Scientific applications of free electrons, such as in electron microscopes and particle accelerators, are limited by the brightness of available electron sources. Accelerators can use phase space cooling to surpass these source limitations, whereas electron microscopes can only rely on particle filtering to increase beam coherence at the cost of reduced brightness. We show that strong electron-light coupling in nanophotonic structures makes it possible to achieve single-pass stochastic cooling inside an electron microscope for a lossless improvement of longitudinal emittance. This approach is laser-free and compatible with normal CW operation of electron microscopes. We derive a fully quantum mechanical model of stochastic cooling valid in the strong coupling regime, finding an analytic asymptotic formula for the optimal cooled energy spread $σ_{E_f}\simeq0.88(\hbarω)^{2/3}σ_{E_0}^{1/3}$, with $\hbar ω$ the cooling photon energy and $σ_{E_0}$ the initial energy spread. Numerical simulations confirm that the energy spread reduction is reflected in an increase in the purity of the electron's quantum state and a reduction of the longitudinal phase space area. Our work paves a path towards even brighter beams for electron microscopy, promising higher image quality, enhanced spectral resolution, and a route to reaching fundamental quantum limits on electron beam phase space area.
Scientific applications of free electrons, such as in electron microscopes and particle accelerators, are limited by the brightness of available electron sources. Accelerators can use phase space cooling to surpass these source limitations, whereas electron microscopes can only rely on particle filtering to increase beam coherence at the cost of reduced brightness. We show that strong electron-light coupling in nanophotonic structures makes it possible to achieve single-pass stochastic cooling inside an electron microscope for a lossless improvement of longitudinal emittance. This approach is laser-free and compatible with normal CW operation of electron microscopes. We derive a fully quantum mechanical model of stochastic cooling valid in the strong coupling regime, finding an analytic asymptotic formula for the optimal cooled energy spread σEf≃0.88(ℏω)2/3σE01/3, with ℏω the cooling photon energy and σE0 the initial energy spread. Numerical simulations confirm that the energy spread reduction is reflected in an increase in the purity of the electron's quantum state and a reduction of the longitudinal phase space area. Our work paves a path towards even brighter beams for electron microscopy, promising higher image quality, enhanced spectral resolution, and a route to reaching fundamental quantum limits on electron beam phase space area.
Feynman once asked physicists to build better electron microscopes to be able to watch biology at work. While electron microscopes can now provide atomic resolution, electron beam induced specimen damage precludes high resolution imaging of sensitive materials, such as single proteins or polymers. Here, we use simulations to show that an electron microscope based on a multi-pass measurement protocol enables imaging of single proteins, without averaging structures over multiple images. While we demonstrate the method for particular imaging targets, the approach is broadly applicable and is expected to improve resolution and sensitivity for a range of electron microscopy imaging modalities, including, for example, scanning and spectroscopic techniques. The approach implements a quantum mechanically optimal strategy which under idealized conditions can be considered interaction-free.
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).
One of the astounding consequences of quantum mechanics is that it allows the detection of a target using an incident probe, with only a low probability of interaction of the probe and the target. This 'quantum weirdness' could be applied in the field of electron microscopy to generate images of beam-sensitive specimens with substantially reduced damage to the specimen. A reduction of beam-induced damage to specimens is especially of great importance if it can enable imaging of biological specimens with atomic resolution. Following a recent suggestion that interaction-free measurements are possible with electrons, we now analyze the difficulties of actually building an atomic resolution interaction-free electron microscope, or "quantum electron microscope". A quantum electron microscope would require a number of unique components not found in conventional transmission electron microscopes. These components include a coherent electron beam-splitter or two-state-coupler, and a resonator structure to allow each electron to interrogate the specimen multiple times, thus supporting high success probabilities for interaction-free detection of the specimen. Different system designs are presented here, which are based on four different choices of two-state-couplers: a thin crystal, a grating mirror, a standing light wave and an electro-dynamical pseudopotential. Challenges for the detailed electron optical design are identified as future directions for development. While it is concluded that it should be possible to build an atomic resolution quantum electron microscope, we have also identified a number of hurdles to the development of such a microscope and further theoretical investigations that will be required to enable a complete interpretation of the images produced by such a microscope.
Electron--photon quantum entanglement in an electron microscope paves the way for a new quantum platform, enabling the integration of quantum functionalities into electron microscopy and opening opportunities for quantum imaging and quantum sensing at the nanoscale. To realize such a platform, it is crucial to understand the degree and nature of electron--photon entanglement in cathodoluminescence (CL). However, its dependence on electron-beam properties, particularly transverse coherence, remains unclear. Here, we present a theoretical framework describing the quantum state of an electron--photon pair generated in coherent CL from a system with translational invariance in the plane perpendicular to the electron beam, as can be realized, for example, in transition radiation at a planar interface. By expressing the scattered state directly in terms of the luminescence spectrum, we evaluate the entanglement using both subsystem purity and an Einstein--Podolsky--Rosen-type criterion. These two measures enable a clear distinction among wave-like, particle-like, and classical regimes in terms of spatial and momentum entanglement in the electron--photon system. Our analysis identifies the roles of the electron's transverse and longitudinal coherence, as well as the photon's spectral width, and reveals the conditions under which strong spatial entanglement emerges. This unified perspective clarifies the nature of electron--photon quantum correlations in coherent CL and advances the development of quantum-enabled functionalities in electron microscopy.
Electron beams are an exceptional tool for probing nanophotonic systems [1]. Combining electron microscopy with external optical excitation in ultrafast transmission electron microscopes has enabled nanoscale [2,3] and attosecond phase-resolved mapping of optical near-fields [4] by stimulated inelastic scattering between electrons and light. Recently, the underlying interaction strength of this process has been increased significantly by harnessing resonant enhancement of the optical field and velocity phase matching [5]. Such an increased interaction strength also benefits the spontaneous scattering of electrons with light, thus promoting single-particle-based scattering experiments [6]. Here, we demonstrate the generation of nonclassical multiphoton states via coherent cathodoluminescence (CL) from an optical waveguide, approaching near-unity coupling in electron spectroscopy of nanophotonic systems [7]. To this end, we scatter swift electrons at the optical mode of a custom silicon nitride photonic chip. Specifically, inside of a transmission electron microscope, a beam of free electrons (100-keV kinetic energy) passes parallel to the waveguide surface in an aloof geometry (cf. Fig. 1a). The electrons can inelastically scatter with the evanescent tail of the guided optical mode, generating photons at a wavelength around 1400 nm in the fundamental quasi-TM mode, while the electrons lose multiples N of the corresponding photon energy of 0.88 eV (cf. Fig. 1b). The photons are then coupled via optical fibers to a balanced beam splitter and two single-photon avalanche diodes (SPADs), implementing a Hanbury Brown and Twiss (HBT) setup (cf. Fig. 1c). Probing the ensemble average using the 2nd-order correlation function g(2), we observe Poissonian photon statistics in accordance with the underlying coherent scattering mechanism (Fig. 1d, top). A parallel single-particle-resolved measurement using an event-based electron camera (Timepix3 ASIC) coupled to an EEL spectrometer provides information on both electron energy and arrival time. This allows us to further investigate the photon statistics of the generated light as a function of the electron energy. Using this electron-heralded HBT setup, we verify the generation of single photons following an energy loss of E = ℏω (Fig. 1d, bot), and photon pairs for double scattering events. Characterizing the electron-driven photon generation using established metrics for heralded single-photon sources, such as spontaneous parametric down-conversion (SPDC), we find an intrinsic single-photon heralding efficiency of 10% and a coincidence-to-accidental ratio > 30. This establishes a new source for electron-heralded quantum light, which may find its applications in quantum photonics. Practically, efficient electron-photon coupling and event-based detention, offers a new pathway for coincidence-enhanced electron spectroscopy of photonic materials [8]. Besides eliminating undesired and formerly unrecoverable averaging, access to the full scattering distribution of the involved particles can strongly suppress noise in ultrafast electron experiments [6]. Furthermore, for systems that can be directly pumped by single electrons, ultrafast dynamics can be studied using continuous electron beams, achieving sub-nanosecond resolution, only limited by the employed detector technology. Finally, this work represent an essential step toward quantum-enhanced electron imaging and enables the heralding of individual electrons for dose-sensitive applications. a) Electrons are scattered at an extended waveguide, generating light by coherent cathodoluminescence. b) Electron energy loss into discrete sidebands is observed, spaced by the photon energy ℏω. c) Event-based coincidence spectroscopy enables electron-heralded detection of photon number states. d) The discrete 2nd-order correlation function g(2)[q] shows Poissonian statistics for unheralded photon detection, while conditioning on an ℏω energy loss produces high-contrast single-photon states.
In electron microscopy, the pursuit of atomic-scale resolution for imaging biological [1] samples and soft-matter systems [2] is perpetually constrained by beam-induced sample degredation. While classical approaches attempt to optimize the trade-off between dose efficiency and image quality, they remain fundamentally limited by the physical interactions between electrons and the sample. Quantum technologies, however, present a transformative opportunity by enhancing information extraction per electron without increasing exposure [3], thereby breaking through classical constraints. In this work, we integrate for the first time a trapped-ion qubit into a transmission electron microscope, leveraging the strong Coulomb interaction between swift electrons and Ca⁺ ions [4], along with the precise control and readout capabilities of trapped Ca⁺ ions [5]. By harnessing quantum coherence and controlled interactions, this hybrid approach seeks to advance the capabilities of low-dose imaging, improving the analysis of radiation-sensitive samples while minimizing damage. For this purpose, we customize a transmission electron microscope to provide the required ultra-high-vacuum integrity and adapt the Ca⁺ trap design, including laser cooling and state readout/manipulation, to the geometric constraints of the microscope’s pole-piece gap.