  The quantum dynamics of the electromagnetic light mode of an optical cavity
filled with a coherently driven Fermi gas of ultracold atoms strongly depends
on geometry of the Fermi surface. Superradiant light generation and
self-organization of the atoms can be achieved at low pumping threshold due to
resonant atom-photon Umklapp processes, where the fermions are scattered from
one side of the Fermi surface to the other by exchanging photon momenta. The
cavity spectrum exhibits sidebands, that, despite strong atom-light coupling
and cavity decay, retain narrow linewidth, due to absorptionless transparency
windows outside the atomic particle-hole continuum and the suppression of
inhomogeneous broadening and thermal fluctuations in the collisionless Fermi
gas.
