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The coherent control of electron beams and ultrafast electron wave packetsdynamics have attracted significant attention in electron microscopy as well asin atomic physics. In order to unify the conceptual pictures developed in bothfields, we demonstrate the generation and manipulation of tailored electronorbital angular momentum (OAM) superposition states either by employingcustomized holographic diffraction masks in a transmission electron microscopeor by atomic multiphoton ionization utilizing pulse-shaper generatedcarrier-envelope phase stable bichromatic ultrashort laser pulses. Bothtechniques follow similar physical mechanisms based on Fourier synthesis ofquantum mechanical superposition states allowing the preparation of a broad setof electron states with uncommon symmetries. We describe both approaches in aunified picture based on an advanced spatial and spectral double slit and pointout important analogies. In addition, we analyze the topological charge anddiscuss the control mechanisms of the free-electron OAM superposition states.Their generation and manipulation by phase tailoring in transmission electronmicroscopy and atomic multiphoton ionization is illustrated on a 7-foldrotationally symmetric electron density distribution.

Orbital angular momentum superposition states in transmission electron microscopy and bichromatic multiphoton ionization