Electron Dynamics Research Articles

Time Resolved Quantum Tomography in Molecular Spectroscopy by the Maximal Entropy Approach.

Attosecond science offers unprecedented precision in probing the initial moments of chemical reactions, revealing the dynamics of molecular electrons that shape reaction pathways. A fundamental question emerges: what role, if any, do quantum coherences between molecular electron states play in photochemical reactions? Answering this question necessitates quantum tomography─the determination of the electronic density matrix from experimental data, where the off-diagonal elements represent these coherences. The Maximal Entropy (MaxEnt) based Quantum State Tomography (QST) approach offers unique advantages in studying molecular dynamics, particularly with partial tomographic data. Here, we explore the application of MaxEnt-based QST on photoexcited ammonia, necessitating the operator form of observables specific to the performed measurements. We present two methodologies for constructing these operators: one leveraging Molecular Angular Distribution Moments (MADMs) which accurately capture the orientation-dependent vibronic dynamics of molecules and another utilizing Angular Momentum Coherence Operators to construct measurement operators for the full rovibronic density matrix in the symmetric top basis. A key revelation of our study is the direct link between Lagrange multipliers in the MaxEnt formalism and the unique set of MADMs. Additionally, we visualize the electron density within the molecular frame, demonstrating charge migration across the molecule. Furthermore, we achieve a groundbreaking milestone by constructing, for the first time, the entanglement entropy of the electronic subsystem─a metric that was previously inaccessible. The entropy vividly reveals and quantifies the effects of coupling between the excited electron and nuclear degrees of freedom. Consequently, our findings open new avenues for research in ultrafast molecular spectroscopy within the broader domain of quantum information science, offering profound implications for the study of molecular systems under excitation using quantum tomographic schemes.

Exploring photoconduction mechanisms in Lead‐Free Cs3Sb2I9 single crystal thin films

The future commercial advancement of lead-halide perovskites (LHPs) faces obstacles due to the existence of harmful lead and the inadequate stability associated with these materials. To tackle this challenge, we have prepared a Cs3Sb2I9 perovskite single-crystalline thin film (Cs3Sb2I9 device) using a technique based on the restricted evaporation of solvents in space, aiming for effective photodetection. The photodetector in the current study shows a responsivity (R) of around 111 mA/W and a detectivity (D∗) of approximately 3.7 × 1012 Jones. While these performance metrics are comparable to other photodetectors, there is a need for additional optimization to match the capabilities of commercial silicon and germanium-based counterparts. The examination of ultrafast transient absorption provides insights into the essential photophysics inherent in Cs3Sb2I9. The synergy between the deformation potential and the Fröhlich effect plays a crucial role in shaping electronic dynamics. This synergy leads to the self-trapping of charge carriers, resulting in the creation of localized polarons within the Cs3Sb2I9 lattice within just some picoseconds. The restriction of carrier mobility within Cs3Sb2I9 arises from the self-capturing and confinement of small polarons (SPs). Furthermore, it was noted that SPs in a localized state could undergo absorption into an elevated state (photon energy ⁓ 1.60 eV). This process effectively facilitates the charge carriers' mobilization to a more dispersed eigenstate. Our research provides essential comprehension into the light-induced processes of lead-free halide perovskites (LFHPs), offering valuable insights for their prospective use in optoelectronics as promising future semiconducting agents.

Coulomb focusing in attosecond angular streaking

Angular streaking technique employs a close-to-circularly polarized laser pulse to build a mapping between the instant of maximum ionization and the most probable emission angle in the photoelectron momentum distribution, thereby enabling the probe of laser-induced electron dynamics in atoms and molecules with attosecond temporal resolution. Here, through the jointed experimental observations and improved Coulomb-corrected strong-field approximation statistical simulations, we identify that electrons emitted at different initial ionization times converge to the most probable emission angle due to the previously-unexpected Coulomb focusing triggered by the nonadiabatic laser-induced electron tunneling. We reveal that the Coulomb focusing induces the observed nonintuitive energy-dependent trend in the angular streaking measurements on the nonadiabatic tunneling, and that tunneling dynamics under the classically forbidden barrier can leave fingerprints on the resulting signals. Our findings have significant implications for the decoding of the intricate tunneling dynamics with attosecond angular streaking.

Dynamics of JET runaway electron beams in D2-rich shattered pellet injection mitigation experiments

Abstract The publication provide further insights into the dynamics of JET runaway electron (RE) beams mitigated by D2-rich shattered pellet injection (SPI) (Reux et al 2022 Plasma Phys. Control. Fusion 64 034002). Multi-diagnostic analyses show that mechanisms causing continuous RE losses and energy transfer from hot electrons to cold background plasma can act before the SPI. After the SPI, measurements are compatible with a reduction of the maximum energy and pitch angle of the RE distribution while the population of supra-thermal electrons increases. The RE population growth is likely due to electron avalanche. Dark island-like pattern chains, characterised by an integer poloidal mode number and a certain minor radius, are identified in the JET RE beam synchrotron radiation videos. The synchrotron island dynamics is studied via a newly developed computer vision code (Sommariva and Silburn https://c4science.ch/source/pSpiPTV/). The radial motion of synchrotron island chains is found to be consistent with the most plausible time evolution of the radial current density profile compatible with both the RE synchrotron videos and the total RE current time trace. Similarly, correlations are identified between the temporal progression of the synchrotron islands poloidal rotation frequency and sudden MHD relaxation events. Loss-of-RE events probably caused by non-linear interactions between synchrotron islands are observed for the first time. Experimental evidences suggest that synchrotron islands are possibly related to the existence of magnetic islands which may lead to the development of new RE beam mitigation strategies.

Assessment of antioxidant, antidiabetic, and antimicrobial properties of hybrid mushroom strains derived through intergeneric hybridization between Pleurotus sajor-caju and Calocybe indica

Our present study aims to evaluate the biological activities of the six hybrid mushrooms (APS) obtained through the protoplast fusion technique between two mushrooms Calocybe indica and Pleurotus sajor-caju, in our previous study. Antioxidant activity of hybridized mushroom samples was determined by the free radical scavenging method, using DPPH radical, Superoxide radical, and Hydroxyl radical. Additionally, all the mushroom extract has shown a good amount of total phenolic content, and total flavonoid content and also has potent Ferric reducing antioxidant power. The Total phenolic content, Total flavonoid content, and Ferric reducing antioxidant power were estimated. Six constituents: gallic acid, catechin, protocatechuic acid, p-hydroxybenzoic acid, p-coumaric acid, and cinnamic acid were identified by UHPLC. The MIC values, zone of inhibition, growth kinetic, and scanning electron microscopy (SEM) were performed to establish the antimicrobial efficacy. The tested samples exhibited antimicrobial activity against selected microorganisms Staphylococcus aureus, Klebsiella pneumoniae, Bacillus subtilis, Pseudomonas aeruginosa. A clear morphological change was observed under SEM when Bacillus subtilis and Pseudomonas aeruginosa were treated with APS-4 and APS-3 mushroom extracts. The ability to inhibit carbohydrate hydrolyzing enzymes such as α-amylase and α-galactosidase has also been studied to explore antidiabetic properties. The inhibitory activity of α-glucosidase was APS-4 reflected a very prominent result with the lowest IC50 value i.e.,118.058 ± 1.515, APS-2 and APS-6 showed almost similar IC50 values. α – galactosidase inhibitory activity of APS-4 and APS-6 exhibit better results than other strains.

Characterizing strong-field tunneling ionization with a phase-dependent THz polarization spectrum

The terahertz radiation emitted by asymmetrically ionized wavepackets in two-color strong-field tunneling ionization is essential for detecting the system's associated electron dynamics and structural properties. We propose to characterize and control tunneling ionization using a phase-dependent terahertz polarization (PTP) spectrum, analyzed through a combination of the classical trajectory Monte Carlo method, an analytical model based on the virial theorem, and the rigorous solution of the time-dependent Schrödinger equation as a benchmark. Our results demonstrate that the PTP spectrum offers a high-precision measure of the Coulomb effect through the relative phase of the two-color laser. Comparisons of PTP results calculated using different methods suggest how the electron can be manipulated by controlling the relative phase and laser intensity. In particular, the PTP spectrum can be used to calibrate the relative phase and provides a convenient and robust reconstruction of the time-averaging of tunneling positions with high precision using the analytical model. These insights reveal that the PTP spectrum as a whole can be a new and useful tool for the all-optical characterization of ultrafast atomic and molecular ionization.

From Coherence to Function: Exploring the Connection in Chemical Systems.

ConspectusThe role of quantum mechanical coherences or coherent superposition states in excited state processes has received considerable attention in the last two decades largely due to advancements in ultrafast laser spectroscopy. These coherence effects hold promise for enhancing the efficiency and robustness of functionally relevant processes, even when confronted with energy disorder and environmental fluctuations. Understanding coherence deeply drives us to unravel mechanisms and dynamics controlled by order and synchronization at a quantum mechanical level, envisioning optical control of coherence to enhance functions or create new ones in molecular and material systems. In this frontier, the interplay between electronic and vibrational dynamics, specifically the influence of vibrations in directing electronic dynamics, has emerged as the leading principle. Here, two energetically disparate quantum degrees of freedom work in-sync to dictate the trajectory of an excited state reaction. Moreover, with the vibrational degree being directly related to the structural composition of molecular or material systems, new molecular designs could be inspired by tailoring certain structural elements.In the realm of chemical kinetics, our understanding of the dynamics of chemical transformations is underpinned by fundamental theories, such as transition state theory, activated rate theory, and Marcus theory. These theories elucidate reaction rates by considering the energy barriers that must be overcome for reactants to transform into products. Those barriers are surmounted by the stochastic nature of energy gap fluctuations within reacting systems, emphasizing that the reaction coordinate, the pathway from reactants to products, is not rigidly defined by a specific vibrational motion but encompasses a diverse array of molecular motions. While less is known about the involvement of specific intramolecular vibrational modes, their significance in certain cases cannot be overlooked.In this Account, we summarize key experimental findings that offer deeper insights into the complex electronic-vibrational trajectories encompassing excited states afforded from state-of-the-art ultrafast laser spectroscopy in three exemplary processes: photoinduced electron transfer, singlet-triplet intersystem crossing, and intramolecular vibrational energy flow in molecular systems. We delve into the rapid decoherence, or loss of phase and amplitude correlations, of vibrational coherences along promoter vibrations during subpicosecond intersystem crossing dynamics in a series of binuclear platinum complexes. This rapid decoherence illustrates the vibration-driven reactive pathways from the Franck-Condon state to the curve crossing region. We also explore the generation of new vibrational coherences induced by impulsive reaction dynamics rather than by the laser pulse in these systems, which sheds light on specific energy dissipation pathways and thereby on the progression of the reaction trajectory in the vicinity of the curve crossing on the product side. Another property of vibrational coherences, amplitude, reveals how energy can flow from one vibration to another in the electronic excited state of a terpyridine-molybdenum complex hosting a nonreactive dinitrogen substrate. A slight change in vibrational energy triggers a quasi-resonant interaction, leading to constructive wavepacket interference and ultimately intramolecular vibrational redistribution from a Franck-Condon active terpyridine vibration to a dinitrogen stretching vibration, energizing the dinitrogen bond.

Enhanced high harmonic efficiency through phonon-assisted photodoping effect

High-harmonic generation (HHG) has emerged as a central technique in attosecond science and strong-field physics, providing a tool for investigating ultrafast dynamics. However, the microscopic mechanism of HHG in solids is still under debate, and it is unclear how it is modified in the ubiquitous presence of phonons. Here we theoretically investigate the role of collectively coherent vibrations in HHG in a wide range of solids (e.g., hBN, graphite, 2H-MoS2, and diamond). We predict that phonon-assisted high harmonic yields can be significantly enhanced, compared to the phonon-free case – up to a factor of ~20 for a transverse optical phonon in bulk hBN. We also show that the emitted harmonics strongly depend on the character of the pumped vibrational modes. Through state-of-the-art ab initio calculations, we elucidate the physical origin of the HHG yield enhancement – phonon-assisted photoinduced carrier doping, which plays a paramount role in both intraband and interband electron dynamics. Our research illuminates a clear pathway toward comprehending phonon-mediated nonlinear optical processes within materials, offering a powerful tool to deliberately engineer and govern solid-state high harmonics.

Particle Simulation Study of Obliquely Propagating Whistler Waves in Low‐Beta Plasmas

AbstractWhistler mode waves, which are electromagnetic emissions commonly observed in various space plasma environments, play critical roles in electron dynamics. While most whistler waves are driven by temperature anisotropy and propagate parallel to the background magnetic field, these waves can also be excited in the oblique direction when electron plasma beta is very low (<0.025). Although linear theory accounts for the excitation processes of obliquely propagating whistler waves, the subsequent evolution and saturation processes remain inadequately understood. This study utilizes two‐dimensional self‐consistent simulations to investigate the complete wave‐particle interaction process. By scanning a broad parameter range, we derive scaling laws for the wave intensity, linking the wave properties to initial and final plasma conditions. The saturated temperature anisotropy from simulations can explain the upper bound anisotropy constraint observed by spacecraft well. Additional phase space analysis shows that both Landau and cyclotron resonance play critical roles in the evolution of electron velocity distribution, albeit in different energy ranges. Oblique whistler waves can effectively heat electrons through Landau resonance, creating a plateau distribution in the parallel direction. This research advances our understanding of the mechanisms behind obliquely propagating whistler waves in low‐beta plasmas and their impact on electron dynamics.

Generation of seed electrons in guided ionization waves in He–O2 mixtures: The effect of negative ion cluster formation

The kinetics of electrons and negative ions was numerically studied under the conditions, which are typical for multi-pulsed guided ionization waves in He flows ejected into ambient air. It was shown that, in He with a small admixture of O2 or air, O2− ions formed due to three-body electron attachment in the discharge afterglow are rapidly converted to O4− cluster ions in pulse off time. We suggested that seed electrons are generated at the leading edge of a pulse in two steps, and these steps are dissociation of O4− ions to form O2− ions followed by electron detachment from the O2− ions. The rate of O4− dissociation was calculated in He–O2 mixtures for various reduced electric fields on the basis of a Monte Carlo simulation. This rate, as well as the rate of electron detachment from O2− ions calculated previously, was used to simulate seed electron generation in a high-voltage nanosecond pulse in He–O2 mixtures for different gas pressures. It was shown that the formation of O4− ions drastically hinders the generation of seed electrons in multi-pulsed guided ionization waves in He–O2 and He–air mixtures.

Experimental studies of H2/Ar plasma in a cylindrical inductive discharge with an expansion region

Abstract The electrical parameters of H2/Ar plasma in a cylindrical inductive discharge with an expansion region are investigated by a Langmuir probe, where Ar fractions range from 0% to 100%. The influence of gas composition and pressure on electron density, the effective electron temperature and the electron energy probability functions (EEPFs) at different spatial positions are present. In driver region, with the introduction of a small amount of Ar at 0.3 Pa, there is a rapid increase in electron density accompanied by a decrease in the effective electron temperature. Additionally, the shape of the EEPF transitions from a three-temperature distribution to a bi-Maxwellian distribution due to an increase in electron–electron collision. However, this phenomenon resulting from the changes in gas composition vanishes at 5 Pa due to the prior depletion of energetic electrons caused by the increase in pressure during hydrogen discharge. The EEPFs for the total energy in expansion region is coincident to these in the driver region at 0.3 Pa, as do the patterns of electron density variation between these two regions for differing Ar fractions. At 5 Pa, as the discharge transitions from H2 to Ar, the EEPFs evolved from a bi-Maxwellian distribution with pronounced low energy electrons to a Maxwellian distribution in expansion region. This evolve may be attributed to a reduction in molecular vibrational excitation reactions of electrons during transport and the transition from localized electron dynamics in hydrogen discharge to non-localized electron dynamics in argon discharge. In order to validate the experimental results, we use the COMSOL simulation software to calculate electrical parameters under the same conditions. The evolution and spatial distribution of the electrical parameters of the simulation results agree well with the trend of the experimental results.

XUV-beamline for photoelectron imaging spectroscopy with shaped pulses.

We introduce an extreme ultraviolet (XUV)-beamline designed for the time-resolved investigation and coherent control of attosecond (as) electron dynamics in atoms and molecules by polarization-shaped as-laser pulses. Shaped as-pulses are generated through high-harmonic generation (HHG) of tailored white-light supercontinua (WLS) in noble gases. The interaction of shaped as-pulses with the sample is studied using velocity map imaging (VMI) techniques to achieve the differential detection of photoelectron wave packets. The instrument consists of the WLS-beamline, which includes a hollow-core fiber compressor and a home-built 4f polarization pulse shaper, and the high-vacuum XUV-beamline, which combines an HHG-stage and a versatile multi-experiment vacuum chamber equipped with a home-built VMI spectrometer. The VMI spectrometer allows the detection of photoelectron wave packets from both the multiphoton ionization (MPI) of atomic or molecular samples by the tailored WLS-pulses and the single-photon ionization (SPI) by the shaped XUV-pulses. To characterize the VMI spectrometer, we studied the MPI of xenon atoms by linearly polarized WLS pulses. To validate the interplay of these components, we conducted experiments on the SPI of xenon atoms with linearly polarized XUV-pulses. Our results include the reconstruction of the 3D photoelectron momentum distribution (PMD) and initial findings on the coherent control of the PMD by tuning the spectrum of the XUV-pulses with the spectral phase of the WLS. Our results demonstrate the performance of the entire instrument for HHG-based photoelectron imaging spectroscopy with prototypical shaped pulses. Perspectively, we will employ polarization-tailored WLS-pulses to generate polarization-shaped as-pulses.

Studies of dynamic spatio-temporal processes of electrons in a 50 kHz/5 MHz dual-frequency dielectric barrier discharge plasma at atmospheric pressure

Dual-frequency excitation of dielectric barrier discharge (DBD) plasma reactors, where the plasma is generated by a low-frequency (LF) source and modulated by a radio-frequency (RF) source, have been widely adopted in the low-pressure regime. However, the impacts of the RF voltage and LF voltage amplitudes on the plasma parameters, including the spatiotemporal distributions of ion and electron densities, electron dynamics, and gas temperatures, remain poorly understood in the atmospheric pressure regime. The present work addresses this issue by conducting joint experimental and simulation studies for an atmospheric-pressure 50 kHz/5 MHz dual-frequency driven DBD plasma reactor based on phase-resolved optical emission spectra and a drift–diffusion model. The results demonstrate that the dynamic spatiotemporal behaviors of electrons change dramatically as the voltage of the RF component increases from 50 V to 300 V with the voltage of the LF component fixed at 1 kV. Moreover, the RF component is further demonstrated to modulate other plasma characteristics, such as particle densities, gas temperature, and argon emissions. These results contribute toward the tailoring of the non-equilibrium and nonlinear plasma parameters obtained under atmospheric pressure conditions.

Dynamics of the Davydov’s soliton in external oscillating magnetic field

The influence of an external oscillating in time magnetic field on the dynamics of the Davydov’s soliton is studied. It is shown that soliton parameters depend on the amplitude and frequency of the magnetic field, as well as on the field orientation with respect to the molecular chain axis. Electron dynamics in the parallel magnetic field is a composition of the “free” soliton coherent propagation along the molecular chain and oscillatory movement in the transverse direction. The latter is described by the functions of the harmonic oscillator with the cyclotron frequency depending on the field frequency. In a perpendicular field the soliton dynamics is a superposition of (i) the free electron plane wave in the plane perpendicular to the molecular chain, and (ii) propagation along the chain which is described by the modified Nonlinear Schrödinger equation with an extra term depending on the field. This equation is solved using the nonlinear perturbation theory. It is shown that the soliton velocity and phase are given by expressions which include the terms oscillating in time with the frequency of the main harmonic, given by the external field frequency, and higher multiple harmonics. Such complex effects of external time-depending magnetic fields on the dynamics of solitons modify the charge transport in low-dimensional molecular systems, which in its turn, can affect the functioning of the devices based on such compounds. These results suggest also the physical mechanism of therapeutic effects of oscillating magnetic fields, based on the field influence on the dynamics of solitons which provide charge transport through biological macromolecules in the redox processes.

Electronic correlations and partial gap in the bilayer nickelate La3Ni2O7

The discovery of superconductivity with a critical temperature of about 80 K in La3Ni2O7 single crystals under pressure has received enormous attention. La3Ni2O7 is not superconducting under ambient pressure but exhibits a transition at T ∗ ≃ 115 K. Understanding the electronic correlations and charge dynamics is an important step towards the origin of superconductivity and other instabilities. Here, our optical study shows that La3Ni2O7 features strong electronic correlations which significantly reduce the electron’s kinetic energy and place this system in the proximity of the Mott phase. The low-frequency optical conductivity reveals two Drude components arising from multiple bands at the Fermi level. The transition at T ∗ removes the Drude component exhibiting non-Fermi liquid behavior, whereas the one with Fermi-liquid behavior is barely affected. These observations in combination with theoretical results suggest that the Fermi surface dominated by the Ni-d3z2−r2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{3{z}^{2}-{r}^{2}}$$\\end{document} orbital is removed due to the transition at T ∗. Our experimental results provide pivotal information for understanding the transition at T ∗ and superconductivity in La3Ni2O7.

Nonsequential double ionization of Ar in two-color inhomogeneous laser fields

With the classical ensemble method, we investigate the correlated electron dynamics in nonsequential double ionization (NSDI) of Ar in parallel two-color inhomogeneous laser fields with different inhomogeneity parameter ϵ. Numerical results show that at low laser intensities, the probability of NSDI is higher for two-color laser fields with a higher inhomogeneity parameter ϵ. At high laser intensities, however, the probability of NSDI decreases as ϵ increases. It is also shown that under low laser intensities, the two-color inhomogeneous laser fields drives the NSDI predominantly dominated by the RII channel, and the ratio of the RII channel increases as ϵ increases. More interestingly, an arc-like structure is found in the correlated electron momentum distributions for the two-color inhomogeneous laser fields. The underlying dynamics are revealed by tracing back to classical trajectories.

Influence of Aliphatic versus Aromatic Ligand Passivation on Intersystem Crossing in Au25(SR)18.

The electronic relaxation dynamics of gold monolayer protected clusters (MPCs) are influenced by the hydrocarbon structure of thiolate protecting ligands. Here, we present ligand-dependent electronic relaxation for a series of Au25(SR)18- (SR = SC8H9, SC6H13, SC12H25) MPCs using femtosecond time-resolved transient absorption spectroscopy. Relaxation pathways included a ligand-independent femtosecond internal conversion and a competing ligand-dependent picosecond intersystem crossing process. Intersystem crossing was accelerated for the aliphatic (SC6H13, SC12H25) thiolate MPCs compared to the aromatic (SC8H9) thiolate MPCs. Additionally, a 1.2 THz quadrupolar acoustic mode and a 2.4 THz breathing acoustic mode was identified in each cluster, which indicated that differences in ligand structure did not result in significant structural changes to the metal core of the MPCs. Considering that the difference in relaxation rates did not result from ligand-induced core deformation, the accelerated intersystem crossing was attributed to greater electron-vibrational coupling to Au-S vibrational modes. The results suggested that the organometallic semiring was less rigid for the aliphatic thiolate MPCs due to reduced steric effects, and in turn, increases in nonradiative decay rates were observed. Overall, these results imply that the protecting ligand structure can be used to modify carrier relaxation in MPCs.

Exact factorization of the photon-electron-nuclear wavefunction: Formulation and coupled-trajectory dynamics.

We employ the exact-factorization formalism to study the coupled dynamics of photons, electrons, and nuclei at the quantum mechanical level, proposing illustrative examples of model situations of nonadiabatic dynamics and spontaneous emission of electron-nuclear systems in the regime of strong light-matter coupling. We make a particular choice of factorization for such a multi-component system, where the full wavefunction is factored as a conditional electronic amplitude and a marginal photon-nuclear amplitude. Then, we apply the coupled-trajectory mixed quantum-classical (CTMQC) algorithm to perform trajectory-based simulations, by treating photonic and nuclear degrees of freedom on equal footing in terms of classical-like trajectories. The analysis of the time-dependent potentials of the theory along with the assessment of the performance of CTMQC allows us to point out some limitations of the current approximations used in CTMQC. Meanwhile, comparing CTMQC with other trajectory-based algorithms, namely multi-trajectory Ehrenfest and Tully surface hopping, demonstrates the better quality of CTMQC predictions.

Modification of the electronic oscillation spectrum in metallic clusters, caused by the presence of a large spatial scale of inhomogeneity

This work presents a theoretical analysis of the oscillations of a system of degenerate electrons in metallic submicron clusters, taking into account the presence of a large-scale spatial inhomogeneity caused by quantum shell effects. The analysis was carried out in a model formulation in which the large-scale effect was taken into account by the presence of an effective external field acting on the electrons. Two approaches to the description of electron dynamics were considered: kinetic and hydrodynamic. The results obtained within these approaches are in good qualitative and quantitative agreement with each other and demonstrate that for certain cluster sizes, a spectrum of oscillations of the electronic system appears with frequencies differing by the value Δω ∼ ω0/R20 and localized in the vicinity of plasmon frequency ω0 (R0, radius of cluster). The impact of the large-scale effect on the processes of light and electron scattering by metal clusters is estimated. It is shown that maxima appear in the absorption spectrum of the electromagnetic waves, and they turn out to be shifted from the plasmon frequency by value Δω ∼ ω0/R20. Within the framework of the Born approximation, it is shown that a maximum at kR0 ∼ 4π appears in the cross section of elastic scattering of electrons on a metal cluster. The results obtained are important from the point of view of interpreting experiments on plasmonic structures, in particular, on metal films.

Self-Heterodyne Diffractive Imaging of Ultrafast Electron Dynamics Monitored by Single-Electron Pulses.

The direct imaging of time-evolving molecular charge densities on atomistic scale and at femtosecond resolution has long been an elusive task. In this theoretical study, we propose a self-heterodyne electron diffraction technique based on single electron pulses. The electron is split into two beams, one passes through the sample and its interference with the second beam produces a heterodyne diffraction signal that images the charge density. Application to probing the ultrafast electronic dynamics in Mg-phthalocyanine demonstrates its potential for imaging chemical dynamics.