Recent developments in laser technology, in particular the advances in high-harmonic generation,\ enable the generation of ultrashort extreme ultraviolet (XUV) pulses with attosecond (1\ as = 10^{-18} s) duration. Such tools open the opportunity to study electron dynamics in atoms\ and molecules on its intrinsic time scale. As an example, the attosecond streaking technique was\ recently applied to time resolve the photoionization process in atomic and solid systems. In this\ technique, an isolated attosecond XUV pulse that ionizes the electron in the target system, is superimposed\ with a few-cycle streaking pulse (usually of near-infrared wavelengths). The streaking\ pulse modulates the final momentum (or energy) of the photoelectron. The measured streaking\ trace, i.e., the final momentum (or energy) as a function of the relative delay between these two\ pulses, contains time information of the photoionization process. By comparing two streaking\ traces measured for photoionization from the 2s and 2p orbitals in a neon atom, Schultze et al.\ [Science 328, 1658 (2010)] found a temporal offset of 21 {\textpm} 5 as between them and interpreted this\ value as the time delay between photoionization from the 2s and 2p orbitals. This experiment has\ initiated a debate among theoreticians, in particular about the origin of the measured time delay. A\ correct interpretation of the delay is extremely important for our understanding of the attosecond\ streaking technique and an exact analysis of time resolved measurements of this and other ultrafast\ processes.

In this thesis we systematically study the attosecond time delays in photoionization using\ numerical simulations. We first propose a new method, based on the fundamental definition of a\ time delay, to theoretically study the photoionization process induced by an XUV pulse from a time-dependent\ perspective. We then turn to analyze the time delays measured in streaking experiments.\ Our results show that for single-photon ionization the observed streaking time delay arises from\ the finite-range propagation of the photoelectron in the coupled field of the ionic potential and the\ streaking pulse. Consequently, we conclude that the photon absorption occurs instantaneously atthe center of the XUV pulse, i.e., with no time delay. Our analysis further reveals that the streaking\ time delay can be interpreted as a finite sum of piecewise field-free time delays weighted by the\ relative instantaneous streaking field strength and provides itself as a useful tool for imaging the\ presence of an additional potential located at a distance from the ionic core. We finally extend our\ time delay studies to the two-photon ionization process and show that the absorption time delay is\ significantly different for nonresonant and resonant two-photon ionization. Our results imply that\ the absorption of two photons in the nonresonant case occurs instantaneously, without time delay,\ at the center of the XUV pulse. However, in the resonant scenario we find a substantial absorption\ time delay that changes linearly with the duration of the XUV pulse. Our further theoretical\ analysis shows that this absorption time delay can be related to the phase acquired by the electron\ during its transition from the initial ground state to the continuum.

}, author = {J. Su} }