Superfluorescence, Free-Induction Decay, and Four-Wave Mixing: Propagation of Free-Electron Laser Pulses through a Dense Sample of Helium Ions.

We report an experimental and numerical study of the propagation of free-electron laser pulses (wavelength 24.3 nm) through helium gas. Ionization and excitation populates the He^{+} 4p state. Strong, directional emission was observed at wavelengths of 469, 164, 30.4, and 25.6 nm. We interpret the emissions at 469 and 164 nm as 4p-3s-2p cascade superfluorescence, that at 30.4 nm as yoked superfluorescence on the 2p-1s transition, and that at 25.6 nm as free-induction decay of the 3p state.