Control of quantum electrodynamical processes by shaping electron wavepackets

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.

Topologically Protected Strong-Interaction of Photonics with Free Electrons

We propose a robust scheme of studying the strong interactions between free electrons and photons using topological photonics. Our study reveals that the topological corner state can be used to enhance the interaction between light and a free electron significantly. The quality factor of the topological cavity can exceed 20 000 and the corner state has a very long lifetime even after the pump pulse is off. And thus, the platform enables us to achieve a strong interaction without the need for zero delay and phase matching as in traditional photon-induced near-field electron microscopy (PINEM). This work provides the new perspective that the topological photonic structures can be utilized as a platform to shape free electron wave packets, which facilitates the control of quantum electrodynamical (QED) processes and quantum optics with free electrons in the future.

Free-electron crystals for enhanced X-ray radiation

Bremsstrahlung-the spontaneous emission of broadband radiation from free electrons that are deflected by atomic nuclei-contributes to the majority of X-rays emitted from X-ray tubes and used in applications ranging from medical imaging to semiconductor chip inspection. Here, we show that the bremsstrahlung intensity can be enhanced significantly-by more than three orders of magnitude-through shaping the electron wavefunction to periodically overlap with atoms in crystalline materials. Furthermore, we show how to shape the bremsstrahlung X-ray emission pattern into arbitrary angular emission profiles for purposes such as unidirectionality and multi-directionality. Importantly, we find that these enhancements and shaped emission profiles cannot be attributed solely to the spatial overlap between the electron probability distribution and the atomic centers, as predicted by the paraxial and non-recoil theory for free electron light emission. Our work highlights an unprecedented regime of free electron light emission where electron waveshaping provides multi-dimensional control over practical radiation processes like bremsstrahlung. Our results pave the way towards greater versatility in table-top X-ray sources and improved fundamental understanding of quantum electron-light interactions.

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.

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.

Free-electron interactions with van der Waals heterostructures: a source of focused X-ray radiation

The science and technology of X-ray optics have come far, enabling the focusing of X-rays for applications in high-resolution X-ray spectroscopy, imaging, and irradiation. In spite of this, many forms of tailoring waves that had substantial impact on applications in the optical regime have remained out of reach in the X-ray regime. This disparity fundamentally arises from the tendency of refractive indices of all materials to approach unity at high frequencies, making X-ray-optical components such as lenses and mirrors much harder to create and often less efficient. Here, we propose a new concept for X-ray focusing based on inducing a curved wavefront into the X-ray generation process, resulting in the intrinsic focusing of X-ray waves. This concept can be seen as effectively integrating the optics to be part of the emission mechanism, thus bypassing the efficiency limits imposed by X-ray optical components, enabling the creation of nanobeams with nanoscale focal spot sizes and micrometer-scale focal lengths. Specifically, we implement this concept by designing aperiodic vdW heterostructures that shape X-rays when driven by free electrons. The parameters of the focused hotspot, such as lateral size and focal depth, are tunable as a function of an interlayer spacing chirp and electron energy. Looking forward, ongoing advances in the creation of many-layer vdW heterostructures open unprecedented horizons of focusing and arbitrary shaping of X-ray nanobeams.

Jaynes-Cummings interaction between low-energy free electrons and cavity photons

The Jaynes-Cummings Hamiltonian is at the core of cavity quantum electrodynamics; however, it relies on bound-electron emitters fundamentally limited by the binding Coulomb potential. In this work, we propose theoretically a new approach to realizing the Jaynes-Cummings model using low-energy free electrons coupled to dielectric microcavities and exemplify several quantum technologies made possible by this approach. Using quantum recoil, a large detuning inhibits the emission of multiple consecutive photons, effectively transforming the free electron into a few-level system coupled to the cavity mode. We show that this approach can be used for generation of single photons, photon pairs, and even a quantum SWAP gate between a photon and a free electron, with unity efficiency and high fidelity. Tunable by their kinetic energy, quantum free electrons are inherently versatile emitters with an engineerable emission wavelength. Hence, they pave the way toward new possibilities for quantum interconnects between photonic platforms at disparate spectral regimes.

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.

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.

Quantum terahertz Cherenkov radiation: theory and experimental feasibility

A quantum approach is developed for describing the behavior of Cherenkov radiation (CR). Then we propose a scheme of terahertz CR operating in a quantum regime for which the discreteness of momentum exchange in the free electrons-light interaction is significant. In this quantum regime, the spectrum of the emitted radiation appears as discrete spectral lines with a significantly narrow linewidth. The resonant wavelength, wavelength spacing, and linewidth of the emission lines can be tuned by adjusting the parameters of electron beam and waveguide. It is verified that the criteria and constraints of the requirements for essential experimental parameters are practically feasible. This work has implications for future studies of the quantum interaction of free electrons with light as well as visualization of quantum light applications in sensing, imaging, and spectroscopy.

Enhanced Versatility of Table-Top X-Rays from Van der Waals Structures

Van der Waals (vdW) materials have attracted much interest for their myriad unique electronic, mechanical, and thermal properties. In particular, they are promising candidates for monochromatic, table-top X-ray sources. This work reveals that the versatility of the table-top vdW X-ray source goes beyond what has been demonstrated so far. By introducing a tilt angle between the vdW structure and the incident electron beam, it is theoretically and experimentally shown that the accessible photon energy range is more than doubled. This allows for greater versatility in real-time tuning of the vdW X-ray source. Furthermore, this work shows that the accessible photon energy range is maximized by simultaneously controlling both the electron energy and the vdW structure tilt. These results will pave the way for highly tunable, compact X-ray sources, with potential applications including hyperspectral X-ray fluoroscopy and X-ray quantum optics.

Space-Time Wave Packets from Smith-Purcell Radiation

Space-time wave packets are electromagnetic waves with strong correlations between their spatial and temporal degrees of freedom. These wave packets have gained much attention for fundamental properties like propagation invariance and user-designed group velocities, and for potential applications like optical microscopy, micromanipulation, and laser micromachining. Here, free-electron radiation is presented as a natural and versatile source of space-time wave packets that are ultra-broadband and highly tunable in frequency. For instance, ab initio theory and numerical simulations show that the intensity profile of space-time wave packets from Smith-Purcell radiation can be directly tailored through the grating properties, as well as the velocity and shape of the electron bunches. The result of this work indicates a viable way of generating space-time wave packets at exotic frequencies such as the terahertz and X-ray regimes, potentially paving the way toward new methods of shaping electromagnetic wave packets through free-electron radiation.

Superradiance and Subradiance due to Quantum Interference of Entangled Free Electrons

When multiple quantum emitters radiate, their emission rate may be enhanced or suppressed due to collective interference in a process known as super- or subradiance. Such processes are well known to occur also in light emission from free electrons, known as coherent cathodoluminescence. Unlike atomic systems, free electrons have an unbounded energy spectrum, and, thus, all their emission mechanisms rely on electron recoil, in addition to the classical properties of the dielectric medium. To date, all experimental and theoretical studies of super- and subradiance from free electrons assumed only classical correlations between particles. However, dependence on quantum correlations, such as entanglement between free electrons, has not been studied. Recent advances in coherent shaping of free-electron wave functions motivate the investigation of such quantum regimes of super- and subradiance. In this Letter, we show how a pair of coincident path-entangled electrons can demonstrate either super- or subradiant light emission, depending on the two-particle wave function. By choosing different free-electron Bell states, the spectrum and emission pattern of the light can be reshaped, in a manner that cannot be accounted for by a classical mixed state. We show these results for light emission in any optical medium and discuss their generalization to many-body quantum states. Our findings suggest that light emission can be sensitive to the explicit quantum state of the emitting matter wave and possibly serve as a nondestructive measurement scheme for measuring the quantum state of many-body systems.

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.