  We report a formation of sharp, solitonlike structures in an experimentally
accessible ultracold Fermi gas, as a quantum carpet solution is analyzed in a
many body system. The effect is perfectly coherent in a noninteracting gas, but
in the presence of repulsive interaction in a two-component system, the
structures vanish at a finite time. As they disappear, the system enters a
dynamical equilibrium, in which kinetic energies of atoms tend to the same
average value. The coherence is revived in a strong interaction regime, with
the onset of phase separation, and with a double quantum carpet appearing.
