Ultrafast electron beams are essential for many applications, yet space-charge interactions in high-intensity beams lead to energy dissipation, coherence loss, and pulse broadening. Existing techniques mitigate these effects by using low-flux beams, preserving beam coherence into the quantum regime. Here, we propose a novel approach by treating the electrons as a strongly correlated Fermi gas rather than merely as an ensemble of charged point-like particles. We introduce a photon-induced pairing mechanism that generates a net attractive force between two electrons, thereby forming "flying bound states" analogous to Cooper pairs of conduction electrons in superconductors. Employing the setting of photon-induced near-field electron microscopy (PINEM), we demonstrate that the effective interaction via single-photon exchange among PINEM electrons can suppress the inherent repulsive Coulomb interaction, enabling a pairing instability mediated by structured electromagnetic fields at near-resonant velocity matching regimes. Finally, we analyze the dynamics of the free-electron pairs in a bunched beam, underscoring the potential to facilitate a phase-coherent condensate of electrons, which can further enhance beam coherence and multi-particle correlation for high-intensity electrons.
Ultrafast electron beams are essential for many applications, yet space-charge interactions in high-intensity beams lead to energy dissipation, coherence loss, and pulse broadening. Existing techniques mitigate these effects by using low-flux beams, preserving beam coherence into the quantum regime. Here, we propose a novel approach by treating the electrons as a strongly correlated Fermi gas rather than merely as an ensemble of charged point-like particles. We introduce a photon-induced pairing mechanism that generates a net attractive force between two electrons, thereby forming "flying bound states" analogous to Cooper pairs of conduction electrons in superconductors. Employing the setting of photon-induced near-field electron microscopy (PINEM), we demonstrate that the effective interaction via single-photon exchange among PINEM electrons can suppress the inherent repulsive Coulomb interaction, enabling a pairing instability mediated by structured electromagnetic fields at near-resonant velocity matching regimes. Finally, we analyze the dynamics of the free-electron pairs in a bunched beam, underscoring the potential to facilitate a phase-coherent condensate of electrons, which can further enhance beam coherence and multi-particle correlation for high-intensity electrons.
Coherent optical modulation of free-electron wavepackets offers a route to ultrafast beam steering, energy exchange, temporal compression, and quantum-state shaping. Recent advances in photon-induced near-field electron microscopy (PINEM), ultrafast Kapitza-Dirac effect (KDE) and dielectric laser acceleration (DLA) have demonstrated strong light-electron coupling, but longitudinal energy modulation, transverse momentum transfer, and wavepacket-dependent diffraction are still commonly described with separate models. Here, we develop a unified Light-Electron Modulation (LEM) framework that treats optical near fields as programmable phase modulators for free-electron wavepackets. Within this framework, we identify longitudinal and transverse modulation channels, analogous to electro-optic phase modulation and acousto-optic diffraction of light, respectively, and show how their operation depends on wavepacket extent, recoil, phase matching, and optical-field geometry. This formulation organizes PINEM, Raman-Nath and Bragg diffraction, DLA-like acceleration, and anomalous PINEM as limiting regimes of a common modulation picture. The resulting framework provides design principles for free-electron modulators that can control energy spectra, temporal density, transverse wavefronts, and electron-photon quantum interfaces, establishing LEM as a device-level platform for programmable femtosecond-to-attosecond matter-wave control.
Electron beams are a formidable tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled the mapping of optical near-fields [2] and the bunching of electrons in attosecond pulses [3, 4]. These developments are based on the stimulated inelastic scattering between electrons and light [5, 6], in which the electrons gain energy from or lose energy to the optical field. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [7]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promising applications like generating complex quantum states of light [8]. In this presentation, we discuss a set of experiments on free electron quantum optics that investigate single-electron-single-photon interactions and probe the resulting entanglement. Specifically, we consider scenarios in which optical waveguide structures are placed inside a transmission electron microscope (TEM) facilitating the interaction. Electrons passing by, for example, an integrated photonic structure (cf. Fig. 1a) can inelastically scatter with the optical mode, leading to the emergence of electron-photon pair states [9]. The resulting correlation between energy-loss electrons and photons, illustrated in Fig. 1b, can be probed employing time- and energy-resolved detection of both particles, revealing a pronounced coincidence peak between their arrival times, schematically shown in Fig. 1c. Extending the photon detection setup by a second detector to allow for Hanbury Brown and Twiss (HBT) measurements, the photon statistics heralded by such energy-loss electrons can be studied [10]. The observed anti-bunching behavior indicates a nonclassical optical state with single-photon properties. The inelastic electron-light scattering underlying the electron-photon pair generation is further expected to induce entanglement in the particle energies [11], however, direct observation of quantum entanglement would be exceedingly difficult given the large number of independent quantum states available in these degrees of freedom. Therefore, we propose experiments based on the quantum eraser scheme to demonstrate this free-electron-photon entanglement in different degrees of freedom [12,13]. Specifically, we consider a double-slit geometry coherently illuminated by an electron beam such that an interference pattern can be observed on a distant screen (cf. Fig. 2a). If electrons passing through the left or right (denoted |Land |R, respectively) slit generate distinct marker photons with vertical (|V)or horizontal (|H) polarization, this interference pattern would disappear due to the entanglement of electron path and photon polarisation (cf. Fig. 2b). However, if this which-path information carried by the marker photon is erased, e.g. by mixing the polarisation states, the interference pattern can be recovered when detecting electrons and photons in coincidence. We describe an extension of this idea to an entanglement test, before discussing possible realistic implementations and presenting preliminary results on several experimental key aspects. In summary, we discuss the inelastic electron-light scattering at integrated photonic structures with applications ranging from coherent electron beam modulation using continuous-wave optical fields to the electron-driven generation of quantum optical states of light. Delving deeper into single electron-single photon interactions, we outline feasible experiments to generate and verify electron-photon entanglement with a potential extension to electron pairs based on entanglement swapping. All this adds to the toolbox of free electron quantum optics, potentially enabling novel sources of quantum light as well as quantum-enhanced sensing in electron microscopy. Generation of correlated electron-photon pairs. (a) Electrons pass over a photonic integrated circuit placed in the sample plane of a TEM, generating photons in the optical waveguides via inelastic scattering. Energy-loss electrons are detected and time-tagged behind an imaging spectrometer in coincidence with photons exiting the waveguide. (b) Inelastic scattering links the electron energy loss (green, right ladder) to the generation of photons (red, left ladder), creating correlations in energy and time. (c) A strong temporal correlation between the loss electrons and detected photons, indicated by the red dot, is observed relative to the uncorrelated zero-loss background electrons (blue line). Free-electron-photon quantum eraser. (a) Coherent electron illumination of a double-slit structure results in interference between the two pathways |Land |R.(b) If the electrons generate distinguishable marker photons, e.g. of orthogonal polarizations |Vand |H, no interference pattern can be observed due to the electron-photon entanglement. (c) Collecting these marker photons and erasing the which-path information, e.g. using a half-wave plate (λ/2), the electron interference can be recovered using electron-photon coincidence detection with single-photon detectors (SPDs) placed behind a polarizing beam splitter (PBS).
Controlling and generating ultrafast free-electron wavepackets via laser is pivotal for photon-induced near-field electron microscopes (PINEM) and also for developing compact, coherent free-electron radiation sources. Here, we present a quantum echo-enabled high-harmonic generation (QEEHG) scheme that manipulates the quantum phase of electron wavepackets to produce tunable, coherent high-harmonic radiation at ultrashort wavelengths. This framework, inspired by the EEHG concept for free-electron lasers by Stupikov et al. (2009), leverages multiphoton PINEM scattering followed by dispersive chirp sections to induce quantum interference among photon sidebands. Such interference selectively enhances a targeted harmonic order - for instance, the 60th harmonic at 13.3nm from an 800nm seeding - while suppressing unwanted radiations. The optimization of harmonic orders and its non-classical spectral characteristics are analyzed. This quantum echo technique establishes a promising paradigm for compact coherent sources and provides new perspectives for quantum wavefunction shaping in ultrafast electron microscopy and diffraction.
Since the birth of quantum optics, the measurement of quantum states of nonclassical light has been of tremendous importance for advancement in the field. To date, conventional detectors such as photomultipliers, avalanche photodiodes, and superconducting nanowires, all rely at their core on linear excitation of bound electrons with light, posing fundamental restrictions on the detection. In contrast, the interaction of free electrons with light in the context of quantum optics is highly nonlinear and offers exciting possibilities. The first experiments that promoted this direction appeared over the past decade as part of photon-induced nearfield electron microscopy (PINEM), wherein free electrons are capable of high-order multi-photon absorption and emission. Here we propose using free electrons for quantum-optical detection of the complete quantum state of light. We show how the precise control of the electron before and after its interaction with quantum light enables to extract the photon statistics and implement full quantum state tomography using PINEM. This technique can reach sub-attosecond time resolutions, measure temporal coherence of any degree (e.g., g(1), g(2)), and simultaneously detect large numbers of photons with each electron. Importantly, the interaction of the electron with light is non-destructive, thereby leaving the photonic state (modified by the interaction) intact, which is conceptually different from conventional detectors. By using a pulse of multiple electrons, we envision how PINEM quantum detectors could achieve a single-shot measurement of the complete state of quantum light, even for non-reproducible emission events. Altogether, our work paves the way to novel kinds of photodetectors that utilize the ultrafast duration, high nonlinearity, and non-destructive nature of electron-light interactions.
Recent quantum gas cavity-QED experiments demonstrated simultaneous coupling of photons to single atom transitions as well as correlated pairs of ultracold fermions trapped inside optical cavities. This enables simultaneous control over density ordering and pairing. Using extensive numerical simulations, we show that in a transversely driven, two-component degenerate Fermi gas, the interplay of cavity-induced and bare atom--atom interactions controls not only the power threshold for self-organization, but also the type of spatial ordering in the Z2-symmetry-broken superradiant state. In the repulsive interaction regime, unpaired or weakly paired fermions first self-organize through a charge-density-wave instability, and finite-momentum pairing only occurs at much stronger pump strengths. In contrast, an attractive superfluid undergoes a joint density--pairing instability, directly entering into intertwined phase with charge-density-wave and pair-density-wave orders. At strong pumping the photon-enhanced pair interaction generates localized density and pairing order even when the bare contact interaction is repulsive. In this cavity-dominated regime strong spatial localization suppresses the long range superfluid coherence. Our results identify the role of cavity-induced atomic interactions in supporting intertwined fermionic orders and pave the way for exploring exotic states with multiple orders in highly controlled hybrid light-matter systems.
Ultrafast strong-field laser--plasma physics is shown to offer a promising framework for relativistic nonlinear quantum electrodynamics (QED). As one of its key advantages, this approach to relativistic nonlinear QED does not require an external beam of relativistic particles. Instead, high-energy electrons are produced in this setting as a part of ultrafast strong-field laser--plasma interactions. An intense ultrashort laser pulse generates and accelerates dense electron bunches to relativistic energies, giving rise to photon-pair emission confined to the nanometer scale in space and the attosecond scale in time. As a lowest-order nonlinear QED process, relativistic electrons in laser-driven plasmas are shown to give rise to attosecond bursts of two-photon emission, providing an ultrabroadband source of correlated photon pairs. As a physically insightful estimate, the rate of this two-photon emission is expressed via a product $ α^2 γω_{turn}$, where α is the fine-structure constant, γ is the Lorentz factor, and $ ω_{turn}$ is the local relativistic curvature frequency. Photon pairs with strongest correlations, providing a resource for photon entanglement, are emitted at a much lower rate, estimated as $ α^2 γ^2 ω_{turn} E_{\perp} /E_S$, where E⊥ is the laser electromagnetic field, determining the transverse Lorentz force, and ES is the Schwinger critical field. Our study offers a clear guidance on how quantum aspects of laser-driven relativistic plasma electrodynamics can be isolated from their classical counterparts, enabling a physically justifiable approach to the analysis of nonlinear QED phenomena in complex laser--plasma interactions driven by ultrashort high-intensity laser pulses.