  We consider a cold two-species atomic Fermi gas confined in a trap. We
combine the Hermitian coupling between the states (we assume them to be the
states with different spins) with the Cooper pairing of atoms with these
different spins. This opens up a new prospect for investigation of interplay
between various phenomena involving Raman coupling (e.g., atom lasers,
dark-state polaritons) and effects caused by Cooper pairing of particles (e.g.,
superfluidity). We have obtained a threshold of transition from oscillatory to
amplifying behavior of matter waves.
