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 $T/T_F\sim {10}^{-2}$. The corresponding critical final value of $k_F|a|$, which leads to the BCS transition, is found to be about one-half, where $k_F$ is the Fermi momentum.

Figure 1

Final temperature of the Fermi gas (left axis) and critical condition for a BCS transition (right axis) as a function of the initial temperature of the Bose condensed molecular gas that has been transformed to a normal attractive Fermi gas via adiabatic switching of the scattering length. The curves, from upper to lower, correspond to ${\mu }_{\mathrm{mol}}/k_B{T}_{\mathrm{BEC}}=1$, $1/2$, and $1/4$, where ${\mu }_{\mathrm{mol}}$ is the molecular chemical potential.