Manipulating the critical temperature for the superfluid phase transition in trapped atomic Fermi gases

We examine the effect of the trapping potential on the critical temperature ${T}_{C}$ for the BCS transition to a superfluid state in trapped atomic gases of fermions. ${T}_{C}$ for an arbitrary power-law trap is calculated in the Thomas-Fermi approximation. For anharmonic traps, ${T}_{C}$ can be increased by several orders of magnitude in comparison to a harmonic trap. Our theoretical results indicate that, in practice, one could manipulate the critical temperature for the BCS phase transition by shaping the traps confining the atomic Fermi gases.