Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy

Ultrafast electron and X-ray imaging and spectroscopy are the basis for an ongoing revolution in the understanding of dynamical atomic-scale processes in matter. The underlying technology relies heavily on laser science for the generation and characterization of ever shorter pulses. Recent findings suggest that ultrafast electron microscopy with attosecond-structured wavefunctions may be feasible. However, such future technologies call for means to both prepare and fully analyse the corresponding free-electron quantum states. Here, we introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond electron pulse trains. Phase-locked optical fields coherently control the electron wavefunction along the beam direction. We establish a new variant of quantum state tomography-'SQUIRRELS'-for free-electron ensembles. The ability to tailor and quantitatively map electron quantum states will promote the nanoscale study of electron-matter entanglement and new forms of ultrafast electron microscopy down to the attosecond regime.