Zeptosecond Electron Pulse Train and Ultrafast Coherent Control of Quantum States via Multiphoton Inelastic Cherenkov Diffraction

We investigate the quantum dynamics of fermionic particles interacting with a laser field in a gaseous medium, in the regime of inelastic diffraction scattering on the phase lattice of a slowed travelling wave, below the critical field of induced Cherenkov process. Using a relativistic quantum kinetic framework and numerical solutions of Dirac equation in the rest frame of the slowed wave, we analyze the evolution of actual electron wave packets and beams at the inelastic scattering on the actual laser pulses of finite duration. Our results reveal coherent multiphoton exchange involving up to $10^{4}$ photons and the emergence of attosecond-zeptosecond electron sub-bunches after the free-space propagation. The pulse compression by such mechanism is robust to laser pulse duration but sensitive to the initial momentum spread of the particles/beams. We propose a mechanism to achieve electron pulses in zeptosecond time scales with potentiality for ultrafast coherent control of quantum states that opens new avenues in high-resolution temporal structuring of electron beams for time-resolved quantum technologies and attosecond-zeptosecond science, as well as, for application in high-resolution electron microscopy.