  Since the birth of quantum optics, the measurement of quantum states of
nonclassical light has been of tremendous importance for advancement in the
field. To date, conventional detectors such as photomultipliers, avalanche
photodiodes, and superconducting nanowires, all rely at their core on linear
excitation of bound electrons with light, posing fundamental restrictions on
the detection. In contrast, the interaction of free electrons with light in the
context of quantum optics is highly nonlinear and offers exciting
possibilities. The first experiments that promoted this direction appeared over
the past decade as part of photon-induced nearfield electron microscopy
(PINEM), wherein free electrons are capable of high-order multi-photon
absorption and emission. Here we propose using free electrons for
quantum-optical detection of the complete quantum state of light. We show how
the precise control of the electron before and after its interaction with
quantum light enables to extract the photon statistics and implement full
quantum state tomography using PINEM. This technique can reach sub-attosecond
time resolutions, measure temporal coherence of any degree (e.g., g(1), g(2)),
and simultaneously detect large numbers of photons with each electron.
Importantly, the interaction of the electron with light is non-destructive,
thereby leaving the photonic state (modified by the interaction) intact, which
is conceptually different from conventional detectors. By using a pulse of
multiple electrons, we envision how PINEM quantum detectors could achieve a
single-shot measurement of the complete state of quantum light, even for
non-reproducible emission events. Altogether, our work paves the way to novel
kinds of photodetectors that utilize the ultrafast duration, high nonlinearity,
and non-destructive nature of electron-light interactions.
