## 4 Conclusions  
In summary, we have utilized a numerical two- and three-level system to investigate the influence of the near-resonant detuning on the resonant absorption line shape for a strongly coupled XUV transition to an excited or autoionizing state in the impulsive limit, respectively. We used the relation between the Fano q asymmetry parameter and the dipole phase shift [8] and linked the observed phase shift to energy level shifts of a strongly coupled resonant transition. We could therefore explain how the near-resonant detuning of a strong XUV driving pulse can change and control the observed absorption line shape. We verified this assumption with a comparison to an analytical approximation based on the generalized Rabi formalism which yields a very good agreement. With the help of this analytical approximation we concluded that the broadband spectrum of the XUV pulse cannot be neglected, which is inherently connected to its ultrashort temporal duration in the limit of impulsive dressing of resonant transitions. Spectrally averaging over the detuning-dependent shift of the analytical approximation agrees well with the numerical results. Our numerical model also reveals line-shape asymmetry changes for the autoionizing 2s2p resonance in helium driven directly from the 1s\({}^{2}\) ground state. Hereby, the line-shape modification and dipole phase shift induced by the intense XUV pulse reveals different trends for different detunings in an asymmetric manner. This asymmetry can be qualitatively explained by the weak-field limit of an initially asymmetric absorption profile. Notably, for a detuning around \(-0.2\) eV the resonance line shape approximately keeps its weak-field asymmetry. We have shown in agreement with previous experimental results [16], that an intense and slightly red detuned XUV pulse may modify the absorption line shape of the weak-field Fano resonance to  
Figure 4: (**a**) dipole phase shift \(\Delta\varphi^{\prime}_{\mathrm{D}}\) and (**b**) q parameter of the autoionizing 2s2p resonance in helium under variation of the driving pulse peak intensity and detuning. The dipole phase shift of the autoionizing resonance is comparable to the case of the two-level system, but an asymmetry along the detuning axis arises from the weak-field asymmetric Fano absorption profile. More details are given in the text. In (**a**), the superimposed violet line indicates an unchanged dipole phase, \(\Delta\varphi^{\prime}_{\mathrm{D}}\approx 0\) rad, whereas in (**b**), the jump around \(\mathrm{q\to\pm\infty}\), corresponding to a Lorentzian profile, is also marked in violet in the parameter region \(\mathrm{I_{0}=(3\ldots 4.7)\times 10^{15}\ W/cm^{2}}\) and \(\Delta=(-0.65\ldots-0.2)\) eV.  
a Lorentzian-like shape at high XUV intensity, with sensitivity to impulsively induced energy level shifts. Since our approach can be straightforwardly extended to any core-excited electron resonances in atomic targets, we expect these results to be of great interest for any spectroscopy and imaging experiments that are based on intense and short XUV and x-ray pulses generated from FEL facilities, where the average (X)FEL spectral bandwidth may become (much) broader than the natural spectral bandwidth of the coupled transition.  
Conceptualization, A.M. and T.P.; methodology, A.M., T.D. and L.A.; software, A.M. and L.A.; validation, A.M., L.A., T.D., P.R., M.R., C.O. and T.P.; formal analysis, A.M., L.A., T.D., P.R., M.R., C.O. and T.P.; investigation, C.O. and T.P.; data curation, A.M. and L.A.; writing--original draft preparation, A.M.; writing--review and editing, L.A., T.D., P.R., M.R., C.O. and T.P.; visualization, A.M. and C.O.; supervision, C.O. and T.P.; project administration, C.O. and T.P.; All authors have read and agreed to the published version of the manuscript.  
This research received funding from the European Research Council (ERC) (X-MuSiC-616783).  
The authors declare no conflict of interest.