Strong-Field Extreme-Ultraviolet Dressing of Atomic Double Excitation

We report on the experimental observation of a strong-field dressing of an autoionizing two-electron state in helium with intense extreme-ultraviolet laser pulses from a free-electron laser. The asymmetric Fano line shape of this transition is spectrally resolved, and we observe modifications of the resonance asymmetry structure for increasing free-electron-laser pulse energy on the order of few tens of Microjoules. A quantum-mechanical calculation of the time-dependent dipole response of this autoionizing state, driven by classical extreme-ultraviolet (XUV) electric fields, evidences strong-field-induced energy and phase shifts of the doubly excited state, which are extracted from the Fano line-shape asymmetry. The experimental results obtained at the Free-Electron Laser in Hamburg (FLASH) thus correspond to transient energy shifts on the order of a few meV, induced by strong XUV fields. These results open up a new way of performing nonperturbative XUV nonlinear optics for the light-matter interaction of resonant electronic transitions in atoms at short wavelengths.

Figure 1

Conceptual design of the measurement and the physics scheme. (a) An intense XUV pulse (violet shading and arrows) is focused through a dense gas medium, tuned to the resonance of a single-photon two-electron excitation. The transmitted XUV light is spectrally dispersed after a grating (cyan to magenta color gradient) and measured with an XUV-CCD camera. The average transmitted experimental spectra without (black curve) and with (red curve) the helium target are plotted. (b) Energy level scheme of the helium atom. The two-electron ground state ($1s^2$) is resonantly coupled (violet arrow and shading) to the two-electron excited state ($2s2p$), which is embedded in the single-electron ionization continuum ($1sEp$). Strong-field dressing leads to a transient energy shift $\mathrm{\Delta }E$ during the interaction with the pulse duration $\mathrm{\Delta }T$, which translates into a phase shift $\mathrm{\Delta }\varphi$ of the dipole response.

Figure 2

Model simulation of transient excitation and dressing of the $2s2p$ Fano line in helium with a 5-fs-duration (FWHM) Gaussian-shaped pulse centered at photon energy 60.10 eV. (a) Intensity dependence of the resonant absorption, indicated in color scale in units of normalized optical density. (b)–(d) Lineouts (blue solid lines) of the resonant absorption [as shown in (a)] for a high [(b) $1.1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$], intermediate [(c) $5.6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$], and low [(d) $1.9\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$] XUV intensity. The fit of the Fano line shape (orange dashed lines) reveals a change of $q$ and corresponding relative phase shift $\mathrm{\Delta }\varphi$ due to the dressing during the pulse. (e) Time-dependent phase evolution ${\varphi }_e(t)$ of the $2s2p$ excited state for low ($1.9\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, green line), intermediate ($5.6\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, orange line), and high ($1.1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$, blue line) XUV intensity. The numerical values and horizontal dotted lines denote the phase shifts after the dressing, which agree well with the results obtained through fitting the line profiles for the respective photon fluence (b)–(d). (f) Transient energy shift $\mathrm{\Delta }E(t)=-\hslash \partial /\partial t[{\varphi }_e(t)]$ for the three XUV intensity settings with the line colors corresponding to the curves shown in (e). (g) Time evolution of the two-electron populations for high XUV intensity ($1.1\times {10}^{15}\mathrm{W}/{\mathrm{cm}}^2$).

Figure 3

Measured absorbance of intense XUV FEL pulses transmitted through a dense helium target, retrieved from an average over at least 50 and up to 300 single-shot FEL spectra for each pulse-energy bin. (a) Pulse-energy dependence of the resonant absorption, indicated in color scale in units of the optical density. (b)–(d) Lineouts (blue solid line) of the resonant absorption [as shown in (a)] for a high [(b) $42\mu \mathrm{J}$], intermediate [(c) $22\mu \mathrm{J}$], and low [(d) $2.5\mu \mathrm{J}$] pulse energy. The fit of a Fano spectral profile (orange dashed line) quantifies the increasing magnitude of $q$ with increasing pulse energy, which agrees well with the predicted results of the model calculation in Fig. 2. In the weak-field limit (d), the orange dashed line is drawn according to the resonance parameters reported in literature ($q=-2.8$).