Demonstration of weak measurements, projective measurements, and quantum-to-classical transitions in ultrafast 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-laser-beam interaction can be represented as an outcome of a 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 quantifies the measurement regimes and their transition from quantum to classical, where Gamma corresponds 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 dielectric laser accelerator. Our results shed new light on the transition from quantum to classical electrodynamics, enabling to employ the essence of wave-particle duality of both light and electrons in quantum measurement for exploring and applying many quantum and classical light-matter interactions.