Tunable quantum light by modulated free electrons

Nonclassical states of light are fundamental in various applications, spanning quantum computation to enhanced sensing. Fast free electrons, which emit light into photonic structures through the mechanism of spontaneous emission, represent a promising platform for generating diverse types of states. Indeed, the intrinsic connection between the input electron wave function and the output light field suggests that electron-shaping schemes, based on light-induced scattering, facilitate their synthesis. In this article, we present a theoretical framework capable of predicting the final optical density matrix emitted by a generic N-electron state that can also account for post-sample energy filtering. By using such a framework, we study the modulation-dependent fluctuations of the N-electron emission and identify regions of superradiant scaling characterized by Poissonian and super-Poissonian statistics. In this context, we predict that high-N modulated electron pulses can yield a tenfold shot-noise suppression in the estimation of the electron-light coupling when the output radiation intensity is analyzed. In the single-electron case, we show how coherent states with nearly 90 % purity can be formed by pre-filtering a portion of the spectrum after modulation, and how non-Gaussian states are generated after a precise energy measurement. Furthermore, we present a strategy combining a single-stage electron modulation and post-filtering to harness tailored light states, such as squeezed vacuum, cat, and triangular cat states, with fidelities close to 100 %.