen Structural Dynamics in Ammonia Imaged with Ultrafast Electron Diffraction

Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of the nuclear and corresponding electronic structure changes resulting from the dissociation dynamics in the time-dependent diffraction. Both assignments are confirmed by ab initio simulations of the photochemical dynamics and the resulting diffraction observable. While the temporal resolution of the experiment is insufficient to resolve the dissociation in time, our results represent an important step towards the observation of proton dynamics in real space and time.

Time-Resolved X-ray Photoelectron Spectroscopy: Ultrafast Dynamics in CS2 Probed at the S 2p Edge

Recent developments in X-ray free-electron lasers have enabled a novel site-selective probe of coupled nuclear and electronic dynamics in photoexcited molecules, time-resolved X-ray photoelectron spectroscopy (TRXPS). We present results from a joint experimental and theoretical TRXPS study of the well-characterized ultraviolet photodissociation of CS2, a prototypical system for understanding non-adiabatic dynamics. These results demonstrate that the sulfur 2p binding energy is sensitive to changes in the nuclear structure following photoexcitation, which ultimately leads to dissociation into CS and S photoproducts. We are able to assign the main X-ray spectroscopic features to the CS and S products via comparison to a first-principles determination of the TRXPS based on ab initio multiple-spawning simulations. Our results demonstrate the use of TRXPS as a local probe of complex ultrafast photodissociation dynamics involving multimodal vibrational coupling, nonradiative transitions between electronic states, and multiple final product channels.

Filming enhanced ionization in an ultrafast triatomic slingshot

Filming atomic motion within molecules is an active pursuit of molecular physics and quantum chemistry. A promising method is laser-induced Coulomb Explosion Imaging (CEI) where a laser pulse rapidly ionizes many electrons from a molecule, causing the remaining ions to undergo Coulomb repulsion. The ion momenta are used to reconstruct the molecular geometry which is tracked over time (i.e., filmed) by ionizing at an adjustable delay with respect to the start of interatomic motion. Results are distorted, however, by ultrafast motion during the ionizing pulse. We studied this effect in water and filmed the rapid "slingshot" motion that enhances ionization and distorts CEI results. Our investigation uncovered both the geometry and mechanism of the enhancement which may inform CEI experiments in many other polyatomic molecules.

Multiparticle Cumulant Mapping for Coulomb Explosion Imaging

We extend covariance velocity map ion imaging to four particles, establishing cumulant mapping and allowing for measurements that provide insights usually associated with coincidence detection, but at much higher count rates. Without correction, a fourfold covariance analysis is contaminated by the pairwise correlations of uncorrelated events, but we have addressed this with the calculation of a full cumulant, which subtracts pairwise correlations. We demonstrate the approach on the four-body breakup of formaldehyde following strong field multiple ionization in few-cycle laser pulses. We compare Coulomb explosion imaging for two different pulse durations (30 and 6 fs), highlighting the dynamics that can take place on ultrafast timescales. These results have important implications for Coulomb explosion imaging as a tool for studying ultrafast structural changes in molecules, a capability that is especially desirable for high-count-rate x-ray free-electron laser experiments.

Transient vibration and product formation of photoexcited CS2 measured by time-resolved x-ray scattering

We have observed details of the internal motion and dissociation channels in photoexcited carbon disulfide (CS2) using time-resolved x-ray scattering (TRXS). Photoexcitation of gas-phase CS2 with a 200 nm laser pulse launches oscillatory bending and stretching motion, leading to dissociation of atomic sulfur in under a picosecond. During the first 300 fs following excitation, we observe significant changes in the vibrational frequency as well as some dissociation of the C-S bond, leading to atomic sulfur in the both 1D and 3P states. Beyond 1400 fs, the dissociation is consistent with primarily 3P atomic sulfur dissociation. This channel-resolved measurement of the dissociation time is based on our analysis of the time-windowed dissociation radial velocity distribution, which is measured using the temporal Fourier transform of the TRXS data aided by a Hough transform that extracts the slopes of linear features in an image. The relative strength of the two dissociation channels reflects both their branching ratio and differences in the spread of their dissociation times. Measuring the time-resolved dissociation radial velocity distribution aids the resolution of discrepancies between models for dissociation proposed by prior photoelectron spectroscopy work.

Disentangling sequential and concerted fragmentations of molecular polycations with covariant native frame analysis

We present results from an experimental ion imaging study into the fragmentation dynamics of 1-iodopropane and 2-iodopropane following interaction with extreme ultraviolet intense femtosecond laser pulses with a photon energy of 95 eV. Using covariance imaging analysis, a range of observed fragmentation pathways of the resulting polycations can be isolated and interrogated in detail at relatively high ion count rates (∼12 ions shot^-1). By incorporating the recently developed native frames analysis approach into the three-dimensional covariance imaging procedure, contributions from three-body concerted and sequential fragmentation mechanisms can be isolated. The angular distribution of the fragment ions is much more complex than in previously reported studies for triatomic polycations, and differs substantially between the two isomeric species. With support of simple simulations of the dissociation channels of interest, detailed physical insights into the fragmentation dynamics are obtained, including how the initial dissociation step in a sequential mechanism influences rovibrational dynamics in the metastable intermediate ion and how signatures of this nuclear motion manifest in the measured signals.

Attosecond coherent electron motion in Auger-Meitner decay

In quantum systems, coherent superpositions of electronic states evolve on ultrafast time scales (few femtoseconds to attoseconds; 1 attosecond = 0.001 femtoseconds = 10^-18 seconds), leading to a time-dependent charge density. Here we performed time-resolved measurements using attosecond soft x-ray pulses produced by a free-electron laser, to track the evolution of a coherent core-hole excitation in nitric oxide. Using an additional circularly polarized infrared laser pulse, we created a clock to time-resolve the electron dynamics and demonstrated control of the coherent electron motion by tuning the photon energy of the x-ray pulse. Core-excited states offer a fundamental test bed for studying coherent electron dynamics in highly excited and strongly correlated matter.

Multi-Particle Three-Dimensional Covariance Imaging: "Coincidence" Insights into the Many-Body Fragmentation of Strong-Field Ionized D2O

We demonstrate the applicability of covariance analysis to three-dimensional velocity-map imaging experiments using a fast time stamping detector. Studying the photofragmentation of strong-field doubly ionized D₂O molecules, we show that combining high count rate measurements with covariance analysis yields the same level of information typically limited to the "gold standard" of true, low count rate coincidence experiments, when averaging over a large ensemble of photofragmentation events. This increases the effective data acquisition rate by approximately 2 orders of magnitude, enabling a new class of experimental studies. This is illustrated through an investigation into the dependence of three-body D₂O²⁺ dissociation on the intensity of the ionizing laser, revealing mechanistic insights into the nuclear dynamics driven during the laser pulse. The experimental methodology laid out, with its drastic reduction in acquisition time, is expected to be of great benefit to future photofragment imaging studies.

Resolving multiphoton processes with high-order anisotropy ultrafast X-ray scattering

We present the first results on experimentally measured ultrafast X-ray scattering of strongly driven molecular iodine and analysis of high-order anisotropic components of the scattering signal. We discuss the technical details of retrieving high fidelity high-order anisotropy components from the measured scattering data and outline a method to analyze such signals using Legendre decomposition. We describe how anisotropic motions can be extracted from the various Legendre orders using simulated anisotropic scattering signals and Fourier analysis. We implement the method on the measured signal and observe a multitude of dissociation and vibration motions simultaneously arising from various multiphoton transitions occurring in the sample. We use the anisotropic scattering information to disentangle the different processes and assign their dissociation velocities on the Angstrom and femtosecond scales de novo.

Electronic Population Transfer via Impulsive Stimulated X-Ray Raman Scattering with Attosecond Soft-X-Ray Pulses

Free-electron lasers provide a source of x-ray pulses short enough and intense enough to drive nonlinearities in molecular systems. Impulsive interactions driven by these x-ray pulses provide a way to create and probe valence electron motions with high temporal and spatial resolution. Observing these electronic motions is crucial to understand the role of electronic coherence in chemical processes. A simple nonlinear technique for probing electronic motion, impulsive stimulated x-ray Raman scattering (ISXRS), involves a single impulsive interaction to produce a coherent superposition of electronic states. We demonstrate electronic population transfer via ISXRS using broad bandwidth (5.5 eV full width at half maximum) attosecond x-ray pulses produced by the Linac Coherent Light Source. The impulsive excitation is resonantly enhanced by the oxygen 1s→2π^{*} resonance of nitric oxide (NO), and excited state neutral molecules are probed with a time-delayed UV laser pulse.

Ionization induced dynamic alignment of water

Two-body dissociation resulting from strong-field double ionization of water is investigated. Two distinct features are seen in the alignment of the fragment momenta with respect to the laser polarization. One feature shows alignment of the H-OH axis with the laser polarization, while the other indicates polarization alignment normal to the H-OH axis. By analyzing kinematic differences between the OH⁺/D⁺ and OD⁺/H⁺ channels of HOD, these two alignment features are shown to result from dissociation from different states in the dication. Only dissociation from one of these states has an alignment dependence consistent with predictions of sequential strong-field tunneling ionization models. The alignment dependence of dissociation from the other state can only be explained by dynamic alignment launched by the unbending of the molecule during ionization.

Attosecond transient absorption spooktroscopy: a ghost imaging approach to ultrafast absorption spectroscopy

Recently demonstrated isolated attosecond XFEL pulses should allow the probing of ultrafast electron dynamics at X-ray wavelengths. The authors use ghost imaging to enable high-resolution transient absorption spectroscopy at fluctuating XFEL sources.

On the limits of observing motion in time-resolved X-ray scattering

Limits on the ability of time-resolved X-ray scattering (TRXS) to observe harmonic motion of amplitude, A and frequency, ω₀, about an equilibrium position, R₀, are considered. Experimental results from a TRXS experiment at the LINAC Coherent Light Source are compared to classical and quantum theories that demonstrate a fundamental limitation on the ability to observe the amplitude of motion. These comparisons demonstrate dual limits on the spatial resolution through Q_max and the temporal resolution through ω_max for observing the amplitude of motion. In the limit where ω_max ≈  ω₀, the smallest observable amplitude of motion is A = 2 π/ Q_max. In the limit where ω_max≥2 ω₀, A≤2 π/ Q_max is observable provided there are sufficient statistics. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Characterization of high-harmonic emission from ZnO up to 11 eV pumped with a Cr:ZnS high-repetition-rate source

We report the measurement of high-order harmonics from a ZnO crystal with photon energies up to 11 eV generated by a high-repetition-rate femtosecond Cr:ZnS laser operating in the mid-infrared at 2-3 μm, delivering few-cycle pulses with multi-watt average power and multi-megawatt peak power. High-focus intensity is achieved in a single pass through the crystal without a buildup cavity or nanostructued pattern for field enhancement. We measure in excess of 10⁸ high-harmonic photons/second.

Geometric dependence of strong field enhanced ionization in D2O

We have studied strong-field enhanced dissociative ionization of D₂O in 40 fs, 800 nm laser pulses with focused intensities of <1-3 × 10¹⁵W/cm² by resolving the charged fragment momenta with respect to the laser polarization. We that observe dication dissociation into OD⁺/D⁺ dominates when the polarization is out of the plane of the molecule, whereas trication dissociation into O⁺/D⁺/D⁺ is strongly dominant when the polarization is aligned along the D-D axis. Dication dissociation into O/D⁺/D⁺ and O⁺/D₂⁺ is not seen nor is there any significant fragmentation into multiple ions when the laser is polarized along the C_2v symmetry axis of the molecule. Even below the saturation intensity for OD⁺/D⁺, the O⁺/D⁺/D⁺ channel has higher yield. By analyzing how the laser field is oriented within the molecular frame for both channels, we show that enhanced ionization is driving the triply charged three body breakup but is not active for the doubly charged two body breakup. We conclude that laser-induced distortion of the molecular potential suppresses multiple ionization along the C_2v axis but enhances ionization along the D-D direction.

Accurate prediction of X-ray pulse properties from a free-electron laser using machine learning

Free-electron lasers providing ultra-short high-brightness pulses of X-ray radiation have great potential for a wide impact on science, and are a critical element for unravelling the structural dynamics of matter. To fully harness this potential, we must accurately know the X-ray properties: intensity, spectrum and temporal profile. Owing to the inherent fluctuations in free-electron lasers, this mandates a full characterization of the properties for each and every pulse. While diagnostics of these properties exist, they are often invasive and many cannot operate at a high-repetition rate. Here, we present a technique for circumventing this limitation. Employing a machine learning strategy, we can accurately predict X-ray properties for every shot using only parameters that are easily recorded at high-repetition rate, by training a model on a small set of fully diagnosed pulses. This opens the door to fully realizing the promise of next-generation high-repetition rate X-ray lasers.

Self-Referenced Coherent Diffraction X-Ray Movie of Ångstrom- and Femtosecond-Scale Atomic Motion

Time-resolved femtosecond x-ray diffraction patterns from laser-excited molecular iodine are used to create a movie of intramolecular motion with a temporal and spatial resolution of 30 fs and 0.3 Å. This high fidelity is due to interference between the nonstationary excitation and the stationary initial charge distribution. The initial state is used as the local oscillator for heterodyne amplification of the excited charge distribution to retrieve real-space movies of atomic motion on ångstrom and femtosecond scales. This x-ray interference has not been employed to image internal motion in molecules before. Coherent vibrational motion and dispersion, dissociation, and rotational dephasing are all clearly visible in the data, thereby demonstrating the stunning sensitivity of heterodyne methods.

Observation of Quantum Interferences via Light-Induced Conical Intersections in Diatomic Molecules

We observe energy-dependent angle-resolved diffraction patterns in protons from strong-field dissociation of the molecular hydrogen ion H_{2}^{+}. The interference is a characteristic of dissociation around a laser-induced conical intersection (LICI), which is a point of contact between two surfaces in the dressed two-dimensional Born-Oppenheimer potential energy landscape of a diatomic molecule in a strong laser field. The interference magnitude and angular period depend strongly on the energy difference between the initial state and the LICI, consistent with coherent diffraction around a cone-shaped potential barrier whose width and thickness depend on the relative energy of the initial state and the cone apex. These findings are supported by numerical solutions of the time-dependent Schrödinger equation for similar experimental conditions.

Transient lattice contraction in the solid-to-plasma transition

In condensed matter systems, strong optical excitations can induce phonon-driven processes that alter their mechanical properties. We report on a new phenomenon where a massive electronic excitation induces a collective change in the bond character that leads to transient lattice contraction. Single large van der Waals clusters were isochorically heated to a nanoplasma state with an intense 10-fs x-ray (pump) pulse. The structural evolution of the nanoplasma was probed with a second intense x-ray (probe) pulse, showing systematic contraction stemming from electron delocalization during the solid-to-plasma transition. These findings are relevant for any material in extreme conditions ranging from the time evolution of warm or hot dense matter to ultrafast imaging with intense x-ray pulses or, more generally, any situation that involves a condensed matter-to-plasma transition.

Observation of Bloch Oscillations in Molecular Rotation

We report the observation of rotational Bloch oscillations in a gas of nitrogen molecules kicked by a periodic train of femtosecond laser pulses. A controllable detuning from the quantum resonance creates an effective accelerating potential in angular momentum space, inducing Bloch-like oscillations of the rotational excitation. These oscillations are measured via the temporal modulation of the refractive index of the gas. Our results introduce room-temperature laser-kicked molecules as a new laboratory for studies of localization phenomena in quantum transport.