PHYSICAL REVIEW LETTERS 123, 060401 (2019) 0031-9007=19=123(6)=060401 (7) 060401-1

The interaction between free electrons and light stands at the base of both classical and quantum physics, with applications in free-electron acceleration, radiation sources, and electron microscopy. Yet, to this day, all experiments involving free-electron–light interactions are fully explained by describing the light as a classical wave. Here, we observe quantum statistics effects of photons on free-electron–light interactions. We demonstrate interactions passing continuously from Poissonian to super-Poissonian and up to thermal statistics, revealing a transition from quantum walk to classical random walk on the free-electron energy ladder. The electron walker serves as the probe in non-destructive quantum detection, measuring the second order photon-correlation g(2)(0) and higher-orders g(n)(0). Unlike conventional quantum-optical detectors, the electron can perform both quantum weak measurements and projective measurements by evolving into an entangled joint-state with the photons. These findings inspire hitherto inaccessible concepts in quantum optics, including free-electron-based ultrafast quantum tomography of light.

It is a long-standing goal to create light with unique quantum properties such as squeezing and entanglement. We propose the generation of quantum light using free-electron interactions, going beyond their already ubiquitous use in generating classical light. This concept is motivated by developments in electron microscopy, which recently demonstrated quantum free-electron interactions with light in photonic cavities. Such electron microscopes provide platforms for shaping quantum states of light through a judicious choice of the input light and electron states. Specifically, we show how electron energy combs implement photon displacement operations, creating displaced-Fock and displaced-squeezed states. We develop the theory for consecutive electron-cavity interactions with a common cavity and show how to generate any target Fock state. Looking forward, exploiting the degrees of freedom of electrons, light, and their interaction may achieve complete control over the quantum state of the generated light, leading to novel light statistics and correlations.

Coherent emission of light by free charged particles is believed to be successfully captured by classical electromagnetism in all experimental settings. However, recent advances triggered fundamental questions regarding the role of the particle wave function in these processes. Here, we find that even in seemingly classical experimental regimes, light emission is fundamentally tied to the quantum coherence and correlations of the emitting particle. We use quantum electrodynamics to show how the particle’s momentum uncertainty determines the optical coherence of the emitted light. We find that the temporal duration of Cherenkov radiation, envisioned for almost a century as a shock wave of light, is limited by underlying entanglement between the particle and light. Our findings enable new capabilities in electron microscopy for measuring quantum correlations of shaped electrons. Last, we propose new Cherenkov detection schemes, whereby measuring spectral photon autocorrelations can unveil the wave function structure of any charged high-energy particle.