  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.
