Weak measurement, projective measurement and quantum-to-classical transitions in electron-photon interactions
Yiming Pan, Eliahu Cohen, Ebrahim Karimi, Avraham Gover, Ido E. Kaminer, Yakir Aharonov · arXiv (Cornell University) · 2019
How does the quantum-to-classical transition of measurement occur? This question is vital for both foundations and applications of quantum mechanics. We developed a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions. We first analyze the transition from projective measurement 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 decay factor $\exp(-\Gamma^2/2)$, 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 presentation of the measurement transition from projective to weak sheds new light on the transition from quantum-to-classical electrodynamics, enabling to employ the very essence of wave-particle duality in quantum measurement for exploring and applying a variety of quantum and classical types of electron-photon interactions.