Attosecond Electron Pulse Trains and Quantum State Reconstruction in Ultrafast Transmission Electron Microscopy

We introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond pulse trains for electron microscopy. Specifically, we employ phase-locked single-color and two-color optical fields to coherently control the electron wave function along the beam direction. We establish a new variant of quantum state tomography - "SQUIRRELS" - to reconstruct the density matrices of free-electron ensembles and their attosecond temporal structure. The ability to tailor and quantitatively map electron quantum states will promote the nanoscale study of electron-matter entanglement and the development of new forms of ultrafast electron microscopy and spectroscopy down to the attosecond regime.