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Spatial modulation of electron beams is an essential tool for various applications such as nanolithography and imaging1–3 , yet its implementations4–11 are severely limited and inherently non-tunable. Conversely, light-driven electron spatial modulation12–15 could potentially allow arbitrary electron wavefront shaping16–18 via the underlying mechanism of photon-induced nearfield electron microscopy (PINEM)19–21 . Here, we present tunable photon-induced spatial modulation of electrons through their externally-controlled interaction with surface plasmon polaritons (SPPs). Using recently developed methods of shaping SPP patterns 22,23, we demonstrate a dynamic control of the electron beam with a variety of high-quality electron distributions. Intriguingly, by utilizing the intrinsic interaction nonlinearity24, we attain the first observation of 2D spatial Rabi oscillations25,26 and generate electron features below the SPP wavelength. Our work paves the way to on-demand electron wavefront shaping at ultrafast timescales, with prospects for aberration correction, nano-fabrication and material characterization., The results supporting the findings of this articles have received additional fundings from the Israel Science Foundation grants 3334/19 and 831/19

Imaging polariton dynamics Two-dimensional (2D) materials can confine light to volumes much shorter than the wavelength, and, together, the long propagation lengths make them attractive materials for developing nanophotonic platforms. Characterizing the spatiotemporal control of 2D polariton wave packets has been hindered for the same reasons that make their potential applications exciting: They have extremely small wavelengths and are strongly confined inside the material. Kurman et al. developed a new pump-probe technique based on electron emission that provides access to the spatiotemporal dynamics of 2D polaritons. The nanometric spatial resolution and femtosecond temporal resolution will be useful for probing the excitation dynamics of these materials. Science , abg9015, this issue p. 1181

Quantum light–matter interactions of bound electron systems have been studied extensively. By contrast, quantum interactions of free electrons with light have only become accessible in recent years, following the discovery of photon-induced near-field electron microscopy (PINEM). So far, the fundamental free electron–light interaction in all PINEM experiments has remained weak due to its localized near-field nature, which imposes an energy–momentum mismatch between electrons and light. Here, we demonstrate a strong interaction between free-electron waves and light waves, resulting from precise energy–momentum phase-matching with the extended propagating light field. By exchanging hundreds of photons with the field, each electron simultaneously accelerates and decelerates in a coherent manner. Consequently, each electron’s quantum wavefunction evolves into a quantized energy comb, spanning a bandwidth of over 1,700 eV, requiring us to extend the PINEM theory. Our observation of coherent electron phase-matching with a propagating wave is a type of inverse-Cherenkov interaction that occurs with a quantum electron wavefunction, demonstrating how the extended nature of the electron wavefunction can alter stimulated electron–light interactions. Energy–momentum phase-matching enables strong interactions between free electrons and light waves. As a result, the wavefunction of the electron exhibits a comb structure, which was observed using photon-induced near-field electron microscopy.

Recent advances in laser interactions with coherent free electrons have enabled to shape the electron's quantum state. Each electron becomes a superposition of energy levels on an infinite quantized ladder, shown to contain up to thousands of energy levels. We propose to utilize the quantum nature of such laser-driven free electrons as a "synthetic Hilbert space" in which we construct and control qudits (quantum digits). The question that motivates our work is what qudit states can be accessed using electron-laser interactions, and whether it is possible to implement any arbitrary quantum gate. We find how to encode and manipulate free-electron qudit states, focusing on dimensions which are powers of 2, where the qudit represents multiple qubits implemented on the same single electron – algebraically separated, but physically joined. As an example, we prove the possibility to fully control a 4-dimenisonal qudit, and reveal the steps required for full control over any arbitrary dimension. Our work enriches the range of applications of free electrons in microscopy and spectroscopy, offering a new platform for continuous-variable quantum information.

The interactions of free electrons with optical cavities enable the creation of novel quantum photonic states., 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.

Free-electron interactions with laser-driven nanophotonic nearfields can quantize the electrons' energy spectrum and provide control over this quantized degree of freedom. We propose to use such interactions to promote free electrons as carriers of quantum information and find how to create a qubit on a free electron. We find how to implement the qubit's non-commutative spin-algebra, then control and measure the qubit state with a universal set of 1-qubit gates. These gates are within the current capabilities of femtosecond-pulsed laser-driven transmission electron microscopy. Pulsed laser driving promise configurability by the laser intensity, polarizability, pulse duration, and arrival times.

We present active spatial shaping of free-electron wavepackets through their interaction with specially-designed interference patterns of surface plasmons and via the nonlinear intensity dependence of the electron-plasmon interaction.

We find that laser-driven free-electrons can be coherently-shaped to induce superradiance from many-body quantum emitters. This effect provides new capabilities in electron microscopy&spectroscopy, using high spatio-temporal resolution for coherent control and enhancement of cathodoluminescence.

Since its inception, research of cavity quantum electrodynamics (CQED) has extended our understanding of light-matter interactions and our ability to utilize them. Thus far, all the work in this field has been focused on light interacting with bound electron systems - such as atoms, molecules, quantum dots, and quantum circuits. In contrast, markedly different physical phenomena are found in free-electron systems, the energy distribution of which is continuous and not discrete, implying tunable transitions and selection rules. In addition to their uses for electron microscopy, the interaction of free electrons with light enables important phenomena such as Cherenkov radiation, Compton scattering, and free-electron lasing. However, no experiment has shown the integration of free electrons into the framework of CQED, because the fundamental electron-light interaction is limited in strength and lifetime. This limit explains why many phenomena have remained out of reach for experiments with free electrons. In this work, we developed the platform for studying CQED at the nanoscale with free electrons and demonstrated it by observing their coherent interaction with cavity photons for the first time. We also directly measure the cavity photon lifetime via a free electron probe and show more than an order of magnitude enhancement in the electron-photon interaction strength. These capabilities may open new paths toward using free electrons as carriers of quantum information, even more so after strong coupling between free electrons and cavity photons will have been demonstrated. Efficient electron-cavity photon coupling could also allow new nonlinear phenomena of cavity opto-electro-mechanics and the ultrafast exploration of soft matter or other beam-sensitive materials using low electron current and low laser exposure., 16 pages, 5 figures

By engineering the boundary conditions of plasmonic excitations, we present a novel method for electron wavefront shaping utilizing the ultrafast interaction of femtosecond free- electron and laser pulses in plasmonic samples.

We observe an increased interaction strength and time between quantum electron wavepackets and laser pulses due to the large Q-factor of a photonic crystal slab, promoting the integration of free-electron emitters into cavity quantum electrodynamics.

We present the quantum theory governing the interaction between short laser pulses and relativistic free electrons, and reveal intrinsic conservation laws for such quantum interactions. Through the...

We show that pulsed laser-driven free electrons undergo quantum walk with coherent uncertainty in the electron energy levels, characterized by their spread. We study this quantum walk experimentally and develop its analytic theory.

Superoscillating functions are band-limited functions that oscillate in some region faster than their largest Fourier frequency. In past years, this phenomenon triggered great scientific interest as a building block which could promote research in many fields. In this article, the effect of superoscillating coupling is investigated in the context of quantum physics. Our purpose was to find out whether a quantum system responds in the same way to a time-dependent potential oscillating at some given frequency and to the same potential oscillating at the corresponding superoscillation frequency. This is done by analyzing the quantum mechanics of a one-dimensional particle in the presence of a time dependent delta function potential. The main finding obtained by numerical solution of the Schrodinger equation is that in a carefully prepared situation, the responses in those two cases are similar.

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 wave function. 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 wave function of charged composite particles, such as protons, and how it can be used to probe their internal structure., 14 pages, 4 figures

The weak coupling between free electrons and light remains the limiting factor that has prevented access to versatile electron–photon physics, such as the entanglement of individual photons and electrons. This year, we demonstrated that photonic cavities can increase the coupling strength of electrons and light by more than an order of magnitude.

We find that electrons in strong electromagnetic fields exhibit Bloch oscillations, in analogy to light propagation in index-gradient waveguide arrays. Our relativistic non-perturbative approach generalizes to multifrequency fields, producing rich variety of oscillations.

Free electrons interacting with the frequency comb of an attosecond laser pulse follow intricate quantum dynamics. We present an analytic treatment of the interaction and use it to shape the electron energy spectrum.

Silica-on-Silica technology enables fabrication of waveguide-based on-chip devices for high-power applications. We demonstrate a 25µm thick Yb/Al-codoped fused silica slab waveguide with 0.2dB/cm loss and 0.6dB/cm gain, and a 25X25µm all-fused-silica rectangular waveguide.

Free electrons can efficiently absorb or emit plasmons excited in a thin conductor, giving rise to multiple energy peaks in the transmitted electron spectra separated by multiples of the plasmon energy. When the plasmons are chiral, this can also give rise to transfer of orbital angular momentum (OAM). Here, we show that large amounts of OAM can be efficiently transferred between chiral plasmons supported by a thin film and free electrons traversing it. Under realistic conditions, our predictive simulations reveal efficient absorption of $\ell\gg1$ chiral plasmons of vorticity $m\gg1$, resulting in an OAM transfer $\ell m\hbar\gg\hbar$. Our work supports the use of chiral plasmons sustained by externally illuminated thin films as a way of generating high-vorticity electrons, resulting in a remarkably large fraction of kinetic energy associated with motion along the azimuthal direction, perpendicular to the incident beam., Comment: 8 pages, 5 figures