  The coherent control of electron beams and ultrafast electron wave packets
dynamics have attracted significant attention in electron microscopy as well as
in atomic physics. In order to unify the conceptual pictures developed in both
fields, we demonstrate the generation and manipulation of tailored electron
orbital angular momentum (OAM) superposition states either by employing
customized holographic diffraction masks in a transmission electron microscope
or by atomic multiphoton ionization utilizing pulse-shaper generated
carrier-envelope phase stable bichromatic ultrashort laser pulses. Both
techniques follow similar physical mechanisms based on Fourier synthesis of
quantum mechanical superposition states allowing the preparation of a broad set
of electron states with uncommon symmetries. We describe both approaches in a
unified picture based on an advanced spatial and spectral double slit and point
out important analogies. In addition, we analyze the topological charge and
discuss the control mechanisms of the free-electron OAM superposition states.
Their generation and manipulation by phase tailoring in transmission electron
microscopy and atomic multiphoton ionization is illustrated on a 7-fold
rotationally symmetric electron density distribution.
