Pair condensation in a Finite Trapped Fermi Gas

Superfluidity in the cold atomic two-species Fermi gas system in the unitary limit of infinite scattering length remains incompletely understood. In particular, a pseudogap phase has been proposed to exist above the superfluid critical temperature. Here we apply the auxiliary-field quantum Monte Carlo method to perform the first ab initio calculations of the temperature dependence of three quantities -- the energy-staggering pairing gap, the condensate fraction and the heat capacity -- in a trapped finite-size cold atom system. As the calculations of the energy-staggering pairing gap require the use of the canonical ensemble, we employ a novel algorithm for the stabilization of particle-number projection that is essential for reaching convergence in the size of the model space. We observe clear signatures of the superfluid phase transition in all three quantities, including a signature of the recently measured lambda peak in the heat capacity, but find no evidence of a pseudogap effect in the energy-staggering pairing gap.