Large-Nexpansion for unitary superfluid Fermi gases

We analyze strongly interacting Fermi gases in the unitary regime by considering the generalization to an arbitrary number N of spin-$1∕2$ fermion flavors with Sp(2N) symmetry. For N→∞ this problem is exactly solved by the Bardeen-Cooper-Schrieffer--Bose-Einstein condensate mean-field theory, with corrections small in the parameter $1∕N$. The large-N expansion provides a systematic way to determine corrections to mean-field predictions, allowing the calculation of a variety of thermodynamic quantities at (and in proximity to) unitarity, including the energy, the pairing gap, and the upper-critical polarization (in the case of a polarized gas) for the normal to superfluid instability. For the physical case of $N=1$, among other quantities, we predict in the unitarity regime, the energy of the gas to be ξ=0.28 times that for the noninteracting gas and the pairing gap to be 0.52 times the Fermi energy.