Weak measurements and quantum-to-classical transitions in free electron-photon interactions

How does the quantum-to-classical transition of measurement occur?This question is vital for both foundations and applications of quantum mechanics.Here,we develop a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions and then experimentally test it.We first analyze the transition from projective to weak measurement in generic light-matter interactions and show that any classical electron-laserbeam interaction can be represented as an outcome of weak measurement.In particular,the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement.A universal factor,exp(-Γ^(2)=2),quantifies the measurement regimes and their transition from quantum to classical,whereΓcorresponds to the ratio between the electron wavepacket size and the optical wavelength.This measurement-based formulation is experimentally verified in both limits of photon-induced near-field electron microscopy and the classical acceleration regime using a DLA.Our results shed new light on the transition from quantum to classical electrodynamics,enabling us to employ the essence of the wave-particle duality of both light and electrons in quantum measurement for exploring and applying many quantum and classical light-matter interactions.