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How does the quantum-to-classical transition of measurement occur? Thisquestion is vital for both foundations and applications of quantum mechanics.Here, we develop a new measurement-based framework for characterizing theclassical and quantum free electron-photon interactions and then experimentallytest it. We first analyze the transition from projective to weak measurement ingeneric light-matter interactions and show that any classicalelectron-laser-beam interaction can be represented as an outcome of a weakmeasurement. In particular, the appearance of classical point-particleacceleration is an example of an amplified weak value resulting from weakmeasurement. A universal factor quantifies the measurement regimes and theirtransition from quantum to classical, where Gamma corresponds to the ratiobetween the electron wavepacket size and the optical wavelength. Thismeasurement-based formulation is experimentally verified in both limits ofphoton-induced near-field electron microscopy and the classical accelerationregime using a dielectric laser accelerator. Our results shed new light on thetransition from quantum to classical electrodynamics, enabling to employ theessence of wave-particle duality of both light and electrons in quantummeasurement for exploring and applying many quantum and classical light-matterinteractions.

Demonstration of weak measurements, projective measurements, and quantum-to-classical transitions in ultrafast free electron-photon interactions