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Free electron vortices (FEVs) generated by multiphoton ionization (MPI) with ultrashort laser pulses have attracted significant attention due to their varied symmetries and unusual topological properties. We study two physical mechanisms of coherent control in atomic MPI with bichromatic polarization-shaped femtosecond laser pulses which give rise to the rich variety of FEVs. In the experiments, we combine pulse shaping of a carrier-envelope phase-stable supercontinuum with photoelectron tomography to generate and reconstruct three-dimensional photoelectron momentum distributions (PMDs). Simultaneous measurements of energetically separated photoelectrons from intraband and interband interference in a single PMD allow us to compare phase and polarization control of the angular distributions by both mechanisms. We investigate phase control in three scenarios: first, counterrotating circularly polarized pulses are employed to contrast the phase-insensitive angular momentum eigenstate created by intraband interference via frequency mixing with the phase-sensitive c 7 rotationally symmetric FEV from pure interband interference of two single-color ionization pathways. In the second scenario, we use orthogonal linearly polarized pulses to compare the phase control properties of a six-lobed angular momentum wave packet from intraband interference to those of a complex shaped interband PMD in the presence of phase fluctuations. Finally, we demonstrate phase control of a photoelectron hologram from mixed interband interference. In a (3 + 1) resonance enhanced MPI scheme, the red pump pulse induces a bound electron wave packet probed by the time-delayed blue pulse. The latter simultaneously creates a reference wave packet by three-photon ionization to form the photoelectron hologram. Rotation of the hologram with c 1 or c 5 rotational symmetry maps the time evolution of the bound wave packet. To analyze our results, we develop analytical expressions for the wave functions of intraband and interband interference in perturbative non-resonant MPI. The experiments are complemented with two-dimensional TDSE simulations to follow the FEV formation dynamics and to validate the physical pictures.

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We present the generation, optimization and full control of superimposed optical vortices (SOVs) using tailored computer generated holograms by utilizing a 2D liquid crystal spatial light modulator. To perform full radial and azimuthal control over the targeted SOVs we apply spatial amplitude modulation via window functions as well as radial and azimuthal phases, encoded in the diffraction mask. In particular we discuss the influence of spatial linear and quadratic radial phases, which is supplemented by an analytical description. The developed formalism further permits the direct shaping in k-space which is highlighted by the radial and azimuthal confinement of SOV states. Our technique enables full real-time control over the spatial structure, the symmetry and azimuthal orientation of the generated SOVs in a common path geometry, which is useful in the context of optical information transfer. We also study the topological properties, i.e. the orbital current S ⃗ O to determine the topological charge ℓ of the generated SOVs.