Free electrons provide a powerful tool to probe material properties at atomic-scale spatial resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free electron wavefunctions using laser pulses. It would be of great importance if one could combine the spatial resolution of electron probes with the ability of laser pulses to probe coherent phenomena in quantum systems. To this end, we propose a novel technique that leverages free electrons that are coherently-shaped by laser pulses to measure quantum coherence in materials. Developing a quantum theory of electronqubit interactions in materials, we show how the energy spectrum of laser-shaped electrons enables measuring the qubit Block-sphere state and decoherence time (𝑻 𝟐 ).Finally, we present how such shaped electrons can detect and quantify superradiance from multiple qubits. Our scheme could be implemented in an ultrafast transmission electron microscope (UTEM), opening the way towards the full characterization of the state of quantum systems at atomic-scale resolution.

Entanglement of photons is a fundamental feature of quantum mechanics, which stands at the core of quantum technologies such as photonic quantum computing, communication, and sensing. An ongoing challenge in all these is finding an efficient and controllable mechanism to entangle photons. Recent experimental developments in electron microscopy enable to control the quantum interaction between free electrons and light. Here, we show that free electrons can create entanglement and bunching of light. Free electrons can control the second-order coherence of initially independent photonic states, even in spatially separated cavities that cannot directly interact. Free electrons thus provide a type of optical nonlinearity that acts in a nonlocal manner, offering a way of heralding the creation of entanglement. Intriguingly, pre-shaping the electron’s wavefunction provides the knob for tuning the photonic quantum correlations. The concept can be generalized to entangle not only photons but also photonic quasiparticles such as plasmon-polaritons and phonons.

Dielectric laser accelerators (DLAs) are fundamentally based on the interaction of photons with free electrons, where energy and momentum conservation are satisfied by mediation of a nanostructure. In this scheme, the photonic nanostructure induces near-fields which transfer energy from the photon to the electron, similar to the inverse-Smith–Purcell effect described in metallic gratings. This, in turn, may provide ground-breaking applications, as it is a technology promising to miniaturize particle accelerators down to the chip scale. This fundamental interaction can also be used to study and demonstrate quantum photon-electron phenomena. The spontaneous and stimulated Smith–Purcell effect and the photon-induced near-field electron-microscopy (PINEM) effect have evolved to be a fruitful ground for observing quantum effects. In particular, the energy spectrum of the free electron has been shown to have discrete energy peaks, spaced with the interacting photon energy. This energy spectrum is correlated to the photon statistics and number of photon exchanges that took place during the interaction. We give an overview of DLA and PINEM physics with a focus on electron phase-space manipulation.

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