A technique is proposed to cool Fermi gases to the regime of quantum degeneracy based on the expected inhibition of spontaneous emission due to the Pauli principle. The reduction of the linewidth for spontaneous emission originates a corresponding reduction of the Doppler temperature, which under specific conditions may give rise to a runaway process through which fermions are progressively cooled. The approach requires a combination of a magneto-optical trap as a cooling system and an optical dipole trap to enhance quantum degeneracy. This results in expected Fermi degeneracy factors $T/T_F$ comparable to the lowest values recently achieved, with potential for a direct implementation in optical lattices. The experimental demonstration of this technique should also indirectly provide a macroscopic manifestation of the Pauli exclusion principle at the atomic physics level.
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