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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 synthesis 8 and quantum nonlinear phenomena such as cavity electro-optomechanics 9 . The strong interaction of coherent free electrons with a photonic-crystal cavity enables the measurement of the lifetimes of the cavity modes and provides a technique for multidimensional near-field imaging and spectroscopy.

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.

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. X-ray self-focusing sources are demonstrated by free electrons coherently interacting with van der Waals heterostructures, bypassing the need for X-ray optics that are often inefficient and challenging to fabricate.

Tunable sources of X-ray radiation are widely used for imaging and spectroscopy in fundamental science, medicine and industry. The growing demand for highly tunable, high-brightness laboratory-scale X-ray sources motivates research into new fundamental mechanisms of X-ray generation. Here, we demonstrate the ability of van der Waals materials to serve as a platform for tunable X-ray generation when irradiated by moderately relativistic electrons available, for example, from a transmission electron microscope. The radiation spectrum can be precisely controlled by tuning the acceleration voltage of the incident electrons, as well as by our proposed approach: adjusting the lattice structure of the van der Waals material. We present experimental results for both methods, observing the energy tunability of X-ray radiation from the van der Waals materials WSe2, CrPS4, MnPS3, FePS3, CoPS3 and NiPS3. Our findings demonstrate the concept of material design at the atomic level, using van der Waals heterostructures and other atomic superlattices, for exploring novel phenomena of X-ray physics.Tunable X-ray generation, from ultrathin van der Waals materials impacted by relativistic electrons, is demonstrated.

A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01178-3.

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.

As charged particles surpass the speed of light in an optical medium they produce radiation - analogously to the way jet planes surpass the speed of sound and produce a sonic boom. This radiation emission, known as the Cherenkov effect, is among the most fundamental processes in electrodynamics. As such, it is used in numerous applications of particle detectors, particle accelerators, light sources, and medical imaging. Surprisingly, all Cherenkov-based applications and experiments thus far were fully described by classical electrodynamics even though theoretical work predicts new Cherenkov phenomena coming from quantum electrodynamics. The quantum description could provide new possibilities for the design of highly controllable light sources and more efficient accelerators and detectors. Here, we provide a direct evidence of the quantum nature of the Cherenkov effect and reveal its intrinsic quantum features. By satisfying the Cherenkov condition for relativistic electron wavefunctions and maintaining it over hundreds of microns, each electron simultaneously accelerates and decelerates by absorbing and emitting hundreds of photons in a coherent manner. We observe this strong interaction in an ultrafast transmission electron microscope, achieving for the first time a phase-matching between a relativistic electron wavefunction and a propagating light wave. Consequently, the quantum wavefunction of each electron evolves into a coherent plateau, analogous to a frequency comb in ultrashort laser pulses, containing hundreds of quantized energy peaks. Our findings prove that the delocalized wave nature of electrons can become dominant in stimulated interactions. In addition to prospects for known applications of the Cherenkov effect, our work provides a platform for utilizing quantum electrodynamics for applications in electron microscopy and in free-electron pump-probe spectroscopy.