## 3 Results and Discussion  
### Two-Level System  
In Figure 1f-h, modified absorption profiles of a two-level system driven by Gaussian laser pulses of 3 fs duration with high peak intensity \(\mathrm{I}_{0}=4.7\times 10^{15}\) W/cm\({}^{2}\) and with detunings \(\Delta/\mathrm{E}_{\mathrm{e}}=0\) (Figure 1f, resonant), \(\Delta/\mathrm{E}_{\mathrm{e}}=-0.01\) (Figure 1g, red detuned) and \(\Delta/\mathrm{E}_{\mathrm{e}}=+0.01\) (Figure 1h, blue detuned) are shown in comparison to the unperturbed absorption profile (grey). Hereby the detuning is defined as  
\[\Delta=\hbar\omega_{\mathrm{c}}-\mathrm{E}_{\mathrm{r}}, \tag{6}\]  
where \(\hbar\omega_{\mathrm{c}}\) is the central photon energy of the XUV pulse. It should be noted that the corresponding spectral bandwidth of the XUV laser pulse amounts to \(\sim\)0.6 eV (intensity full width at half maximum), which corresponds to \(\lesssim\)1% of the central photon energy. The detuning is thus changed only within the spectral bandwidth of the XUV pulse which leads to near-resonant couplings at all detunings. To further investigate the mechanism behind the modified line shapes, we now systematically vary the XUV intensity and detuning. In Figure 2c we plot the fit results of the q parameter for the two-level resonance under the influence of an XUV pulse with peak intensities ranging from \(\mathrm{I}_{0}\approx 0.1\times 10^{15}\) W/cm\({}^{2}\) to \(\mathrm{I}_{0}\approx 4.7\times 10^{15}\) W/cm\({}^{2}\) and detunings ranging from \(\Delta=-0.65\) eV to  
Figure 1: **(a)** the interaction of an ultrashort extreme-ultraviolet (XUV) pulse (violet) with an atom, e.g., helium, leads to the emission of a dipole response (blue) interfering with the driving XUV pulse. (**b**) simplified energy level scheme of helium. With a photon energy of 60.15 eV the helium atom can be either singly ionized or excited into a doubly excited state, which autoionizes due to its configuration interaction \(\mathrm{V}_{\mathrm{CI}}\) with the ionization continuum. Corresponding absorption spectra are shown in (**d**,**e**). If the configuration interaction is disregarded, the absorption profile is Lorentzian (**d**), whereas the inclusion of the configuration interaction leads to a Fano absorption line shape (**e**). (**c**) dressed states are generated in the presence of an intense XUV pulse. The states’ energy separation increases with increasing XUV laser intensity and depends on the detuning [1,2], therefore their energy shift follows the Gaussian pulse envelope in time (compare to a), here illustrated for a red-detuned case. This leads to a temporal dipole phase shift \(\Delta\varphi_{\mathrm{D}}\) with respect to the weak-field response (grey in a) [8]. **(f)**–**(h)** manipulated absorption profiles of the two-level system (without configuration interaction) initiated by the strong coupling with an XUV pulse of different detunings. (**f**) the peak intensity of a resonant laser pulse is increased to \(4.7\times 10^{15}\) W/cm\({}^{2}\) leading to a decreased amplitude of the resonance, but leaving the line shape unchanged (\(\mathrm{q}\rightarrow\pm\infty\) ). (**g**,**h**) the additional detuning of the laser pulse to central photon energies \(\hbar\omega_{\mathrm{c}}\) of 59.55 eV or 60.75 eV, leads to modified now asymmetric absorption line shapes with a positive or negative q -parameter, respectively. \(\Delta=+0.65\) eV. For low intensities, the resonance is unperturbed and forms a Lorentzian shape, where the fit yields \(\mathrm{q}\rightarrow\pm\infty\). The divergence of \(\mathrm{q}\) for a Lorentzian line shape is better quantified with the corresponding dipole phase shift \(\Delta\varphi_{\mathrm{D}}\) (see Equation (5)), which is shown in Figure 2b. Instead of the divergent \(\mathrm{q}\) parameter, the phase shift is now smoothly changing around zero for low intensities.