Achieving a BCS transition in an atomic Fermi gas

We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length $a$. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length $a$ from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature $T\mathrm{/}{T}_F\sim {10}^{-2}$. The corresponding critical final value of $k_F\mathrm{\mid }a\mathrm{\mid }$ which leads to the BCS transition is found to be about one half, where $k_F$ is the Fermi momentum.