Introduction to attosecond time-delays in photoionization

TL;DR

This tutorial explains the theoretical basis of attosecond time-delays in photoionization experiments, highlighting measurement-induced effects and how to distinguish them from true single-photon ionization delays.

Contribution

It provides analytical expressions to separate measurement artifacts from genuine photoionization delays in attosecond experiments.

Findings

Identification of the continuum-continuum phase as a measurement artifact.

Analytical methods to extract true photoionization delays.

Clarification of the role of laser-stimulated transitions in delay measurements.

Abstract

This tutorial presents an introduction to the interaction of light and matter on the attosecond timescale. Our aim is to detail the theoretical description of ultra-short time-delays, and to relate these to the phase of extreme ultraviolet (XUV) light pulses and to the asymptotic phase-shifts of photoelectron wave packets. Special emphasis is laid on time-delay experiments, where attosecond XUV pulses are used to photoionize target atoms at well-defined times, followed by a probing process in real time by a phase-locked, infrared laser field. In this way, the laser field serves as a "clock" to monitor the ionization event, but the observable delays do not correspond directly to the delay associated with single-photon ionization. Instead, a significant part of the observed delay originates from a measurement induced process, which obscures the single-photon ionization dynamics. This artifact is traced back to a phase-shift of the above-threshold ionization transition matrix element, which we call the continuum-continuum phase. It arises due to the laser-stimulated transitions between Coulomb continuum states. As we shall show here, these measurement-induced effects can be separated from the single-photon ionization process, using analytical expressions of universal character, so that eventually the attosecond time-delays in photoionization can be accessed.