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The coherent control of electron beams and ultrafast electron wave packet 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.

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.

We present a three-dimensional (3D) photoelectron wave packet holography scheme based on polarization-tailored trichromatic femtosecond laser pulses for the determination of quantum phases in atomic multiphoton ionization (MPI). Experimentally, we combine supercontinuum polarization pulse shaping with photoelectron tomography for the reconstruction of the 3D photoelectron momentum distribution (PMD). To demonstrate the 3D photoelectron holography scheme, we superimpose a sculptured wave packet encoding a relative continuum phase with a reference wave packet. In particular, we create a sculptured angular momentum superposition wave packet by (2+1) resonance-enhanced MPI of potassium atoms using a counter-rotating circularly polarized bichromatic pulse sequence. The sculptured wave packet, consisting of states with different orbital angular momentum quantum numbers, interferes with the reference wave packet generated by direct 3-photon ionization with a circularly polarized pulse of the third color. Depending on the circularity of the reference pulse, interference of both wave packets gives rise to 3D photoelectron holograms with c 2 or c 4 rotational symmetry in the laser polarization plane, i.e., in the azimuthal direction. In the polar direction, the azimuthal interference pattern undergoes a phase-shift revealing the relative quantum phase between the p- and f-type continuum partial waves in the sculptured wave packet. We determine the relative continuum phase by fitting the parameters of an analytical model of the hologram to the measured 3D PMD and confirm the result by direct extraction of the continuum phase difference from the polar-angle-dependent azimuthal phase-shift of the photoelectron angular distribution.

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