  We investigate the depletion of single-electron states in small molecules
under the influence of very short XUV pulses. In N$_2$, for a certain window of
XUV energies around 50 eV, we observe a marked occupation inversion, i.e. a
situation where depletion of the deepest bound valence electron state is much
larger than for any other state. This represents a realistic mechanism which is
able to cut, almost instantaneously, a hole into a deep lying state, a
situation which is often assumed ad hoc in numerous theoretical studies of
energetic ultrafast processes. This occupation inversion furthermore drives a
dipole instability, i.e. a spontaneous reappearance of the dipole signal long
after the laser pulse is over and the dipole signal has died out. The dipole
signal that emerges from this instability can be identified as a particular
low-energy structure in photo-electron spectra.
