We investigate the coherent control of the photo-electron angular distribution in bichromatic atomic ionization. Neon is selected as target since it is one of the most popular systems in current gas-phase experiments with free-electron lasers (FELSs). In particular, we tackle practical questions, such as the role of the fine-structure splitting, the pulse length, and the intensity. Time-dependent and stationary perturbation theory are employed, and we also solve the time-dependent Schrodinger equation in a single-active electron model. We consider neon ionized by a FEL pulse whose fundamental frequency is in resonance with either $2p-3s$ or $2p-4s$ excitation. The contribution of the non-resonant two-photon process and its potential constructive or destructive role for quantum coherent control is investigated.
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