Photoelectron -- residual-ion entanglement in streaked shake-up ionization of helium

Streaked photoelectron emission spectra access the correlated dynamics of photoelectrons and residual target electrons with attosecond temporal resolution. We calculated ab initio single-ionization spectra for photoemission from helium atoms by co-linearly polarized ultrashort XUV and assisting few-femtosecond IR pulses. Distinguishing direct and shake-up ionization resulting in ground-state and excited (n=2,3) He+ residual ions, respectively, we examined the effects of the correlated photoemission dynamics on the photoelectron phase-accumulation as a function of the observable photoelectron detection direction and kinetic energy, and XUV-IR pulse delay. We tracked the dynamical evolution of the residual ion in relative streaked photoemission delays and found dominant contributions for shake-up emission from the residual ion - photoelectron interaction. These are in very good and fair agreement, respectively, for n=2 and n=3 shake-up photoemission along the pulse-polarization directions, with previous experimental and theoretical investigations [Ossiander et. al. 2017] and reveal a strong photoemission-direction dependence for shake-up ionization due to the coupling between the photoelectron and evolving residual-ion charge distribution in the IR-laser field.