Towards atomic-resolution quantum measurements with coherently-shaped free electrons

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 electron-qubit interactions in materials, we show how the energy spectrum of laser-shaped electrons enables measuring the qubit Block-sphere state and decoherence time (T2). 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.