  The short de Broglie wavelength and strong interaction empower free electrons
to probe scattering and excitations in materials and resolve the structure of
biomolecules. Recent advances in using nanophotonic structures to mediate
bilinear electron-photon interaction have brought novel optical manipulation
schemes to electron beams, enabling high space-time-energy resolution electron
microscopy, quantum-coherent optical modulation, attosecond metrology and pulse
generation, transverse electron wavefront shaping, dielectric laser
acceleration, and electron-photon pair generation. However, photonic
nanostructures also exhibit nonlinearities, which have to date not been
exploited for electron-photon interactions. Here, we report the interaction of
electrons with spontaneously generated Kerr nonlinear optical states inside a
continuous-wave driven photonic chip-based microresonator. Optical parametric
processes give rise to spatiotemporal pattern formation, or dissipative
structures, corresponding to coherent or incoherent optical frequency combs. By
coupling such microcombs in situ to electron beams, we demonstrate that
different dissipative structures induce distinct fingerprints in the electron
spectra and Ramsey-type interference patterns. In particular, using
spontaneously formed femtosecond temporal solitons, we achieve ultrafast
temporal gating of the electron beam without the necessity of a pulsed laser
source or a pulsed electron source. Our work elucidates the interaction of free
electrons with a variety of nonlinear dissipative states, demonstrates the
ability to access solitons inside an electron microscope, and extends the use
of microcombs to unexplored territories, with ramifications in novel ultrafast
electron microscopy, light-matter interactions driven by on-chip temporal
solitons, and ultra-high spatiotemporal resolution sampling of nonlinear
optical dynamics and devices.
