Quantum effects in the interaction of low-energy electrons with light.

The interaction between free electrons and optical fields constitutes a unique platform to investigate ultrafast processes in matter and explore fundamental quantum phenomena. Specifically, optically modulated electrons in ultrafast electron microscopy act as noninvasive probes that push space-time-energy resolution to the picometer-attosecond-microelectronvolt range. Electron energies well above the involved photon energies are commonly used, rendering a low electron-light coupling and, thus, only providing limited access to the wealth of quantum nonlinear phenomena underlying the dynamical response of nanostructures. Here, we theoretically investigate electron-light interactions between photons and electrons of comparable energies, revealing quantum and recoil effects that include a nonvanishing coupling of surface-scattered electrons to light plane waves, inelastic electron backscattering from confined optical fields, and strong electron-light coupling under grazing electron diffraction by an illuminated crystal surface. Our exploration of electron-light-matter interactions holds potential for applications in ultrafast electron microscopy.

Gigahertz streaking and compression of low-energy electron pulses.

Although radio frequency (RF) technology is routinely employed for controlling high-energy pulses of electrons, corresponding technology has not been developed at beam energies below several kiloelectronvolts. In this work, we demonstrate transverse and longitudinal phase-space manipulation of low-energy electron pulses using RF fields. A millimeter-sized photoelectron gun is combined with synchronized streaking and compression cavities driven at frequencies of 0.5 and 2.5 GHz, respectively. The phase-controlled acceleration and deceleration of photoelectron pulses is characterized in the energy range of 50-100 eV. Deflection from a transient space-charge cloud at a metal grid is used to measure a fourfold compression of 80-eV electron pulses, from τ=34 to τ=8 ps pulse duration.

Non-thermal phonon dynamics and a quenched exciton condensate probed by surface-sensitive electron diffraction.

Interactions among and between electrons and phonons steer the energy flow in photo-excited materials and govern the emergence of correlated phases. The strength of electron-phonon interactions, decay channels of strongly coupled modes and the evolution of three-dimensional order are revealed by electron or X-ray pulses tracking non-equilibrium structural dynamics. Despite such capabilities, the growing relevance of inherently anisotropic two-dimensional materials and functional heterostructures still calls for techniques with monolayer sensitivity and, specifically, access to out-of-plane phonon polarizations. Here, we resolve non-equilibrium phonon dynamics and quantify the excitonic contribution to the structural order parameter in 1T-TiSe2. To this end, we introduce ultrafast low-energy electron diffuse scattering and trace strongly momentum- and fluence-dependent phonon populations. Mediated by phonon-phonon scattering, a few-picosecond build-up near the zone boundary precedes a far slower generation of zone-centre acoustic modes. These weakly coupled phonons are shown to substantially delay overall equilibration in layered materials. Moreover, we record the surface structural response to a quench of the material's widely investigated exciton condensate, identifying an approximate 30:70 ratio of excitonic versus Peierls contributions to the total lattice distortion in the charge density wave phase. The surface-sensitive approach complements the ultrafast structural toolbox and may further elucidate the impact of phonon scattering in numerous other phenomena within two-dimensional materials, such as the formation of interlayer excitons in twisted bilayers.

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.

High-sensitivity extreme-ultraviolet transient absorption spectroscopy enabled by machine learning.

We present a novel denoising scheme for spectroscopy experiments employing broadband light sources and demonstrate its capabilities using transient absorption measurements with a high-harmonic source. Our scheme relies on measuring the probe spectra before and after interacting with the sample while capturing correlations between spectral components through machine learning approaches. With the present setup we achieve up to a tenfold improvement in noise suppression in XUV transient absorption spectra compared to the conventional pump on/ pump off referencing method. By utilizing strong spectral correlations in source fluctuations, the use of an artificial neural network facilitates pixel-wise noise reduction without requiring wavelength calibration of the reference spectrum. Our method can be adapted to a wide range of experiments and may be particularly advantageous for low repetition-rate systems, such as free electron lasers as well as laser-driven plasma and HHG sources. The enhanced sensitivity enables the investigation of subtle electron and lattice dynamics in the weak excitation regime, which is relevant for studying photovoltaics and photo-induced phase transitions in strongly correlated materials.

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.

Light-induced hexatic state in a layered quantum material.

The tunability of materials properties by light promises a wealth of future applications in energy conversion and information technology. Strongly correlated materials such as transition metal dichalcogenides offer optical control of electronic phases, charge ordering and interlayer correlations by photodoping. Here, we find the emergence of a transient hexatic state during the laser-induced transformation between two charge-density wave phases in a thin-film transition metal dichalcogenide, 1T-type tantalum disulfide (1T-TaS2). Introducing tilt-series ultrafast nanobeam electron diffraction, we reconstruct charge-density wave rocking curves at high momentum resolution. An intermittent suppression of three-dimensional structural correlations promotes a loss of in-plane translational order caused by a high density of unbound topological defects, characteristic of a hexatic intermediate. Our results demonstrate the merit of tomographic ultrafast structural probing in tracing coupled order parameters, heralding universal nanoscale access to laser-induced dimensionality control in functional heterostructures and devices.

Spatiotemporal Electron Beam Focusing through Parallel Interactions with Shaped Optical Fields.

The ability to modulate free electrons with light has emerged as a powerful tool to produce attosecond electron wave packets. However, research has so far aimed at the manipulation of the longitudinal wave function component, while the transverse degrees of freedom have primarily been utilized for spatial rather than temporal shaping. Here, we show that the coherent superposition of parallel light-electron interactions in transversally separate zones allows for a simultaneous spatial and temporal compression of a convergent electron wave function, enabling the formation of sub-Ångström focal spots of attosecond duration. Specifically, spots spanning just ∼3% of the light optical cycle are shown to be formed, accompanied by an increase by only a factor of 2 in spatial extension relative to an unperturbed beam. The proposed approach will facilitate the exploration of previously inaccessible ultrafast atomic-scale phenomena, in particular enabling attosecond scanning transmission electron microscopy.

Mode-selective ballistic pathway to a metastable electronic phase.

Exploiting vibrational excitation for the dynamic control of material properties is an attractive goal with wide-ranging technological potential. Most metal-to-insulator transitions are mediated by few structural modes and are, thus, ideal candidates for selective driving toward a desired electronic phase. Such targeted navigation within a generally multi-dimensional potential energy landscape requires microscopic insight into the non-equilibrium pathway. However, the exact role of coherent inertial motion across the transition state has remained elusive. Here, we demonstrate mode-selective control over the metal-to-insulator phase transition of atomic indium wires on the Si(111) surface, monitored by ultrafast low-energy electron diffraction. We use tailored pulse sequences to individually enhance or suppress key phonon modes and thereby steer the collective atomic motion within the potential energy surface underlying the structural transformation. Ab initio molecular dynamics simulations demonstrate the ballistic character of the structural transition along the deformation vectors of the Peierls amplitude modes. Our work illustrates that coherent excitation of collective modes via exciton-phonon interactions evades entropic barriers and enables the dynamic control of materials functionality.

Cavity-mediated electron-photon pairs.

Quantum information, communication, and sensing rely on the generation and control of quantum correlations in complementary degrees of freedom. Free electrons coupled to photonics promise novel hybrid quantum technologies, although single-particle correlations and entanglement have yet to be shown. In this work, we demonstrate the preparation of electron-photon pair states using the phase-matched interaction of free electrons with the evanescent vacuum field of a photonic chip-based optical microresonator. Spontaneous inelastic scattering produces intracavity photons coincident with energy-shifted electrons, which we employ for noise-suppressed optical mode imaging. This parametric pair-state preparation will underpin the future development of free-electron quantum optics, providing a route to quantum-enhanced imaging, electron-photon entanglement, and heralded single-electron and Fock-state photon sources.

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.

Ultrafast high-harmonic nanoscopy of magnetization dynamics.

Light-induced magnetization changes, such as all-optical switching, skyrmion nucleation, and intersite spin transfer, unfold on temporal and spatial scales down to femtoseconds and nanometers, respectively. Pump-probe spectroscopy and diffraction studies indicate that spatio-temporal dynamics may drastically affect the non-equilibrium magnetic evolution. Yet, direct real-space magnetic imaging on the relevant timescales has remained challenging. Here, we demonstrate ultrafast high-harmonic nanoscopy employing circularly polarized high-harmonic radiation for real-space imaging of femtosecond magnetization dynamics. We map quenched magnetic domains and localized spin structures in Co/Pd multilayers with a sub-wavelength spatial resolution down to 16 nm, and strobosocopically trace the local magnetization dynamics with 40 fs temporal resolution. Our compact experimental setup demonstrates the highest spatio-temporal resolution of magneto-optical imaging to date. Facilitating ultrafast imaging with high sensitivity to chiral and linear dichroism, we envisage a wide range of applications spanning magnetism, phase transitions, and carrier dynamics.

Chiral high-harmonic generation and spectroscopy on solid surfaces using polarization-tailored strong fields.

Strong-field methods in solids enable new strategies for ultrafast nonlinear spectroscopy and provide all-optical insights into the electronic properties of condensed matter in reciprocal and real space. Additionally, solid-state media offers unprecedented possibilities to control high-harmonic generation using modified targets or tailored excitation fields. Here we merge these important points and demonstrate circularly-polarized high-harmonic generation with polarization-matched excitation fields for spectroscopy of chiral electronic properties at surfaces. The sensitivity of our approach is demonstrated for structural helicity and termination-mediated ferromagnetic order at the surface of silicon-dioxide and magnesium oxide, respectively. Circularly polarized radiation emanating from a solid sample now allows to add basic symmetry properties as chirality to the arsenal of strong-field spectroscopy in solids. Together with its inherent temporal (femtosecond) resolution and non-resonant broadband spectrum, the polarization control of high harmonics from condensed matter can illuminate ultrafast and strong field dynamics of surfaces, buried layers or thin films.

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.

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.

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.