Theory of attosecond delays in laser-assisted photoionization
We study the temporal aspects of laser-assisted extreme ultraviolet (XUV) photoionization using attosecond pulses of harmonic radiation. The aim of this paper is to establish the general form of the phase of the relevant transition amplitudes and to make the connection with the time-delays that have been recently measured in experiments. We find that the overall phase contains two distinct types of contributions: one is expressed in terms of the phase-shifts of the photoelectron continuum wavefunction while the other is linked to continuum--continuum transitions induced by the infrared (IR) laser probe. Our formalism applies to both kinds of measurements reported so far, namely the ones using attosecond pulse trains of XUV harmonics and the others based on the use of isolated attosecond pulses (streaking). The connection between the phases and the time-delays is established with the help of finite difference approximations to the energy derivatives of the phases. This makes clear that the observed time-delays is a sum of two components: a one-photon Wigner-like delay and an universal delay that originates from the probing process itself.