Analytical estimates of attosecond streaking time delay in photoionization of atoms

Abstract

We present estimates of the attosecond streaking delay in photoionization of atoms based on an analytical formula. In the derivation of the formula we use that the streaking delay depends on the propagation of the photoelectron over a finite range in space. We find that the analytical estimates agree well with results of ab-initio calculations. Application of the formula provides insights into the influence of the streaking field on the field-free time delay in the analysis of streaking measurements.

Attosecond Streaking Time Delays: Finite-Range Interpretation and Applications

“…2(E asym − V(r)) and E asym is the asymptotic kinetic energy of the photoelectron. It has been found [20][21][22][23] that the classical estimates for the streaking time delays remain approximately constant while varying t i over one field cycle. However, we point out that, independent of the representation of the streaking time delay as integral (Equation (7)) or in its finite-difference approximation (Equation (8)), these classical predictions diverge for E s = 0 and, hence, are not applicable at the corresponding times t i .…”

“…Based on the interpretation that the streaking time delay is accumulated by the photoelectron over a finite time only, and hence can be understood as a probe of the (long-range) atomic potential over a finite distance, one can proceed to consider cut-off potentials for a further analysis of the time delay. In order to do so, one may assume a classical-quantum correspondence for the field-free time delay, in which the classical estimate, Equation 8, is decomposed in a sum as [23]:…”

“…This has the advantage that the corresponding phase-shift in the wavefunction is finite and one does not encounter conceptual issues like the divergence of the logarithmic term in a Coulomb potential. It has been shown [23] that each of the terms in Equation (11) can be evaluated analytically for an atom using standard methods, such as the distorted Born approximation and the single-active-electron approximation. Estimates based on the analytical formula (dashed lines, Equation 11) are found to be in good agreement with the results of ab initio simulations and those of classical calculations for the streaking time delay (see Figure 2, [23]).…”

“…It has been shown [23] that each of the terms in Equation (11) can be evaluated analytically for an atom using standard methods, such as the distorted Born approximation and the single-active-electron approximation. Estimates based on the analytical formula (dashed lines, Equation 11) are found to be in good agreement with the results of ab initio simulations and those of classical calculations for the streaking time delay (see Figure 2, [23]). This validation puts us in the position to use this analytical formula for further analysis of certain aspects of the streaking time delay.…”

“…As mentioned in the Introduction, the streaking time delay is often represented as a sum of the Wigner-Smith time delay and a Coulomb-laser coupling term. To gain further insights into this interpretation, the analytical formula, Equation 11, has been used to study the effect of the streaking field on each of the three contributions (short-range, Coulomb phase and logarithmic) [23]. The absolute difference of the results obtained for each contribution with and without considering the prefactor E s (t j )/E s (t i ) in Equation 11is shown as a function of XUV photon energy in Figure 4.…”