Large-N expansion for unitary superfluid Fermi gases

Veillette, M. Y.; Sheehy, D. E.; Radzihovsky, L.

Large-N expansion for unitary superfluid Fermi gases

Authors

Veillette, M. Y.

Sheehy, D. E.

Radzihovsky, L.

Description

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=\infty this problem is exactly solved by the BCS-BEC 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 the proximity to) unitarity, including the energy, the pairing gap, and 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 non-interacting gas and the pairing gap to be 0.52 times the Fermi energy.
13 pages