  The collective Raman cooling of trapped one- and two-component Fermi gases is
considered. We obtain the quantum master equation that describes the laser
cooling in the festina lente regime, for which the heating due to photon
reabsorption can be neglected. For the two-component case the collisional
processes are described within the formalism of quantum Boltzmann master
equation. The inhibition of the spontaneous emission can be overcome by
properly adjusting the spontaneous Raman rate during the cooling. Our numerical
results based in Monte Carlo simulations of the corresponding rate equations,
show that three-dimensional temperatures of the order of $0.08 T_F$
(single-component) and $0.03 T_F$ (two-component) can be achieved. We
investigate the statistical properties of the equilibrium distribution of the
laser-cooled gas, showing that the number fluctuations are enhanced compared
with the thermal distribution close to the Fermi surface. Finally, we analyze
the heating related to the background losses, concluding that our laser-cooling
scheme should maintain the temperature of the gas without significant
additional losses.
