Holographic imaging of electromagnetic fields via electron-light quantum interference

Terahertz control and timing correlations in a transmission electron microscope

Ultrafast electron microscopy provides a movie-like access to structural dynamics of materials in space and time, but fundamental atomic motions or electron dynamics are, so far, too quick to be resolved. Here, we report the all-optical control, compression, and characterization of electron pulses in a transmission electron microscope by the single optical cycles of laser-generated terahertz light. This concept provides isolated electron pulses and merges the spatial resolution of a transmission electron microscope with the temporal resolution that is offered by a single cycle of laser light. We also report the all-optical control of multi-electron states and find a substantial two-electron and three-electron anticorrelation in the time domain. These results open up the possibility to visualize atomic and electronic motions together with their quantum correlations on fundamental dimensions in space and time.

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.

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.

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.

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.

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.

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.

Spatiotemporal imaging of 2D polariton wave packet dynamics using free electrons

Coherent optical excitations in two-dimensional (2D) materials, 2D polaritons, can generate a plethora of optical phenomena that arise from the extraordinary dispersion relations that do not exist in regular materials. Probing of the dynamical phenomena of 2D polaritons requires simultaneous spatial and temporal imaging capabilities and could reveal unknown coherent optical phenomena in 2D materials. Here, we present a spatiotemporal measurement of 2D wave packet dynamics, from its formation to its decay, using an ultrafast transmission electron microscope driven by femtosecond midinfrared pulses. The ability to coherently excite phonon-polariton wave packets and probe their evolution in a nondestructive manner reveals intriguing dispersion-dependent dynamics that includes splitting of multibranch wave packets and, unexpectedly, wave packet deceleration and acceleration. Having access to the full spatiotemporal dynamics of 2D wave packets can be used to illuminate puzzles in topological polaritons and discover exotic nonlinear optical phenomena in 2D materials.

Control of quantum electrodynamical processes by shaping electron wavepackets

Fundamental quantum electrodynamical (QED) processes, such as spontaneous emission and electron-photon scattering, encompass phenomena that underlie much of modern science and technology. Conventionally, calculations in QED and other field theories treat incoming particles as single-momentum states, omitting the possibility that coherent superposition states, i.e., shaped wavepackets, can alter fundamental scattering processes. Here, we show that free electron waveshaping can be used to design interferences between two or more pathways in a QED process, enabling precise control over the rate of that process. As an example, we show that free electron waveshaping modifies both spatial and spectral characteristics of bremsstrahlung emission, leading for instance to enhancements in directionality and monochromaticity. The ability to tailor general QED processes opens up additional avenues of control in phenomena ranging from optical excitation (e.g., plasmon and phonon emission) in electron microscopy to free electron lasing in the quantum regime.

Heterodyne phase shifting method in scanning probe microscopy

The present paper describes a novel implementation of the continuous phase shifting method (PSM), named heterodyne holography, in a scanning probe microscope configuration, able to retrieve the complex scattered field in on-axis configuration. This can be achieved by acquiring a continuous sequence of holograms at different wavelengths in just a single scan through the combination of scanning interference microscopy and a low-coherent signal acquired in the frequency domain. This method exploits the main advantages of the phase shifting technique and avoids some limits relative to off-axis holography in providing quantitative phase imaging.

Attosecond metrology in a continuous-beam transmission electron microscope

Electron microscopy can visualize the structure of complex materials with atomic and subatomic resolution, but investigations of reaction dynamics and light-matter interaction call for time resolution as well, ideally on a level below the oscillation period of light. Here, we report the use of the optical cycles of a continuous-wave laser to bunch the electron beam inside a transmission electron microscope into electron pulses that are shorter than half a cycle of light. The pulses arrive at the target at almost the full average brightness of the electron source and in synchrony to the optical cycles, providing attosecond time resolution of spectroscopic features. The necessary modifications are simple and can turn almost any electron microscope into an attosecond instrument that may be useful for visualizing the inner workings of light-matter interaction on the basis of the atoms and the cycles of light.

Ultrafast electron diffraction from nanophotonic waveforms via dynamical Aharonov-Bohm phases

Electron interferometry via phase-contrast microscopy, holography, or picodiffraction can provide a direct visualization of the static electric and magnetic fields inside or around a material at subatomic precision, but understanding the electromagnetic origin of light-matter interaction requires time resolution as well. Here, we demonstrate that pump-probe electron diffraction with all-optically compressed electron pulses can capture dynamic electromagnetic potentials in a nanophotonic material with sub-light-cycle time resolution via centrosymmetry-violating Bragg spot dynamics. The origin of this effect is a sizable quantum mechanical phase shift that the electron de Broglie wave obtains from the oscillating electromagnetic potentials within less than 1 fs. Coherent electron imaging and scattering can therefore reveal the electromagnetic foundations of light-matter interaction on the level of the cycles of light.

Imaging the Neuroimmune Dynamics Across Space and Time

The immune system is essential for maintaining homeostasis, as well as promoting growth and healing throughout the brain and body. Considering that immune cells respond rapidly to changes in their microenvironment, they are very difficult to study without affecting their structure and function. The advancement of non-invasive imaging methods greatly contributed to elucidating the physiological roles performed by immune cells in the brain across stages of the lifespan and contexts of health and disease. For instance, techniques like two-photon in vivo microscopy were pivotal for studying microglial functional dynamics in the healthy brain. Through these observations, their interactions with neurons, astrocytes, blood vessels and synapses were uncovered. High-resolution electron microscopy with immunostaining and 3D-reconstruction, as well as super-resolution fluorescence microscopy, provided complementary insights by revealing microglial interventions at synapses (phagocytosis, trogocytosis, synaptic stripping, etc.). In addition, serial block-face scanning electron microscopy has provided the first 3D reconstruction of a microglial cell at nanoscale resolution. This review will discuss the technical toolbox that currently allows to study microglia and other immune cells in the brain, as well as introduce emerging methods that were developed and could be used to increase the spatial and temporal resolution of neuroimmune imaging. A special attention will also be placed on positron emission tomography and the development of selective functional radiotracers for microglia and peripheral macrophages, considering their strong potential for research translation between animals and humans, notably when paired with other imaging modalities such as magnetic resonance imaging.

Strong Interaction of Slow Electrons with Near-Field Light Visited from First Principles

Strong interaction between light and matter waves, such as electron beams in electron microscopes, has recently emerged as a new tool for manipulating the electron wave packets. Here, we systematically investigate electron-light interactions from first principles. We show that enhanced coupling can be achieved for systems involving slow electron wave packets interacting with plasmonic nanoparticles, due to simultaneous classical recoil and quantum mechanical photon absorption and emission processes. For slow electrons with longitudinal broadenings longer than the dimensions of nanoparticles, phase matching between slow electrons and plasmonic oscillations is manifested as an additional degree of freedom to control the strength of coupling. Our findings pave the way toward a systematic and realistic understanding of electron-light interactions beyond adiabatic approximations, and lay the ground for the realization of matter-wave interferometry and boson-sampling devices involving light and matter waves.

Probing Chirality with Inelastic Electron-Light Scattering

Circular dichroism spectroscopy is an essential technique for understanding molecular structure and magnetic materials; however, spatial resolution is limited by the wavelength of light, and sensitivity sufficient for single-molecule spectroscopy is challenging. We demonstrate that electrons can efficiently measure the interaction between circularly polarized light and chiral materials with deeply subwavelength resolution. By scanning a nanometer-sized focused electron beam across an optically excited chiral nanostructure and measuring the electron energy spectrum at each probe position, we produce a high-spatial-resolution map of near-field dichroism. This technique offers a nanoscale view of a fundamental symmetry and could be employed as "photon staining" to increase biomolecular material contrast in electron microscopy.

Controlling free electrons with optical whispering-gallery modes

Free-electron beams are versatile probes of microscopic structure and composition^1,2, and have revolutionized atomic-scale imaging in several fields, from solid-state physics to structural biology³. Over the past decade, the manipulation and interaction of electrons with optical fields have enabled considerable progress in imaging methods⁴, near-field electron acceleration^5,6, and four-dimensional microscopy techniques with high temporal and spatial resolution⁷. However, electron beams typically couple only weakly to optical excitations, and emerging applications in electron control and sensing^8-11 require large enhancements using tailored fields and interactions. Here we couple a free-electron beam to a travelling-wave resonant cavity mode. The enhanced interaction with the optical whispering-gallery modes of dielectric microresonators induces a strong phase modulation on co-propagating electrons, which leads to a spectral broadening of 700 electronvolts, corresponding to the absorption and emission of hundreds of photons. By mapping the near-field interaction with ultrashort electron pulses in space and time, we trace the lifetime of the the microresonator following a femtosecond excitation and observe the spectral response of the cavity. The natural matching of free electrons to these quintessential optical modes could enable the application of integrated photonics technology in electron microscopy, with broad implications for attosecond structuring, probing quantum emitters and possible electron-light entanglement.

Coherent interaction between free electrons and a photonic cavity

Advances in the research of interactions between ultrafast free electrons and light have introduced a previously unknown kind of quantum matter, quantum free-electron wavepackets^1-5. So far, studies of the interactions of cavity-confined light with quantum matter have focused on bound electron systems, such as atoms, quantum dots and quantum circuits, which are considerably limited by their fixed energy states, spectral range and selection rules. By contrast, quantum free-electron wavepackets have no such limits, but so far no experiment has shown the influence of a photonic cavity on quantum free-electron wavepackets. Here we develop a platform for multidimensional nanoscale imaging and spectroscopy of free-electron interactions with photonic cavities. We directly measure the cavity-photon lifetime via a coherent free-electron probe and observe an enhancement of more than an order of magnitude in the interaction strength relative to previous experiments of electron-photon interactions. Our free-electron probe resolves the spatiotemporal and energy-momentum information of the interaction. The quantum nature of the electrons is verified by spatially mapping Rabi oscillations of the electron spectrum. The interactions between free electrons and cavity photons could enable low-dose, ultrafast electron microscopy of soft matter or other beam-sensitive materials. Such interactions may also open paths towards using free electrons for quantum information processing and quantum sensing. Future studies could achieve free-electron strong coupling^6,7, photon quantum state synthesis⁸ and quantum nonlinear phenomena such as cavity electro-optomechanics⁹.

The Development of Ultrafast Electron Microscopy

Time-resolved electron microscopy is based on the excitation of a sample by pulsed laser radiation and its probing by synchronized photoelectron bunches in the electron microscope column. With femtosecond lasers, if probing pulses with a small number of electrons—in the limit, single-electron wave packets—are used, the stroboscopic regime enables ultrahigh spatiotemporal resolution to be obtained, which is not restricted by the Coulomb repulsion of electrons. This review article presents the current state of the ultrafast electron microscopy (UEM) method for detecting the structural dynamics of matter in the time range from picoseconds to attoseconds. Moreover, in the imaging mode, the spatial resolution lies, at best, in the subnanometer range, which limits the range of observation of structural changes in the sample. The ultrafast electron diffraction (UED), which created the methodological basis for the development of UEM, has opened the possibility of creating molecular movies that show the behavior of the investigated quantum system in the space-time continuum with details of sub-Å spatial resolution. Therefore, this review on the development of UEM begins with a description of the main achievements of UED, which formed the basis for the creation and further development of the UEM method. A number of recent experiments are presented to illustrate the potential of the UEM method.

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

Vortex-carrying matter waves, such as chiral electron beams, are of significant interest in both applied and fundamental science. Continuous-wave electron vortex beams are commonly prepared via passive phase masks imprinting a transverse phase modulation on the electron's wavefunction. Here, we show that femtosecond chiral plasmonic near fields enable the generation and dynamic control on the ultrafast timescale of an electron vortex beam. The vortex structure of the resulting electron wavepacket is probed in both real and reciprocal space using ultrafast transmission electron microscopy. This method offers a high degree of scalability to small length scales and a highly efficient manipulation of the electron vorticity with attosecond precision. Besides the direct implications in the investigation of nanoscale ultrafast processes in which chirality plays a major role, we further discuss the perspectives of using this technique to shape the wavefunction of charged composite particles, such as protons, and how it can be used to probe their internal structure.