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

Yiming Pan, Eliahu Cohen, Ebrahim Karimi, Avraham Gover, Norbert Schönenberger, Tomáš Chlouba, Kangpeng Wang, Saar Nehemia, Peter Hommelhoff, Ido Kaminer, Yakir Aharonov

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 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, where Γ 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 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.

Original languageEnglish
Article number267
JournalLight: Science and Applications
Issue number1
StatePublished - 8 Nov 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s).


We thank Eilon Poem for helpful discussions, and we also thank Zhaopin Chen and Qingqing Cheng for their help in improving the figures. The work was supported in part by the Israel Innovation Authority Grants No. 70002 and 73795, FQXi Grant No. 224321, Pazy Foundation, Israeli Ministry of Science and Technology, Canada Research Chair and Ontario’s Early Researcher Award, DIP (German-Israeli Project Cooperation), ISF (Israel Science Foundation) Grant No. 00010001000, I-CORE–Israel Center of Research Excellence program of the ISF, by the Crown Photonics Center, Gordon, and Betty Moore Foundation grant 4744 (ACHIP), and ERC Advanced Grant 884217 (AccelOnChip).

FundersFunder number
Betty Moore Foundation4744
Crown Photonics Center
Israeli Ministry of Science and Technology, Canada Research Chair
European Research Council884217
Israel Science Foundation00010001000
Israeli Centers for Research Excellence
PAZY Foundation
Israel Innovation Authority70002, 224321, 73795


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