Delay in Atomic Photoionization

We analyze the time delay between emission of photoelectrons from the outer valence $ns$ and $np$ subshells in noble gas atoms following absorption of an attosecond extreme ultraviolet pulse. Various processes such as elastic scattering of the photoelectron on the parent ion and many-electron correlation affect the apparent “time zero” when the photoelectron leaves the atom. This qualitatively explains the time delay between photoemission from the $2s$ and $2p$ subshells of Ne as determined experimentally by attosecond streaking [Science 328, 1658 (2010)]. However, with our extensive numerical modeling, we were only able to account for less than half of the measured time delay of $21\pm 5\mathrm{as}$. We argue that the extreme ultraviolet pulse alone cannot produce such a large time delay and it is the streaking IR field that is most likely responsible for this effect.

Figure 1

Top: The norm of the wave packets $N(t)$ (scaled arbitrarily) emitted from the $2s$ and $2p$ subshells is plotted as a function of time with the red solid and green dashed lines, respectively. The XUV pulse is overplotted with the black dotted line. In the inset, the norm variation $[N(t)-N(T_1)]/N(T_1)$ is shown on an expanded time scale near the pulse end. Bottom: The crest position of the $2s$ and $2p$ wave packets is shown with the same line styles. The crest position after the pulse end is fitted with the straight line, which corresponds to the free propagation. In the inset, extrapolation of the free propagation inside the atom is shown.

Figure 2

Top: Expansion coefficients $|a_{kl}{|}^2$ plotted versus the photoelectron energy $E_k=k^2/2$, which is expressed in eV. Middle: The HF scattering phases. Bottom: Phases of the RPAE dipole matrix elements $\arg [D_{\lambda }(k)]$.