Evidence of Extreme Ultraviolet Superfluorescence in Xenon

We present a comprehensive experimental and theoretical study on superfluorescence in the extreme ultraviolet wavelength regime. Focusing a free-electron laser pulse in a cell filled with Xe gas, the medium is quasi-instantaneously population inverted by $4d$-shell ionization on the giant resonance followed by Auger decay. On the timescale of $\sim 10\mathrm{ps}$ to $\sim 100\mathrm{ps}$ (depending on parameters) a macroscopic polarization builds up in the medium, resulting in superfluorescent emission of several Xe lines in the forward direction. As the number of emitters in the system is increased by either raising the pressure or the pump-pulse energy, the emission yield grows exponentially over four orders of magnitude and reaches saturation. With increasing yield, we observe line broadening, a manifestation of superfluorescence in the spectral domain. Our novel theoretical approach, based on a full quantum treatment of the atomic system and the irradiated field, shows quantitative agreement with the experiment and supports our interpretation.

Figure 1

Level scheme: The FEL pulse photoionizes the $4d$ shell of the Xe ground state. The resulting ${\mathrm{Xe}}^{+}$ $4d^{-1}$ vacancies decay via Auger process into various ${\mathrm{Xe}}^{2+}$ and ${\mathrm{Xe}}^{3+}$ (not shown) states. Population inversion in ${\mathrm{Xe}}^{2+}$ is established between the upper ($B$, $C$) and lower ($A$, ${}^1{D}_2$, and ${}^3{P}_1$) states of the observed transitions. Valence double ionization (dashed blue arrows) contributes to the population of the ${\mathrm{Xe}}^{2+}$ states. The population branching ratios of each state, relative to all ${\mathrm{Xe}}^{+}$, ${\mathrm{Xe}}^{2+}$, and ${\mathrm{Xe}}^{3+}$ states as deduced from our coincidence measurements are given in red (gray) for ${\omega }_P=92\mathrm{eV}$ (73 eV). Since the ${}^3{P}_1$ and the ${}^3{P}_0$ are not experimentally resolved, the sum of the two ratios is shown.

Figure 2

Single-shot spectra (solid blue and green) and average over 725 spectra (dashed black) obtained with an FEL photon energy of ${\omega }_P=73\mathrm{eV}$ in 7 mbar of Xe. Two laser-like emission lines at 65.18 nm and 68.14 nm are observed. The typical SASE spectrum ($\mathrm{\Delta }{\omega }_P\sim 1\mathrm{eV}$) of the FEL pulse appears in the fourth diffraction at around 68 nm $\widehat{=}$ $73/4\mathrm{eV}$.

Figure 3

Emission yield of the 65.18 nm line as a function of (a) FEL-pulse energy $E_P$ for ${\omega }_P=73\mathrm{eV}$ (at 7 mbar Xe) and 92 eV (at 3.5 mbar Xe) and (b) pressure for fixed $E_P=30\mu \mathrm{J}$ for ${\omega }_P=73\mathrm{eV}$ and $E_P=75\mu \mathrm{J}$ for ${\omega }_P=92\mathrm{eV}$. Symbols: Experimental single-shot data. For each data set, the solid line and error bars are the geometric mean and standard deviation, black lines are the result of the theory.

Figure 4

(a) Measured line width of the Xe 68.14 nm emission line (FWHM of a Gaussian fit) as a function of emission yield for ${\omega }_P=73\mathrm{eV}$. Each data point is obtained by accumulating three consecutive FEL pulses separated by $1\mu \mathrm{s}$. The error bars on the black triangle and circle show the standard deviation of the line width resulting from the fit. The corresponding normalized spectra (symbols) and fits (dashed and dotted lines) to these data points are shown in the inset. The black line is the theoretically determined line width taking into account the spectrometer resolution of 0.4 meV. The three points (colored crosses) mark the results of the theoretically determined temporal (b) and spectral (c) intensity profiles for various pump-pulse energies.