Time Delays in Two-Photon Ionization

We present results of ab initio numerical simulations of time delays in two-photon ionization of the helium atom using the attosecond streaking technique. The temporal shifts in the streaking traces consist of two contributions, namely, a time delay acquired during the absorption of the two photons from the extreme-ultraviolet field and a time delay accumulated by the photoelectron after photoabsorption. In the case of a nonresonant transition, the absorption of the two photons is found to occur without time delay. In contrast, for a resonant transition a substantial absorption time delay is found, which scales linearly with the duration of the ionizing pulse. The latter can be related to the phase acquired during the transition of the electron from the initial ground state to the continuum and the influence of the streaking field on the resonant structure of the atom.

Figure 1

Time delays in attosecond streaking of ① nonresonant and ② resonant TPI by an ultrashort XUV laser pulse. The streaking time delay $\mathrm{\Delta }{t}_s$ obtained from the streaking trace consists of two contributions, namely, the two-photon absorption time delay $\mathrm{\Delta }{t}_a$ and the continuum time delay $\mathrm{\Delta }{t}_c$ that the photoelectron accumulates in the continuum after photoabsorption.

Figure 2

Streaking time delay as a function of XUV pulse duration for (a) 1D Coulomb and (b) 3D He potentials. Three ionization processes are considered: nonresonant TPI (blue lines with circles), resonant TPI (green lines with squares), and single-photon ionization (red lines with asterisks). Laser parameters are given in the text.

Figure 3

Absorption time delay (red lines with asterisks) as a function of XUV pulse duration for nonresonant TPI in 1D Coulomb (a) and 3D He (b) potentials and resonant TPI in 1D Coulomb (c) and 3D He (d) potentials. Also shown are the streaking (blue lines with circles) and the continuum time delays (green lines with squares).

Figure 4

Comparison of absorption time delays extracted from streaking experiments for resonant TPI in the 1D model potential (blue diamonds) and the 3D He potential (red circles). Two fits $\mathrm{\Delta }{t}_a=110.6T-2.175$ (1D case, dashed line) and $\mathrm{\Delta }{t}_a=110.6T-178.0$ (3D case, solid line) account for the predicted linear trend of the delay as a function of the XUV pulse duration.