Diagrammatic approach to attosecond delays in photoionization

We study laser-assisted photoionization by attosecond pulses using a time-independent formalism based on diagrammatic many-body perturbation theory. Our aim is to provide an ab initio route to the “delays” for this above-threshold ionization process, which is essential for a quantitative understanding of attosecond metrology. We present correction curves for characterization schemes of attosecond pulses, such as “streaking,” that account for the delayed atomic response in ionization from neon and argon. We also verify that photoelectron delays from many-electron atoms can be measured using similar schemes if, instead, the so-called continuum-continuum delay is subtracted. Our method is general and it can be extended also to more complex systems and additional correlation effects can be introduced systematically.

Figure 1

(a) Photon picture of laser-assisted photoionization from the outermost orbital of argon ($3p$). (b) Phase (solid) and normalized probability (dashed) calculated from the two-photon matrix elements. The thick curves correspond to absorption of a probe photon ($A$), while the thin curves correspond to emission of a probe photon ($E$). The probe photon $\omega$ is $1.55$ eV.

Figure 2

(a) Absorption of XUV (pump) and IR (probe) photons by the photoelectron. (b) Direct and (c) exchange interactions between the photoelectron and the remaining electrons in the core. (d)–(g) Ground-state correlation interactions. The XUV photon and the IR photon are indicated by the fast wiggle and slow wiggle, respectively, while the interaction between the photoelectron and the remaining hole in the atom is a dashed line.

Figure 3

(a) Typical outgoing PWF, following absorption of one XUV photon, with real (thin red) and imaginary (thick blue) components shown. The damping of the PWF for $r>R_C=100$ Bohr radii is due to the exterior complex scaled basis set. (b) Radial integration path used to evaluate the dipole transition in Eq. (2). Note that $R<R_C$, which implies that the “break point” occurs in the unscaled region of space.

Figure 4

Atomic delays from the outermost orbitals of (a) neon and (b) argon atoms using a probe of 1.55 eV. The data including interorbital correlation is outlined, while the single-active orbital approximation is marked by small black symbols. HF ionization thresholds are shown.

Figure 5

The exact continuum-continuum delay is determined for all outermost $n$-shell electrons in neon and argon as ${\tau }_{\text{CC}}\equiv {\tau }_A-{\tau }_W$ using Eq. (1). The good agreement with the analytical curve (CC) from Ref. [17] shows that a meaningful separation of the delays can be made for atomic many-electron systems.