Analytical model for attosecond time delays and Fano's propensity rules in the continuum

Extracting single photoionization time delays associated with atomic (or molecular) species from attosecond timescale two-photon experiments usually relies on the theoretical description of continuum-continuum transitions. The available models for those processes predict a universal phase contribution, independent of the angular quantum numbers of final states. However, a recent experimental-theoretical study [Fuchs et al., Optica 7, 154 (2020)] determined a sizable time-delay dependence on the angular momentum of near-threshold photoelectrons. In this paper, we present an analytical model for the two-photon two-color transition matrix amplitudes that reproduces the phase dependence on the angular quantum number of final states. Finally, we show that our analytical model can also describe the generalized Fano's propensity rules [Busto et al., Phys. Rev. Lett. 123, 133201 (2019)] for laser-assisted photoionization.

Figure 1

Schematic representation of pathways contributing to consecutive dressed harmonic lines and the sideband in between. For low IR intensities, dressed harmonic lines are mainly populated by transitions from ground state to continuum states, triggered by the absorption of a single photon with energy ${\mathrm{\Omega }}_{\pm }=(2q\pm 1){\omega }_0$ from the attosecond pulse train. The interaction of these primary photoelectron distributions with the IR gives rise to the sidebands. Time-reversed contributions, where the IR photon is absorbed or emitted first, are not shown here.

Figure 2

Dependence of cc phases on photoelectron kinetic energy, as obtained from different methods for hydrogen atoms. Empty circles $(L=0)$ and squares $(L=2)$: TDSE. Filled circles and squares: SOPT. Long-range amplitude-corrected results are given by the full thick lines. ACC-RME results are represented by the dashed lines $(L=0)$ and the dashed-dotted lines $(L=2)$.

Figure 3

Dependence of cc phase differences on photoelectron kinetic energy. ACC-RME, SOPT, and TDSE results correspond to atomic hydrogen targets. The experimental results correspond to helium atoms [13]. Upper panel: Absorption process. Lower panel: Emission process.

Figure 4

Moduli ratios for the absorption (red) and emission (blue) pathways. ACC-RME results for different intermediate states are given by full lines. Second-order perturbation theory calculations are given by empty stars [31] and full squares (emission only). TDSE simulation results are shown by empty squares (emission only). RPAE results [15] for different intermediate states are shown by empty triangles and hexagons.