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The fundamental interaction between free electrons and light stands at thebase of both classical and quantum physics, with applications in free-electronacceleration, radiation sources, and electron microscopy. Yet, to this day, allexperiments involving free-electron light interactions are fully explained bydescribing the light as a classical wave, disregarding its quantum nature.Here, we observe quantum statistics effects of photons on free-electron-lightinteractions. We demonstrate interactions passing continuously from Poissonianto super-Poissonian and up to thermal statistics, unveiling a surprisingmanifestation of Bohr's Correspondence Principle: the transition from quantumwalk to classical random walk on the free-electron energy ladder. The electronwalker serves as the probe in non-destructive quantum detection, measuring thephoton-correlation ${g^{(2)} (0)}$ and higher-orders ${g^{(n)} (0)}$. Unlikeconventional quantum-optical detectors, the electron can perform both quantumweak measurements and projective measurements by evolving into an entangledjoint-state with the photons. Our findings suggest free-electron-basednon-destructive quantum tomography of light, and constitute an important steptowards combined attosecond-temporal and sub-A-spatial resolution microscopy.

Imprinting the quantum statistics of photons on free electrons