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, specifically for transition radiation. By expressing the scattered state directly via 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 between 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, leading to quantum-enabled functionalities in electron microscopy.
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, specifically for transition radiation. By expressing the scattered state directly via 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 between 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, leading to quantum-enabled functionalities in electron microscopy.
Entanglement, a key resource of emerging quantum technologies, describes correlations between particles that defy classical physics. It has been studied extensively on various platforms, but has remained elusive in electron microscopy. Transmission electron microscopes are well-established tools for materials characterisation with unparalleled spatial resolution. They provide control over the preparation and detection of high energy electrons, with largely unexploited potential in the study of many-body quantum correlations. Here, we demonstrate entanglement in electron-photon pairs generated via cathodoluminescence in a transmission electron microscope. Employing coincidence imaging techniques adapted from photonic quantum optics, we reconstruct both near- and far-field ``ghost'' images of periodic transmission masks. By measuring spatial and momentum correlations, we show a violation of the classical uncertainty bound: Δx−2Δk+2=0.502±0.047<1. Hence, we demonstrate entanglement in position and momentum -- the continuous variables at the base of most imaging methods, bridging the fields of electron microscopy and quantum optics. Our work paves the way for exploring quantum correlations in free-electron systems and their application to quantum-enhanced imaging techniques on the nanoscale.
Abstract Transmission electron microscopes (TEMs) enable atomic-scale imaging and characterisation, driving advances across fields from materials science to biology. Quantum correlations, specifically entanglement, may provide a basis for novel hybrid sensing techniques to make TEMs compatible with sensitive samples prone to radiation damage. We present a protocol to certify entanglement between electrons and photons naturally arising from certain coherent cathodoluminescence processes. Using mutually unbiased bases in position and momentum, our method allows robust, state-agnostic entanglement verification and provides a lower bound on the entanglement of formation, enabling quantitative comparisons across platforms. Simulations under experiment-inspired conditions and preliminary experimental data highlight the feasibility of implementing this approach in modern TEM systems with optical specimen access. Our work integrates photonic quantum information techniques with electron microscopy. It establishes a foundation for entanglement-based imaging at the atomic scale, offering a potential pathway to reduce radiation exposure.
Since the introduction of time-resolved direct electron detectors to transmission electron microscopy (TEM), there has been a growing interest in studying the correlations between an electron and the cathodoluminescence (CL) photons it produces [1,2,3]. Recent studies using coincidence measurements in both continuous [4] and discrete variables [5] have shown correlations that exceed the classical limits for separable states, thus demonstrating quantum entanglement between free electrons and photons. We present our continuous-variable approach [4], showing how ghost imaging [6], a method adapted from photonic quantum optics, can be used to demonstrate entanglement and even EPR-like behaviour of the joint electron- photon state. For this purpose, we generate correlated electron-photon pairs via transition radiation from 200 keV electrons passing a 50 nm monocrystalline silicon membrane. We detect the CL photons in a time-resolved manner, using a custom parabolic mirror and a single-photon counter. Employing a Timepix3 based direct electron detector we are able to determine which photons arrive in time with a corresponding electron. These electron-photon pairs exhibit precise (anti-)correlations in momentum and position. Placing a known absorptive mask in the photon beam path while measuring the electron in imaging and diffraction mode allows us to extract the joint position and momentum uncertainties of the electron–photon pair. We use these measurements to evaluate entanglement criteria such as the MGTV inequality [7] and the Reid- EPR bound [8]. We hope that these results will help to make entanglement available as a resource for electron microscopy, enabling novel measurement schemes inspired by photonic quantum optics.
Electron microscopes provide a powerful platform for exploring physical phenomena with nanoscale resolution, based on the interaction of free electrons with the excitations of a sample such as phonons, excitons, bulk plasmons, and surface plasmons. The interaction usually results in the absorption or emission of such excitations, which can be detected directly through cathodoluminescence or indirectly through electron energy loss spectroscopy (EELS). However, as we show here, the underlying interaction of a free electron and an arbitrary optical excitation goes beyond what was predicted or measured so far, due to the interplay of entanglement and decoherence of the electron-excitation system. The entanglement of electrons and optical excitations can provide new analytical tools in electron microscopy. For example, it can enable measurements of optical coherence, plasmonic lifetimes, and electronic length scales in matter (such as the Bohr radius of an exciton). We show how these can be achieved using common configurations in electron diffraction and EELS, revealing significant changes in the electron’s coherence, as well as in other quantum information theoretic measures such as purity. Specifically, we find that the purity after interaction with nanoparticles can only take discrete values, versus a continuum of values for interactions with surface plasmons. We quantify the post-interaction density matrix of the combined electron-excitation system by developing a framework based on macroscopic quantum electrodynamics. The framework enables a quantitative account of decoherence due to excitations in any general polarizable material (optical environment). This framework is thus applicable beyond electron microscopy. Particularly in electron microscopy, our work enriches analytical capabilities and informs the design of quantum information experiments with free electrons, allowing control over their quantum states and their decoherence by the optical environment.
Since the introduction of time-resolved direct electron detectors to transmission electron microscopy (TEM), there has been a growing interest in studying the correlations between an electron and the cathodoluminescence (CL) photons it produces [1,2,3]. In this contribution, we demonstrate “ghost imaging” [4], a method adapted from photonic quantum optics that leverages position or momentum correlations within electron-photon pairs for imaging. In a TEM, working at 200 keV, we generate electron-photon pairs via the process of transition radiation using a thin silicon membrane (see Fig. 1). We collect the photons using a custom-made parabolic mirror and let the photons interact with an arbitrary absorptive mask placed in the image plane of the collection system (see grating mask in Fig. 1b), thus imprinting the shape of this mask in the measured photon distribution. Using a single photon counting module and time tagger, we can match each detected photon to its emitting electron and retrieve the mask shape in the distribution of the corresponding electrons (Fig. 1e). This is remarkable, as the electron did not interact with the object; the information about the mask shape is mediated purely through the correlations between the two particles. In a recent publication [5], we employed ghost imaging in order to demonstrate electron-photon entanglement. We will present ghost imaging with considerably better spatial resolution and explain how this might allow us to show the Einstein-Podolsky-Rosen paradox using electron-photon pairs.
Quantum entanglement is central to both the foundations of quantum mechanics and the development of new technologies in information processing, communication, and sensing. Entanglement has been realised in a variety of physical systems, spanning atoms, ions, photons, collective excitations, and hybrid combinations of particles. Remarkably, however, photons and free electrons -- the quanta of light and their most elementary sources -- have never been observed in an entangled state. Here, we demonstrate quantum entanglement between free electrons and photons. We show that entanglement is produced when an electron, prepared in a superposition of two beams, passes a nanostructure and generates transition radiation in a polarisation state tied to the electron path. By implementing quantum state tomography, we reconstruct the full density matrix of the electron-photon pair, and show that the Peres-Horodecki separability criterion is violated by more than 7 standard deviations. Based on this foundational element of emerging free-electron quantum optics, we anticipate manifold developments in enhanced electron imaging and spectroscopy beyond the standard quantum limit. More broadly, the ability to generate and measure entanglement opens electron microscopy to previously inaccessible quantum observables and correlations in solids and nanostructures.