Resonance Effects in Photoemission Time Delays

We present measurements of single-photon ionization time delays between the outermost valence electrons of argon and neon using a coincidence detection technique that allows for the simultaneous measurement of both species under identical conditions. The analysis of the measured traces reveals energy-dependent time delays of a few tens of attoseconds with high energy resolution. In contrast to photoelectrons ejected through tunneling, single-photon ionization can be well described in the framework of Wigner time delays. Accordingly, the overall trend of our data is reproduced by recent Wigner time delay calculations. However, besides the general trend we observe resonance features occurring at specific photon energies. These features have been qualitatively reproduced and identified by a calculation using the multiconfigurational Hartree-Fock method, including the influence of doubly excited states and ionization thresholds.

Figure 1

Propagation of a wave packet through a square potential barrier. (a) Potential barrier of height $E_b$ (black solid line) and transmission probability (blue dotted line) as a function of the ratio between the kinetic energy of the wave packet $E$ and the barrier height $E_b$. (b) If the average kinetic energy of the wave packet is smaller than the barrier height, propagation involves tunneling. After propagation through the barrier, the wave packet disperses and its peak would be found at a time given by the dashed line. However, the transmission probability, shown in (a) acts as an energy-dependent high-pass filter (blue dotted line), inducing an additional temporal shift [solid line in lower part of panel (b)], which is not related to the time spent within the barrier but rather only depends on the specific shapes of filter and wave packet. (c) The situation where the energy of the wave packet is significantly larger than $E_b$ resembles the situation after absorption of one photon leading to ionization; in this case the group delay is a direct measure of the propagation time of the wave packet because the energy dependence of the filter can be neglected in that regime. Therefore, a meaningful relation between the wave packet peaks before and after the filter persists.

Figure 2

Measured (a) and reconstructed (b) spectrograms for Ne and Ar photoelectrons collected within a cone of only 20° with respect to the XUV polarization axis; before applying the retrieval algorithm the two traces are patched together onto a common energy axis in order to ensure consistency in the reconstruction (see main text). (c) XUV spectra (solid and dashed lines) and group delays (dotted and dash-dotted lines) for Ar (red, solid and dotted) and Ne (blue, dashed and dash-dotted) computed by adding the ionization energy of the two targets to the spectra and group delays of the photoelectron wave packets retrieved with the FROG-CRAB algorithm. The inset in the top right shows the group delay difference $\mathrm{\Delta }\tau$ calculated for electrons ionized by photons of the same XUV photon energy: this procedure ensures that the attochirp contribution to the photoemission time delay is removed.

Figure 3

(a) The measured streaking group delay difference between Ar and Ne electrons (green open circles connected by a solid line) is compared with the theoretical prediction (green solid line). The green solid line represents the sum of the calculated Wigner delay difference of Ar and Ne [7] and the corresponding measurement-induced delay difference [28], shown as a light blue dashed curve. (b) The black open circles connected by a dashed line represent the averaged group delay difference of the 33 independent measurements obtained after subtracting the laser-induced contribution $\mathrm{\Delta }{\tau }_{\mathrm{CLC}}$ shown in (a). The black solid and the magenta dashed lines represent theory curves. The black solid line is computed by using one-photon matrix elements within the RPAE [7] both for Ar and Ne electrons. The magenta dashed line has been obtained by using MCHF [21] for Ar taking into account resonances and RPAE [7] for Ne.