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.
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.
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.
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.
Correlated photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments, two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated photon ghost imaging experiments have scanned a single-pixel detector through the field of view to obtain spatial information. However, scanning leads to poor sampling efficiency, which scales inversely with the number of pixels, N , in the image. In this work, we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far field of the photon pair source, taking advantage of the Einstein–Podolsky–Rosen-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.
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.
Correlated-photon imaging, popularly known as ghost imaging, is a technique whereby an image is formed from light that has never interacted with the object. In ghost imaging experiments two correlated light fields are produced. One of these fields illuminates the object, and the other field is measured by a spatially resolving detector. In the quantum regime, these correlated light fields are produced by entangled photons created by spontaneous parametric down-conversion. To date, all correlated-photon ghost-imaging experiments have scanned a single-pixel detector through the field of view to obtain the spatial information. However, scanning leads to a poor sampling efficiency, which scales inversely with the number of pixels, N, in the image. In this work we overcome this limitation by using a time-gated camera to record the single-photon events across the full scene. We obtain high-contrast images, 90%, in either the image plane or the far-field of the photon pair source, taking advantage of the EPR-like correlations in position and momentum of the photon pairs. Our images contain a large number of modes, >500, creating opportunities in low-light-level imaging and in quantum information processing.
Ghost imaging was first demonstrated with entangled photon pairs and well-known for its peculiar properties. The signal beam that illuminates the object possesses no spatial resolution, whereas the reference beam, which never interacts with the object, is spatially resolved. Either beam alone cannot retrieve the image, which can only be obtained when the signal and reference beams are correlated. Here we will report a ghost imaging experiment with even more peculiar properties, in which the image can be reconstructed when no photon interacts with the object or even no photon in neither signal nor reference beam. All the photons interacted with the object are discarded. Only the time bins with zero photon are employed to retrieve the image, a process referred to as "ghost imaging with zero photons" hereafter. The reason why ghost image can be retrieved with zero photons is jointly determined by photon-number projection measurement and photon statistics of thermal light. The results are helpful to resolve the debate on the physics of ghost imaging and understand the relation between quantum and classical correlations.