Programming Coherent and Quantum Light with a Free-Electron Wavepacket

The pursuit of compact, programmable light sources with high coherence and spectral purity hinges on establishing a precise set of phase relationships in light-matter interactions. Here, we demonstrate that the quadratic dispersion of freely propagating electron wavepacket serves as a programmable quantum medium. Prepared in a coherent momentum-state ladder via a single laser interaction, the electron subsequently undergoes deterministic phase evolution during free propagation-an intrinsic process that compiles its quantum state into two distinct emission channels. This mechanism, quantified by a quantum bunching factor, enables: (i) Talbot-resonant bunching, where the electron density self-structures into sub-cycle combs with tunable harmonic selectivity, and (ii) coherent phase transfer of the programmed quadratic phase to light, generating nonclassical photon states such as multi-component Schrodinger cat states via measurement-conditioned interaction. This quadratic-phase programming establishes a versatile platform for on-demand quantum state synthesis, bridging beam engineering with electron wavefunction shaping for compact quantum light sources, coherent radiation control, and scalable quantum information processing.