Enhanced Nonlinear Double Excitation of He in Intense Extreme Ultraviolet Laser Fields

Nonlinear, three-photon double excitation of He in intense extreme ultraviolet free-electron laser fields ($\sim 24.1\mathrm{eV}$, $\sim 5\mathrm{TW}/{\mathrm{cm}}^2$) is presented. Resonances to the doubly excited states converging to the ${\mathrm{He}}^{+}$ $N=3$ level are revealed by the shot-by-shot photoelectron spectroscopy and identified by theoretical calculations based on the time-dependent Schrödinger equation for the two-electron atom under a laser field. It is shown that the three-photon double excitation is enhanced by intermediate Rydberg states below the first ionization threshold, giving a greater contribution to the photoionization yields than the two-photon process by more than 1 order of magnitude.

Figure 1

(a) Scheme of three-photon double excitation of He using EUV FEL. (b) Density plots of two-electron wave functions in hyperspherical coordinates [31, 32] for the $1s^2$ ground state, the $1s6p$ Rydberg state, and the ${}^{1}P^{\mathrm{o}}$ doubly excited states, ${}_3(1,1)_6{}^{+}$ and ${}_3(0,0)_6{}^{-}$. Strong angular correlation is seen in the doubly excited states. (c) Definition of the hyperspherical coordinates, $\alpha$ and $R$, and the angle ${\theta }_{12}$.

Figure 2

(a) Averaged photoelectron spectrum of He in intense EUV laser fields (24.1 eV). A retardation voltage of $-5.5\mathrm{eV}$ is applied to obtain a high spectral resolution. The doublet peaks around 11 eV are due to Xe introduced for the shot-by-shot photoelectron spectroscopy, while the three peaks ($A$), ($B$), and ($C$) are from He. The spectra recorded at three different fundamental FEL field intensities, $I=I_0$, $\sim 0.6I_0$, and $\sim 0.3I_0$, are shown in the full energy region ($>5.5\mathrm{eV}$), where $I_0$ ($\sim 5\mathrm{TW}/{\mathrm{cm}}^2$) represents the average laser field intensity obtained with no attenuation. Because of the small peak intensity, the variation of peak ($C$) is hardly visible in this scale. (b) Intensities of the three He peaks plotted against the fundamental FEL field intensity. The FEL pulse intensity was monitored for each laser pulse by a photoion yield detector. In order to cover the wide range of intensity, an Ar gas attenuator placed upstream of the FEL beam line was used, which virtually affects the fundamental FEL only. The intensity of the Xe peaks is plotted against the fundamental FEL intensity for comparison. The observed slope is slightly less than 1 due to the saturation of the ionization process [14].

Figure 3

Shot-by-shot photoelectron spectra and the comparison with theoretical calculations. (a) Photoelectron spectra of peak ($A$) for the three-photon excitation of He obtained by the shot-by-shot analysis. Different colors correspond to different mean photon energies. The total spectrum is shown on the top (solid line). (b) Theoretical three-photon photoelectron spectra (8.3 fs, $3.5\mathrm{TW}/{\mathrm{cm}}^2$) of the ${}^{1}P^{\mathrm{o}}$ [light gray (red) line] and ${}^{1}F^{\mathrm{o}}$ [dark gray (blue) line] doubly excited states of He decaying into ${\mathrm{He}}^{+}(2s,2p)+e^{-}$ channels at 24.15 eV in the logarithmic scale. The assignments of the $3ln{l}^{\prime }$ doubly excited states converging to the ${\mathrm{He}}^{+}$ $N=3$ state [26–28] are also shown using the $(K,T{)}^A$ notation. (c) The theoretical spectra for different photon energies convoluted with a Gaussian ($E/\Delta E=17$).

Figure 4

UV photoelectron spectrum of He Rydberg states populated by EUV FEL. The observed spectrum (solid line) shows peaks from the $1snp$ Rydberg states by a UV pulse at 250 nm introduced at a time delay of 50 ps from the FEL pulse. The retardation voltage was $-1.9\mathrm{V}$. The doublet structure is associated with the time delay between the forward and backward photoelectron components. The relative populations of $1snp$ Rydberg states are estimated by the least-squares-fitting (dotted line) incorporating the doublet structure for each peak (gray). The relative populations are to be 0.10, 0.48, 0.26, 0.11, and 0.04 for $n=4–8$, respectively, as shown in the inset.