Interference in Floquet-Volkov transitions

Floquet states are signatured by pseudoeigenvalues which are discretely separated by the photon energy. Similarly, the laser-assisted photoemission effect (LAPE) induces electron-photon energy exchange (with momentum change), and also results in a discrete energy distribution. Both effects result from coherent interactions of electrons and photons. Here, we investigate the coherent interference between a Floquet state and the LAPE effect

Photon-induced near-field electron microscopy (PINEM): theoretical and experimental

Electron imaging in space and time is achieved in microscopy with timed (near relativistic) electron packets of picometer wavelength coincident with light pulses of femtosecond duration. The photons (with an energy of a few electronvolts) are used to impulsively heat or excite the specimen so that the evolution of structures from their nonequilibrium state can be followed in real time. As such, and at relatively low fluences, there is no interaction between the electrons and the photons; certainly that is the case in vacuum because energy–momentum conservation is not possible. In the presence of nanostructures and at higher fluences, energy–momentum conservation is possible and the electron packet can either gain or lose light quanta. Recently, it was reported that, when only electrons with gained energy are filtered, near-field imaging enables the visualization of nanoscale particles and interfaces with enhanced contrast (Barwick et al 2009 Nature 462 902). To explore a variety of applications, it is important to express, through analytical formulation, the key parameters involved in this photon-induced near-field electron microscopy (PINEM) and to predict the associated phenomena of, e.g., forty-photon absorption by the electron packet. In this paper, we give an account of the theoretical and experimental results of PINEM. In particular, the time-dependent quantum solution for ultrafast electron packets in the nanostructure scattered electromagnetic (near) field is solved in the high kinetic energy limit to obtain the evolution of the incident electron packet into a superposition of discrete momentum wavelets. The characteristic length and time scales of the halo of electron–photon coupling are discussed in the framework of Rayleigh and Mie scatterings, providing the dependence of the PINEM effect on size, polarization, material and spatiotemporal localization. We also provide a simple classical description that is based on features of plasmonics. A major part of this paper is devoted to the comparisons between the theoretical results and the recently obtained experimental findings about the imaging of materials and biological systems

Structure of isolated biomolecules by electron diffraction-laser desorption: uracil and guanine

We report the structure of isolated biomolecules, uracil and guanine, demonstrating the capability of a newly developed electron diffraction apparatus augmented with surface-assisted IR laser desorption. This UED-4 apparatus provides a pulsed, dense molecular beam, which is stable for many hours and possibly days. From the diffraction patterns, it is evident that the plume composition is chemically pure, without detectable background from ions, fragmentation products, or molecular aggregates. The vibrational temperature deduced is indeed lower than the translational temperature of the plume indicating that the molecules are intact on such short time scales. The structures of uracil and guanine were refined at the deduced internal temperatures, and we compare the results with those predicted by density functional theory. Such experimental capability opens the door for many other studies of the structure (and dynamics) of biomolecules

Irreversible Chemical Reactions Visualized in Space and Time with 4D Electron Microscopy

We report direct visualization of irreversible chemical reactions in space and time with 4D electron microscopy. Specifically, transient structures are imaged following electron transfer in copper-tetracyanoquinodimethane [Cu(TCNQ)] crystals, and the oxidation/reduction process, which is irreversible, is elucidated using the single-shot operation mode of the microscope. We observed the fast, initial structural rearrangement due to Cu^+ reduction and the slower growth of metallic Cu^0 nanocrystals (Ostwald ripening) following initiation of the reaction with a pulse of visible light. The mechanism involves electron transfer from TCNQ anion-radical to Cu^+, morphological changes, and thermally driven growth of discrete Cu^0 nanocrystals embedded in an amorphous carbon skeleton of TCNQ. This in situ visualization of structures during reactions should be extendable to other classes of reactive systems

Nanofriction Visualized in Space and Time by 4D Electron Microscopy

In this letter, we report a novel method of visualizing nanoscale friction in space and time using ultrafast electron microscopy (UEM). The methodology is demonstrated for a nanoscale movement of a single crystal beam on a thin amorphous membrane of silicon nitride. The movement results from the elongation of the crystal beam, which is initiated by a laser (clocking) pulse, and we examined two types of beams: those that are free of friction and the others which are fixed on the substrate. From observations of image change with time we are able to decipher the nature of microscopic friction at the solid−solid interface: smooth-sliding and periodic slip-stick friction. At the molecular and nanoscale level, and when a force parallel to the surface (expansion of the beam) is applied, the force of gravity as a (perpendicular) load cannot explain the observed friction. An additional effective load being 6 orders of magnitude larger than that due to gravity is attributed to Coulombic/van der Waals adhesion at the interface. For the case under study, metal−organic crystals, the gravitational force is on the order of piconewtons whereas the static friction force is 0.5 μN and dynamic friction is 0.4 μN; typical beam expansions are 50 nm/nJ for the free beam and 10 nm/nJ for the fixed beam. The method reported here should have applications for other materials, and for elucidating the origin of periodic and chaotic friction and their relevance to the efficacy of nano(micro)-scale devices

Photon-induced near-field electron microscopy: Mathematical formulation of the relation between the experimental observables and the optically driven charge density of nanoparticles

Photon-induced near-field electron microscopy (PINEM) enables the visualization of the plasmon fields of nanoparticles via measurement of photon-electron interaction [S. T. Park et al., New J. Phys. 12, 123028 (2010)]. In this paper, the field integral, which is a mechanical work performed on a fast electron by the total electric field, plays a key role in understanding the interaction. Here, we reexamine the field integral and give the physical meaning by decomposing the contribution of the field from the charge-density distribution. It is found that the “near-field integral” (the near-field approximation of the field integral) can be expressed as a convolution of the two-dimensional projection of the optically driven charge-density distribution in the nanoparticle with a broad radial response function. This approach, which we call the “convolution method,” is validated by applying it to Rayleigh scattering cases, where previous analytical expressions for the field integrals in near-field approximations are reproduced by the convolution method. The convolution method is applied to discrete dipole approximation calculations of a silver nanorod, and the nature of the induced charge-density distributions of its plasmons is discussed

Relativisitc Effect in Photon-Induced Near Field Electron Microscopy

Electrons and photons, when interacting via a nanostructure, produce a new way of imaging in space and time, termed photon-induced near field electron microscopy or PINEM [Barwick et al. Nature2009, 462, 902]. The phenomenon was described by considering the evanescent field produced by the nanostructure, but quantification of the experimental results was achieved by solving the Schrödinger equation for the interaction of the three bodies. The question remained, is the nonrelativistic formulation sufficient for this description? Here, relativistic and nonrelativistic quantum mechanical formulations are compared for electron–photon interaction mediated by nanostructures, and it is shown that there is an exact equivalence for the two formulations. The nonrelativistic formulation was found to be valid in the relativistic regime when using in the former formulation the relativistically corrected velocity (and the corresponding values of momentum and energy). In the PINEM experiment, 200 keV electrons were utilized, giving the experimental (relativistically corrected) velocity to be 0.7c(v without relativistic correction is 0.885c). When this value (0.7c), together with those of the corresponding momentum (pc = mv) and energy (Ec = (1/2)mv2), is used in the first order solution of the Schrödinger formulation, an exact equivalence is obtained

Propagation of a relativistic electron wave packet in the Dirac equation

Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from this solution to the Zitterbewegung behavior in a Dirac-like system, where we show that it is crucial to include the first-order term in our solution to correctly describe a Dirac packet

Chirped imaging pulses in four-dimensional electron microscopy: femtosecond pulsed hole burning

The energy and time correlation, i.e. the chirp, of imaging electron pulses in dispersive propagation is measured by time-slicing (temporal hole burning) using photon-induced near-field electron microscopy. The chirp coefficient and the degree of correlation are obtained in addition to the duration of the electron pulse and its energy spread. Improving temporal and energy resolutions by time-slicing and energy-selection is discussed here and we explore their utility in imaging with time and energy resolutions below those of the generated ultrashort electron pulse. Potential applications for these imaging capabilities are discussed