One-dimensional ghost imaging with an electron microscope: a route towards ghost imaging with inelastically scattered electrons

 In quantum mechanics, entanglement and correlations are not sporadic curiosities but ubiquitous phenomena that are at the basis of interacting quantum systems. In electron microscopy, such concepts have not yet been explored extensively. For example, inelastic scattering can be reanalyzed in terms of correlations between an electron beam and a sample. Whereas classical inelastic scattering results in a loss of coherence in the electron beam, a joint measurement performed on both the electron beam and the sample excitation could restore the coherence and “lost information.” Here, we propose to exploit joint measurement in electron microscopy to achieve a counterintuitive application of the concept of ghost imaging, which was first proposed in quantum photonics. The same approach can be applied partially in electron microscopy by performing a joint measurement between a portion of the transmitted electron beam and a photon emitted from the sample, which arrives at a bucket detector, thereby allowing the formation of a one-dimensional virtual image of an object that has not interacted directly with the electron beam. The technique is of particular interest for low-dose imaging of electron-beam-sensitive materials using a minimal radiation dose, as the object interacts with other forms of waves, such as photons or surface plasmon polaritons, rather than with the electron beam itself. We provide a theoretical description of the concept for inelastic electron-sample interactions, in which an electron excites a single quantum of a collective mode, such as a photon, a plasmon, a phonon, a magnon or any optical polariton. The excited collective mode remains correlated with the interacting electron. In optical ghost imaging, spatially-entangled photon pairs or classically-correlated photons are used to extract information (such as phase, transmission 

and birefringence) from an object through a joint measurement. In electron microscopy, a similar approach can be applied to highly correlated systems, such as electron-surface plasmon polaritons, to obtain additional information about the sample. In addition to applications in materials science, the approach can be used to shape electron wavefunctions by post-selecting a particular correlated collective mode. As long as the generated collective mode states are not determined, the quantum state of the electron beam is a maximally mixed state. The approach could be used to broaden the range of applications of electron microscopy, as it enables a sample to be imaged with the “eyes” of a different probe, e.g., a plasmon polariton that originates in the material. In a broader sense, aside from achieving ghost or interaction-free imaging, the possibility to exploit quantum coherent effects is important for developing quantum imaging techniques in electron microscopy.