Ultrafast generation and control of an electron vortex beam via chiral plasmonic near fields

Electron Imaging of Nanoscale Charge Distributions Induced by Femtosecond Light Pulses

Surface charging is ubiquitously observable during in situ transmission electron microscopy of nonconducting specimens as a result of electron beam/sample interactions or optical stimuli and often limits the achievable image stability and spatial or spectral resolution. Here, we report on the electron-optical imaging of surface charging on a nanostructured surface following femtosecond multiphoton photoemission. By quantitatively extracting the light-induced electrostatic potential and studying the charging dynamics on relevant time scales, we gain insights into the details of the multiphoton photoemission process in the presence of an electrostatic background field. We study the interaction of the charge distribution with the high-energy electron beam and secondary electrons and propose a simple model to describe the interplay of electron- and light-induced processes. In addition, we demonstrate how to mitigate sample charging by simultaneously optically illuminating the sample.

Strongly correlated multielectron bunches from interaction with quantum light

Strongly correlated electron systems are a cornerstone of modern physics, being responsible for groundbreaking phenomena from superconducting magnets to quantum computing. In most cases, correlations in electrons arise exclusively because of Coulomb interactions. In this work, we reveal that free electrons interacting simultaneously with a light field can become highly correlated via mechanisms beyond Coulomb interactions. In the case of two electrons, the resulting Pearson correlation coefficient for the joint probability distribution of the output electron energies is enhanced by more than 13 orders of magnitude compared to that of electrons interacting with the light field in succession (one after another). These highly correlated electrons are the result of momentum and energy exchange between the participating electrons via the external quantum light field. Our findings pave the way to the creation and control of highly correlated free electrons for applications including quantum information and ultrafast imaging.

Angular Dispersion of Free-Electron-Light Coupling in an Optical Fiber-Integrated Metagrating

Free electrons can couple to optical material excitations on nanometer-length and attosecond-time scales, opening-up unique opportunities for both the generation of radiation and the manipulation of the electron wave function. Here, we exploit the Smith-Purcell effect to experimentally study the coherent coupling of free electrons and light in a circular metallo-dielectric metagrating that is fabricated onto the input facet of a multimode optical fiber. Using hyperspectral angle-resolved (HSAR) far-field imaging inside a scanning electron microscope, we probe the angular dispersion of Smith-Purcell radiation (SPR) that is simultaneously generated in free space and inside the fiber by an electron beam that grazes the metagrating at a nanoscale distance. Furthermore, we analyze the spectral distribution of SPR that is emitted into guided optical modes and correlate it with the numerical aperture of the fiber. By varying the electron energy between 5 and 30 keV, we observe the emission of SPR from the ultraviolet to the near-infrared spectral range, and up to the third emission order. In addition, we detect incoherent cathodoluminescence that is generated by electrons penetrating the input facet of the fiber and scattering inelastically. As a result, our HSAR measurements reveal a Fano resonance that is coupled to a Rayleigh anomaly of the metagrating, and that overlaps with the angular dispersion of second-order SPR at 20 keV. Our findings demonstrate the potential of optical fiber-integrated metasurfaces as a versatile platform to implement novel ultrafast light sources and to synthesize complex free-electron quantum states with light.

Theoretical Study of Strong Coupling between Molecular Shells and Chiral Plasmons of Gold Nanoparticles Helices

Chiral plasmonic nanostructures can produce strong chiral optical responses and have potential applications in photonics. Experimentally, metallic nanoparticle helices have been synthesized to achieve strong chiral responses. Strong coupling effects between the quantum emitters and the plasmon have attracted significant attention in the past decade and have been recently extended to the chiral plasmon of nanostructures. However, the strong coupling between molecules and metallic nanosphere helices has not been reported yet. In this article we study theoretically such an effect and examine the modulation of chiral and coupling effects by illumination light and molecular layer thickness. Our study may guide further experimental studies.

Reversible Ultrafast Chiroptical Responses in Planar Plasmonic Nano-Oligomer

Ultracompact chiral plasmonic nanostructures with unique chiral light-matter interactions are vital for future photonic technologies. However, previous studies are limited to reporting their steady-state performance, presenting a fundamental obstacle to the development of high-speed optical devices with polarization sensitivity. Here, a comprehensive analysis of ultrafast chiroptical response of chiral gold nano-oligomers using time-resolved polarimetric measurements is provided. Significant differences are observed in terms of the absorption intensity, thus hot electron generation, and hot carrier decay time upon polarized photopumping, which are explained by a phenomenological model of the helicity-resolved optical transitions. Moreover, the chiroptical signal is switchable by reversing the direction of the pump pulse, demonstrating the versatile modulation of polarization selection in a single device. The results offer fundamental insights into the helicity-resolved optical transitions in photoexcited chiral plasmonics and can facilitate the development of high-speed polarization-sensitive flat optics with potential applications in nanophotonics and quantum optics.

Free-electron interaction with nonlinear optical states in microresonators

The short de Broglie wavelength and strong interaction empower free electrons to probe structures and excitations in materials and biomolecules. Recently, electron-photon interactions have enabled new optical manipulation schemes for electron beams. In this work, we demonstrate the interaction of electrons with nonlinear optical states inside a photonic chip-based microresonator. Optical parametric processes give rise to spatiotemporal pattern formation corresponding to coherent or incoherent optical frequency combs. We couple such "microcombs" to electron beams, demonstrate their fingerprints in the electron spectra, and achieve ultrafast temporal gating of the electron beam. Our work demonstrates the ability to access solitons inside an electron microscope and extends the use of microcombs to spatiotemporal control of electrons for imaging and spectroscopy.

Cathodoluminescence Nanoscopy: State of the Art and Beyond

Cathodoluminescence (CL) nanoscopy is proven to be a powerful tool to explore nanoscale optical properties, whereby free electron beams achieve a spatial resolution far beyond the diffraction limit of light. With developed methods for the control of electron beams and the collection of light, the dimension of information that CL can access has been expanded to include polarization, momentum, and time, holding promise to provide invaluable insights into the study of materials and optical near-field dynamics. With a focus on the burgeoning field of CL nanoscopy, this perspective outlines the recent advancements and applications of this technique, as illustrated by the salient experimental works. In addition, as an outlook for future research, several appealing directions that may bring about developments and discoveries are highlighted.

Free-electron Ramsey-type interferometry for enhanced amplitude and phase imaging of nearfields

The complex range of interactions between electrons and electromagnetic fields gave rise to countless scientific and technological advances. A prime example is photon-induced nearfield electron microscopy (PINEM), enabling the detection of confined electric fields in illuminated nanostructures with unprecedented spatial resolution. However, PINEM is limited by its dependence on strong fields, making it unsuitable for sensitive samples, and its inability to resolve complex phasor information. Here, we leverage the nonlinear, overconstrained nature of PINEM to present an algorithmic microscopy approach, achieving far superior nearfield imaging capabilities. Our algorithm relies on free-electron Ramsey-type interferometry to produce orders-of-magnitude improvement in sensitivity and ambiguity-immune nearfield phase reconstruction, both of which are optimal when the electron exhibits a fully quantum behavior. Our results demonstrate the potential of combining algorithmic approaches with state-of-the-art modalities in electron microscopy and may lead to various applications from imaging sensitive biological samples to performing full-field tomography of confined light.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Improving the temporal resolution of event-based electron detectors using neural network cluster analysis

Novel event-based electron detector platforms provide an avenue to extend the temporal resolution of electron microscopy into the ultrafast domain. Here, we characterize the timing accuracy of a detector based on a TimePix3 architecture using femtosecond electron pulse trains as a reference. With a large dataset of event clusters triggered by individual incident electrons, a neural network is trained to predict the electron arrival time. Corrected timings of event clusters show a temporal resolution of 2 ns, a 1.6-fold improvement over cluster-averaged timings. This method is applicable to other fast electron detectors down to sub-nanosecond temporal resolutions, offering a promising solution to enhance the precision of electron timing for various electron microscopy applications.

Sub-terahertz nearfields for electron-pulse compression

The advent of ultrafast science with pulsed electron beams raised the need to control the temporal features of the electron pulses. One promising suggestion is the nano-selective quantum optics with multi-electrons, which scales quadratically with the number of electrons within the coherence time of the quantum system. Terahertz (THz) radiation from optical nonlinear crystals is an attractive methodology to generate the rapidly varying electric fields necessary for electron compression, with the advantage of an inherent temporal locking to laser-triggered electrons, such as in ultrafast electron microscopes. Longer (picosecond-) pulses require a sub-THz field for their compression. However, the generation of such low frequencies requires pumping with energetic optical pulses and their focusability is fundamentally limited by their mm-wavelength. This work proposes electron-pulse compression with sub-THz fields directly in the vicinity of their dipolar origin, thereby avoiding mediation through radiation. We analyze the merits of nearfields for compression of slow electrons, particularly in challenging regimes for THz radiation, such as small numerical apertures, micro-joule-level optical pump pulses, and low frequencies. This scheme can be implemented within the tight constraints of electron microscopes and reach fields of a few kV/cm below 0.1 THz at high repetition rates. Our paradigm offers a realistic approach for controlling electron pulses spatially and temporally in many experiments, opening the path of flexible multi-electron manipulation for analytic and quantum sciences.

Numerical investigation of sequential phase-locked optical gating of free electrons

Recent progress in coherent quantum interactions between free-electron pulses and laser-induced near-field light have revolutionized electron wavepacket shaping. Building on these advancements, we numerically explore the potential of sequential interactions between slow electrons and localized dipolar plasmons in a sequential phase-locked interaction scheme. Taking advantage of the prolonged interaction time between slow electrons and optical near-fields, we aim to explore the effect of plasmon dynamics on the free-electron wavepacket modulation. Our results demonstrate that the initial optical phase of the localized dipolar plasmon at the starting point of the interaction, along with the phase offset between the interaction zones, can serve as control parameters in manipulating the transverse and longitudinal recoil of the electron wavefunction. Moreover, it is shown that the incident angle of the laser light is an additional control knop for tailoring the longitudinal and transverse recoils. We show that a sequential phase-locking method can be employed to precisely manipulate the longitudinal and transverse recoil of the electron wavepacket, leading to selective acceleration or deceleration of the electron energy along specific diffraction angles. These findings have important implications for developing novel techniques for ultrafast electron-light interferometry, shaping the electron wavepacket, and quantum information processing.

Lorentz microscopy of optical fields

In electron microscopy, detailed insights into nanoscale optical properties of materials are gained by spontaneous inelastic scattering leading to electron-energy loss and cathodoluminescence. Stimulated scattering in the presence of external sample excitation allows for mode- and polarization-selective photon-induced near-field electron microscopy (PINEM). This process imprints a spatial phase profile inherited from the optical fields onto the wave function of the probing electrons. Here, we introduce Lorentz-PINEM for the full-field, non-invasive imaging of complex optical near fields at high spatial resolution. We use energy-filtered defocus phase-contrast imaging and iterative phase retrieval to reconstruct the phase distribution of interfering surface-bound modes on a plasmonic nanotip. Our approach is universally applicable to retrieve the spatially varying phase of nanoscale fields and topological modes.

Imaging the field inside nanophotonic accelerators

Controlling optical fields on the subwavelength scale is at the core of nanophotonics. Laser-driven nanophotonic particle accelerators promise a compact alternative to conventional radiofrequency-based accelerators. Efficient electron acceleration in nanophotonic devices critically depends on achieving nanometer control of the internal optical nearfield. However, these nearfields have so far been inaccessible due to the complexity of the devices and their geometrical constraints, hampering the design of future nanophotonic accelerators. Here we image the field distribution inside a nanophotonic accelerator, for which we developed a technique for frequency-tunable deep-subwavelength resolution of nearfields based on photon-induced nearfield electron-microscopy. Our experiments, complemented by 3D simulations, unveil surprising deviations in two leading nanophotonic accelerator designs, showing complex field distributions related to intricate 3D features in the device and its fabrication tolerances. We envision an extension of our method for full 3D field tomography, which is key for the future design of highly efficient nanophotonic devices.

Attosecond electron microscopy of sub-cycle optical dynamics

The primary step of almost any interaction between light and materials is the electrodynamic response of the electrons to the optical cycles of the impinging light wave on sub-wavelength and sub-cycle dimensions¹. Understanding and controlling the electromagnetic responses of a material^2-11 is therefore essential for modern optics and nanophotonics^12-19. Although the small de Broglie wavelength of electron beams should allow access to attosecond and ångström dimensions²⁰, the time resolution of ultrafast electron microscopy²¹ and diffraction²² has so far been limited to the femtosecond domain^16-18, which is insufficient for recording fundamental material responses on the scale of the cycles of light^1,2,10. Here we advance transmission electron microscopy to attosecond time resolution of optical responses within one cycle of excitation light²³. We apply a continuous-wave laser²⁴ to modulate the electron wave function into a rapid sequence of electron pulses, and use an energy filter to resolve electromagnetic near-fields in and around a material as a movie in space and time. Experiments on nanostructured needle tips, dielectric resonators and metamaterial antennas reveal a directional launch of chiral surface waves, a delay between dipole and quadrupole dynamics, a subluminal buried waveguide field and a symmetry-broken multi-antenna response. These results signify the value of combining electron microscopy and attosecond laser science to understand light-matter interactions in terms of their fundamental dimensions in space and time.

Single-Pixel Imaging in Space and Time with Optically Modulated Free Electrons

Single-pixel imaging, originally developed in light optics, facilitates fast three-dimensional sample reconstruction as well as probing with light wavelengths undetectable by conventional multi-pixel detectors. However, the spatial resolution of optics-based single-pixel microscopy is limited by diffraction to hundreds of nanometers. Here, we propose an implementation of single-pixel imaging relying on attainable modifications of currently available ultrafast electron microscopes in which optically modulated electrons are used instead of photons to achieve subnanometer spatially and temporally resolved single-pixel imaging. We simulate electron beam profiles generated by interaction with the optical field produced by an externally programmable spatial light modulator and demonstrate the feasibility of the method by showing that the sample image and its temporal evolution can be reconstructed using realistic imperfect illumination patterns. Electron single-pixel imaging holds strong potential for application in low-dose probing of beam-sensitive biological and molecular samples, including rapid screening during in situ experiments.

Quantum Interference between Fundamentally Different Processes Is Enabled by Shaped Input Wavefunctions

This work presents a general framework for quantum interference between processes that can involve different fundamental particles or quasi-particles. This framework shows that shaping input wavefunctions is a versatile and powerful tool for producing and controlling quantum interference between distinguishable pathways, beyond previously explored quantum interference between indistinguishable pathways. Two examples of quantum interference enabled by shaping in interactions between free electrons, bound electrons, and photons are presented: i) the vanishing of the zero-loss peak by destructive quantum interference when a shaped electron wavepacket couples to light, under conditions where the electron's zero-loss peak otherwise dominates; ii) quantum interference between free electron and atomic (bound electron) spontaneous emission processes, which can be significant even when the free electron and atom are far apart, breaking the common notion that a free electron and an atom must be close by to significantly affect each other's processes. Conclusions show that emerging quantum wave-shaping techniques unlock the door to greater versatility in light-matter interactions and other quantum processes in general.

Tunable photon-induced spatial modulation of free electrons

Spatial modulation of electron beams is an essential tool for various applications such as nanolithography and imaging, yet its conventional implementations are severely limited and inherently non-tunable. Conversely, proposals of light-driven electron spatial modulation promise tunable electron wavefront shaping, for example, using the mechanism of photon-induced near-field electron microscopy. Here we present tunable photon-induced spatial modulation of electrons through their interaction with externally controlled surface plasmon polaritons (SPPs). Using recently developed methods of shaping SPP patterns, we demonstrate a dynamic control of the electron beam with a variety of electron distributions and verify their coherence through electron diffraction. Finally, the nonlinearity stemming from energy post-selection provides us with another avenue for controlling the electron shape, generating electron features far below the SPP wavelength. Our work paves the way to on-demand electron wavefront shaping at ultrafast timescales, with prospects for aberration correction, nanofabrication and material characterization.

Superradiant Electron Energy Loss Spectroscopy

We analyze the interaction between a free electron and an ensemble of identical optical emitters. The mutual coherence and correlations between the emitters can enhance the interaction with each electron and become imprinted on its energy spectrum. We present schemes by which such collective interactions can be realized. As a possible application, we investigate free-electron interactions with superradiant systems, showing how electrons can probe the ultrafast population dynamics of superradiance.

Attosecond electron-beam technology: a review of recent progress

Electron microscopy and diffraction with ultrashort pulsed electron beams are capable of imaging transient phenomena with the combined ultrafast temporal and atomic-scale spatial resolutions. The emerging field of optical electron beam control allowed the manipulation of relativistic and sub-relativistic electron beams at the level of optical cycles. Specifically, it enabled the generation of electron beams in the form of attosecond pulse trains and individual attosecond pulses. In this review, we describe the basics of the attosecond electron beam control and overview the recent experimental progress. High-energy electron pulses of attosecond sub-optical cycle duration open up novel opportunities for space-time-resolved imaging of ultrafast chemical and physical processes, coherent photon generation, free electron quantum optics, electron-atom scattering with shaped wave packets and laser-driven particle acceleration. Graphical Abstract.

Optical manipulation of matter waves

Light is used to steer the motion of atoms in free space, enabling cooling and trapping of matter waves through ponderomotive forces and Doppler-mediated photon scattering. Likewise, light interaction with free electrons has recently emerged as a versatile approach to modulate the electron wave function for applications in ultrafast electron microscopy. Here, we combine these two worlds, theoretically demonstrating that matter waves can be optically manipulated via inelastic interactions with optical fields. This allows us to modulate the translational part of the wave function and produce temporally and spatially compressed atomic beam pulses. We realize such modulation through stimulated photon absorption and emission by atoms traversing phase-matching evanescent optical fields generated upon light scattering by a nanostructure and via stimulated Compton scattering in free space without any assistance from material media. Our results support optical manipulation of matter waves as a powerful tool for microscopy, spectroscopy, and exploration of fundamental phenomena associated with light-atom interactions.

Ultrafast Transverse Modulation of Free Electrons by Interaction with Shaped Optical Fields

Spatiotemporal electron-beam shaping is a bold frontier of electron microscopy. Over the past decade, shaping methods evolved from static phase plates to low-speed electrostatic and magnetostatic displays. Recently, a swift change of paradigm utilizing light to control free electrons has emerged. Here, we experimentally demonstrate arbitrary transverse modulation of electron beams without complicated electron-optics elements or material nanostructures, but rather using shaped light beams. On-demand spatial modulation of electron wavepackets is obtained via inelastic interaction with transversely shaped ultrafast light fields controlled by an external spatial light modulator. We illustrate this method for the cases of Hermite-Gaussian and Laguerre-Gaussian modulation and discuss their use in enhancing microscope sensitivity. Our approach dramatically widens the range of patterns that can be imprinted on the electron profile and greatly facilitates tailored electron-beam shaping.

Asynchronous Inelastic Scattering of Electrons at the Ponderomotive Potential of Optical Waves

We study free electron dynamics during inelastic interaction with the ponderomotive potential of a traveling optical wave using classical and quantum-mechanical models. We show that in the strong interaction regime, the electrons trapped in the periodic potential oscillate leading to periodic revolutions of sharp peaks of the density distributions in the real and momentum spaces. In this regime, the synchronicity between the velocity of the optical wave and the electron propagation velocity is not required. Asynchronous interaction enables acceleration or deceleration of a significant fraction of the electrons to a final spectrum with a relative spectral width of 0.5%-2.5%. This technique allows one to accelerate electrons from rest to keV energies while reaching a narrow spectrum of kinetic energies and femtosecond pulsed operation.

Nuclear Excitation by Electron Capture in Excited Ions

A nuclear excitation following the capture of an electron in an empty orbital has been recently observed for the first time. So far, the evaluation of the cross section of the process has been carried out widely using the assumption that the ion is in its electronic ground state prior to the capture. We show that by lifting this restriction new capture channels emerge resulting in a boost of more than three orders of magnitude to the electron capture resonance strength.

Dynamical Control of Nuclear Isomer Depletion via Electron Vortex Beams

Some nuclear isomers are known to store a large amount of energy over long periods of time, with a very high energy-to-mass ratio. Here, we describe a protocol to achieve the external control of the isomeric nuclear decay by using electron vortex beams whose wave function has been especially designed and reshaped on demand. Recombination of these electrons into the isomer's atomic shell can lead to the controlled release of the stored nuclear energy. On the example of ^{93m}Mo, we show theoretically that the use of tailored electron vortex beams increases the depletion by 4 orders of magnitude compared to the spontaneous nuclear decay of the isomer. Furthermore, specific orbitals can sustain an enhancement of the recombination cross section for vortex electron beams by as much as 6 orders of magnitude, providing a handle for manipulating the capture mechanism. These findings open new prospects for controlling the interplay between atomic and nuclear degrees of freedom, with potential energy-related and high-energy radiation source applications.

Nanoscale-Femtosecond Imaging of Evanescent Surface Plasmons on Silver Film by Photon-Induced Near-Field Electron Microscopy

Surface plasmons on silver nanostructures have a broad range of tunable resonance properties in visible and near-infrared regimes, which possess wide applications in nanophotonics and optoelectronics. Here we use a femtosecond laser to excite surface plasmons on a silver film and trace the subsequent transient dynamics via photon-induced near-field electron microscopy (PINEM). A polarization experiment of PINEM demonstrates a conspicuous polarization dependence of the transient surface plasmon field on the silver film; however, unlike silver nanowires and nanorods, there is no polarization dependence for the PINEM intensity. This compelling finding suggests a thin film platform can be more easily used to identify the temporal and spatial overlaps between the pump laser and probe electron pulses in 4D ultrafast electron microscopy (UEM). Our work illustrates the femtosecond excitation and transient behavior of the surface plasmons on silver film and paves a universal, simple way for identifying the time zero in 4D UEM.

A kiloelectron-volt ultrafast electron micro-diffraction apparatus using low emittance semiconductor photocathodes

We report the design and performance of a time-resolved electron diffraction apparatus capable of producing intense bunches with simultaneously single digit micrometer probe size, long coherence length, and 200 fs rms time resolution. We measure the 5d (peak) beam brightness at the sample location in micro-diffraction mode to be 7 × 10 13   A / m 2   rad 2 . To generate high brightness electron bunches, the system employs high efficiency, low emittance semiconductor photocathodes driven with a wavelength near the photoemission threshold at a repetition rate up to 250 kHz. We characterize spatial, temporal, and reciprocal space resolution of the apparatus. We perform proof-of-principle measurements of ultrafast heating in single crystal Au samples and compare experimental results with simulations that account for the effects of multiple scattering.

Cathodoluminescence in Ultrafast Electron Microscopy

Implementing the modern technologies of light-emitting devices, light harvesting, and quantum information processing requires the understanding of the structure-function relations at spatial scales below the optical diffraction limit and time scales of energy and information flows. Here, we distinctively combine cathodoluminescence (CL) with ultrafast electron microscopy (UEM), termed CL-UEM, because CL and UEM synergetically afford the required spectral and spatiotemporal sensitivities, respectively. For color centers in nanodiamonds, we demonstrate the measurement of CL lifetime with a local sensitivity of 50 nm and a time resolution of 100 ps. It is revealed that the emitting states of the color centers can be populated through charge transfer among the color centers across diamond lattices upon high-energy electron beam excitation. The technical advance achieved in this study will facilitate the specific control over energy conversion at nanoscales, relevant to quantum dots and single-photon sources.

Nanoscale Visualization of a Photoinduced Plasmonic Near-Field in a Single Nanowire by Free Electrons

Swift electrons can undergo inelastic interactions not only with electrons but also with near-fields, which may result in an energy loss or gain. Developments in photon-induced near-field electron microscopy (PINEM) enable direct imaging of the plasmon near-field distribution with nanometer resolution. Here, we report an analysis of the surface plasmonic near-field structure based on PINEM observations of silver nanowires. Single-photon order-selected electron images revealed the wavelike and banded structure of electric equipotential regions for a confined near-field integral associated with typical absorption of photon quanta (nℏω). Multimodal plasmon oscillations and second-harmonic generation were simultaneously observed, and the polarization dependence of plasmon wavelength and symmetry properties were analyzed. Based on advanced imaging techniques, our work has implications for future studies of the localized-field structures at interfaces and visualization of novel phenomena in nanostructures, nanosensors, and plasmonic devices.

Integrated photonics enables continuous-beam electron phase modulation

Integrated photonics facilitates extensive control over fundamental light-matter interactions in manifold quantum systems including atoms1, trapped ions2,3, quantum dots4 and defect centres5. Ultrafast electron microscopy has recently made free-electron beams the subject of laser-based quantum manipulation and characterization6-11, enabling the observation of free-electron quantum walks12-14, attosecond electron pulses10,15-17 and holographic electromagnetic imaging18. Chip-based photonics19,20 promises unique applications in nanoscale quantum control and sensing but remains to be realized in electron microscopy. Here we merge integrated photonics with electron microscopy, demonstrating coherent phase modulation of a continuous electron beam using a silicon nitride microresonator. The high-finesse (Q0 ≈ 106) cavity enhancement and a waveguide designed for phase matching lead to efficient electron-light scattering at extremely low, continuous-wave optical powers. Specifically, we fully deplete the initial electron state at a cavity-coupled power of only 5.35 microwatts and generate >500 electron energy sidebands for several milliwatts. Moreover, we probe unidirectional intracavity fields with microelectronvolt resolution in electron-energy-gain spectroscopy21. The fibre-coupled photonic structures feature single-optical-mode electron-light interaction with full control over the input and output light. This approach establishes a versatile and highly efficient framework for enhanced electron beam control in the context of laser phase plates22, beam modulators and continuous-wave attosecond pulse trains23, resonantly enhanced spectroscopy24-26 and dielectric laser acceleration19,20,27. Our work introduces a universal platform for exploring free-electron quantum optics28-31, with potential future developments in strong coupling, local quantum probing and electron-photon entanglement.

Multidimensional phase singularities in nanophotonics

[Figure: see text].

Imprinting the quantum statistics of photons on free electrons

[Figure: see text].

Vortex beams of atoms and molecules

[Figure: see text].

A quantum vortex made of atoms

[Figure: see text].

Toward Atomic-Resolution Quantum Measurements with Coherently Shaped Free Electrons

Free electrons provide a powerful tool for probing material properties at atomic resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free-electron wave functions using laser pulses. It would be of great importance if one could combine the spatial resolution of electron microscopes with the ability of laser pulses to probe coherent phenomena in quantum systems. To this end, we propose a novel concept that leverages free electrons that are coherently shaped by laser pulses to measure quantum coherence in materials. We develop the quantum theory of interactions between shaped electrons and arbitrary qubit states in materials, and show how the postinteraction electron energy spectrum enables measuring the qubit state (on the Bloch sphere) and the decoherence or relaxation times (T_{2}/T_{1}). Finally, we describe how such electrons can detect and quantify superradiance from multiple qubits. Our scheme can be implemented in ultrafast transmission electron microscopes (UTEM), opening the way toward the full characterization of the state of quantum systems at atomic resolution.

Quantum Entanglement and Modulation Enhancement of Free-Electron-Bound-Electron Interaction

The modulation and engineering of the free-electron wave function bring new ingredients to the electron-matter interaction. We consider the dynamics of a free-electron passing by a two-level system fully quantum mechanically and study the enhancement of interaction from the modulation of the free-electron wave function. In the presence of resonant modulation of the free-electron wave function, we show that the electron energy loss and gain spectrum is greatly enhanced for a coherent initial state of the two-level system. Thus, a modulated electron can function as a probe of the atomic coherence. We further find that distantly separated two-level atoms can be entangled through interacting with the same free electron. Effects of modulation-induced enhancement can also be observed using a dilute beam of modulated electrons.

Revealing the Chiroptical Response of Plasmonic Nanostructures at the Nanofemto Scale

The spatiotemporal origin of plasmonic chiroptical responses in nanostructures remains unexplored and unclear. Here, two orthogonally oriented Au nanorods as a prototype were investigated, with a giant chiroptical response caused by antisymmetric and symmetric mode excitations for obliquely incident left-handed circular polarization (LCP) and right-handed circular polarization (RCP) light. Time-resolved photoemission electron microscopy (PEEM) was employed to measure the near-field spatial distributions, spectra, and spatiotemporal dynamics of plasmonic modes associated with the chiroptical responses at the nanofemto scale, verifying the characteristic near-field distributions at the resonant wavelengths of the two modes and a very large spectral dichroism for LCP and RCP. More importantly, eigenmode excitations and their contributions to the ultrafast plasmonic chiroptical response in the space-time domain were directly revealed, promoting a full understanding of the ultrafast chiral origin in complex nanostructures. These findings open a way to design chiroptical nanophotonic devices for spatiotemporal control of chiral light-matter interactions.

Modulation of Cathodoluminescence Emission by Interference with External Light

Spontaneous processes triggered in a sample by free electrons, such as cathodoluminescence, are commonly regarded and detected as stochastic events. Here, we supplement this picture by showing through first-principles theory that light and free-electron pulses can interfere when interacting with a nanostructure, giving rise to a modulation in the spectral distribution of the cathodoluminescence light emission that is strongly dependent on the electron wave function. Specifically, for a temporally focused electron, cathodoluminescence can be canceled upon illumination with a spectrally modulated dimmed laser that is phase-locked relative to the electron density profile. We illustrate this idea with realistic simulations under attainable conditions in currently available ultrafast electron microscopes. We further argue that the interference between excitations produced by light and free electrons enables the manipulation of the ultrafast materials response by combining the spectral and temporal selectivity of the light with the atomic resolution of electron beams.

Optical Excitations with Electron Beams: Challenges and Opportunities

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

Spontaneous and stimulated electron-photon interactions in nanoscale plasmonic near fields

The interplay between free electrons, light, and matter offers unique prospects for space, time, and energy resolved optical material characterization, structured light generation, and quantum information processing. Here, we study the nanoscale features of spontaneous and stimulated electron-photon interactions mediated by localized surface plasmon resonances at the tips of a gold nanostar using electron energy-loss spectroscopy (EELS), cathodoluminescence spectroscopy (CL), and photon-induced near-field electron microscopy (PINEM). Supported by numerical electromagnetic boundary-element method (BEM) calculations, we show that the different coupling mechanisms probed by EELS, CL, and PINEM feature the same spatial dependence on the electric field distribution of the tip modes. However, the electron-photon interaction strength is found to vary with the incident electron velocity, as determined by the spatial Fourier transform of the electric near-field component parallel to the electron trajectory. For the tightly confined plasmonic tip resonances, our calculations suggest an optimum coupling velocity at electron energies as low as a few keV. Our results are discussed in the context of more complex geometries supporting multiple modes with spatial and spectral overlap. We provide fundamental insights into spontaneous and stimulated electron-light-matter interactions with key implications for research on (quantum) coherent optical phenomena at the nanoscale.

Fractional Angular Momenta, Gouy and Berry Phases in Relativistic Bateman-Hillion-Gaussian Beams of Electrons

A new Bateman-Hillion solution to the Dirac equation for a relativistic Gaussian electron beam taking explicit account of the four-position of the beam waist is presented. This solution has a pure Gaussian form in the paraxial limit but beyond it contains higher order Laguerre-Gaussian components attributable to the tighter focusing. One implication of the mixed mode nature of strongly diffracting beams is that the expectation values for spin and orbital angular momenta are fractional and are interrelated to each other by intrinsic spin-orbit coupling. Our results for these properties align with earlier work on Bessel beams [Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.174802] and show that fractional angular momenta can be expressed by means of a Berry phase. The most significant difference arises, though, due to the fact that Laguerre-Gaussian beams naturally contain Gouy phase, while Bessel beams do not. We show that Gouy phase is also related to Berry phase and that Gouy phase fronts that are flat in the paraxial limit become curved beyond it.

Optical coherence transfer mediated by free electrons

We theoretically investigate the quantum-coherence properties of the cathodoluminescence (CL) emission produced by a temporally modulated electron beam. Specifically, we consider the quantum-optical correlations of CL produced by electrons that are previously shaped by a laser field. Our main prediction is the presence of phase correlations between the emitted CL field and the electron-modulating laser, even though the emission intensity and spectral profile are independent of the electron state. In addition, the coherence of the CL field extends to harmonics of the laser frequency. Since electron beams can be focused to below 1 Å, their ability to transfer optical coherence could enable the ultra-precise excitation, manipulation, and spectrally resolved probing of nanoscale quantum systems.

Optical Modulation of Electron Beams in Free Space

We exploit free-space interactions between electron beams and tailored light fields to imprint on-demand phase profiles on the electron wave functions. Through rigorous semiclassical theory involving a quantum description of the electrons, we show that monochromatic optical fields focused in vacuum can be used to correct electron beam aberrations and produce selected focal shapes. Stimulated elastic Compton scattering is exploited to imprint the required electron phase, which is proportional to the integral of the optical field intensity along the electron path and depends on the transverse beam position. The required light intensities are attainable in currently available ultrafast electron microscope setups, thus opening the field of free-space optical manipulation of electron beams.

Shaping quantum photonic states using free electrons

It is a long-standing goal to create light with unique quantum properties such as squeezing and entanglement. We propose the generation of quantum light using free-electron interactions, going beyond their already ubiquitous use in generating classical light. This concept is motivated by developments in electron microscopy, which recently demonstrated quantum free-electron interactions with light in photonic cavities. Such electron microscopes provide platforms for shaping quantum states of light through a judicious choice of the input light and electron states. Specifically, we show how electron energy combs implement photon displacement operations, creating displaced-Fock and displaced-squeezed states. We develop the theory for consecutive electron-cavity interactions with a common cavity and show how to generate any target Fock state. Looking forward, exploiting the degrees of freedom of electrons, light, and their interaction may achieve complete control over the quantum state of the generated light, leading to novel light statistics and correlations.

Supramolecular Chirality Synchronization in Thin Films of Plasmonic Nanocomposites

Mirror symmetry breaking in materials is a fascinating phenomenon that has practical implications for various optoelectronic technologies. Chiral plasmonic materials are particularly appealing due to their strong and specific interactions with light. In this work we broaden the portfolio of available strategies toward the preparation of chiral plasmonic assemblies, by applying the principles of chirality synchronization-a phenomenon known for small molecules, which results in the formation of chiral domains from transiently chiral molecules. We report the controlled cocrystallization of 23 nm gold nanoparticles and liquid crystal molecules yielding domains made of highly ordered, helical nanofibers, preferentially twisted to the right or to the left within each domain. We confirmed that such micrometer sized domains exhibit strong, far-field circular dichroism (CD) signals, even though the bulk material is racemic. We further highlight the potential of the proposed approach to realize chiral plasmonic thin films by using a mechanical chirality discrimination method. Toward this end, we developed a rapid CD imaging technique based on the use of polarized light optical microscopy (POM), which enabled probing the CD signal with micrometer-scale resolution, despite of linear dichroism and birefringence in the sample. The developed methodology allows us to extend intrinsically local effects of chiral synchronization to the macroscopic scale, thereby broadening the available tools for chirality manipulation in chiral plasmonic systems.

Anomalous Thermodiffusion of Electrons in Graphene

We reveal a dramatic departure of electron thermodiffusion in solids relative to the commonly accepted picture of the ideal free-electron gas model. In particular, we show that the interaction with the lattice and impurities, combined with a strong material dependence of the electron dispersion relation, leads to counterintuitive diffusion behavior, which we identify by comparing a two-dimensional electron gas (2DEG) and single-layer graphene. When subject to a temperature gradient ∇T, thermodiffusion of massless Dirac fermions in graphene exhibits an anomalous behavior with electrons moving along ∇T and accumulating in hot regions, in contrast to normal electron diffusion in a 2DEG with parabolic dispersion, where net motion against ∇T is observed, accompanied by electron depletion in hot regions. These findings bear fundamental importance for the understanding of the spatial electron dynamics in emerging materials, establishing close relations with other branches of physics dealing with electron systems under nonuniform temperature conditions.

Light-Induced Anisotropic Morphological Dynamics of Black Phosphorus Membranes Visualized by Dark-Field Ultrafast Electron Microscopy

Black phosphorus (BP) is an elemental layered material with a strong in-plane anisotropic structure. This structure is accompanied by anisotropic optical, electrical, thermal, and mechanical properties. Despite interest in BP from both fundamental and technical aspects, investigation into the structural dynamics of BP caused by strain fields, which are prevalent for two-dimensional (2D) materials and tune the material physical properties, has been overlooked. Here, we report the morphological dynamics of photoexcited BP membranes observed using time-resolved diffractograms and dark-field images obtained via ultrafast electron microscopy. Aided by 4D reconstruction, we visualize the nonequilibrium bulging of thin BP membranes and reveal that the buckling transition is driven by impulsive thermal stress upon photoexcitation in real time. The bulging, buckling, and flattening (on strain release) showed anisotropic spatiotemporal behavior. Our observations offer insights into the fleeting morphology of anisotropic 2D matter and provide a glimpse into the mapping of transient, modulated physical properties upon impulsive excitation, as well as strain engineering at the nanoscale.

Electrons Generate Self-Complementary Broadband Vortex Light Beams Using Chiral Photon Sieves

Planar electron-driven photon sources have been recently proposed as miniaturized light sources, with prospects for ultrafast conjugate electron-photon microscopy and spectral interferometry. Such sources usually follow the symmetry of the electron-induced polarization: transition-radiation-based sources, for example, only generate p-polarized light. Here we demonstrate that the polarization, the bandwidth, and the directionality of photons can be tailored by utilizing photon-sieve-based structures. We design, fabricate, and characterize self-complementary chiral structures made of holes in an Au film and generate light vortex beams with specified angular momentum orders. The incoming electron interacting with the structure generates chiral surface plasmon polaritons on the structured Au surface that scatter into the far field. The outcoupled radiation interferes with transition radiation creating TE- and TM-polarized Laguerre-Gauss light beams with a chiral intensity distribution. The generated vortex light and its unique spatiotemporal features can form the basis for the generation of structured-light electron-driven photon sources.