When irradiated with focused x-ray / XUV free-electron laser (FEL) pulse, each atom within a sample absorbs a high-energy photon and thus drives the sample in a highly excited state. Under these conditions, population inversion for inner-shell transitions can occur, thus leading to collective spontaneous emission phenomena such as amplified spontaneous emission (ASE) or superfluorescence. Recently, XUV superfluorescence at 65 nm was observed from Xe gas irradiated by FLASH FEL pulses with photon energies 92 eV and 73 eV. In the present contribution, we investigate ASE from ensemble of nm‑sized Xe clusters that were irradiated by similar FEL pulses.
The experiment was performed at FLASH FEL. Xe clusters were produced by the expansion of a supersonic jet out of a conical nozzle. FEL pulses were focused to cluster jet resulting in an elongated, cylindrical-shaped active medium. We observed two intense emission lines at 65 and 68 nm emitted in the forward direction. Superfluorescence of same lines was observed in the gas phase experiment, however, the emission yield of an ensemble of clusters is 3-4 orders of magnitude smaller than that of a gas-phase sample.
We interpret the observed emission in the forward direction as ASE. To model the evolution of population inversion, we combined an atomic kinetic code (on a configuration-averaged level), a 1D hydrodynamic code, and a 4-level model to include the population dynamics of the Xe2+ states involved in the amplification of 65-nm line. Electron collision phenomena, that take place in the harsh environment of the expanding cluster, play a twofold role. On one hand, calculations show that high values of population inversion can be reached as a combined effect of collisional excitation, de‑excitation, ionization, and recombination. On the other hand, collisions cause strong decoherence that hinders collective spontaneous emission. To model the evolution of the emitted fluorescence radiation in the population-inverted medium, we apply a recently developed formalism that treats superfluorescence and ASE for transient conditions. Using the calculated population inversion as input, and taking an effective decoherence rate as an adjustable parameter, we were able to explain experimental trends and estimate the decoherence time to be in the range of 100 – 200 fs. In particular, the observed line‑width decrease with increasing stagnation pressure (resulting in an increase of cluster size and optical density) was explained based on the phenomenon of gain-narrowing.