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. © 2007 The American Physical Society.
Publication Source (Journal or Book title)
Physical Review A - Atomic, Molecular, and Optical Physics
Veillette, M., Sheehy, D., & Radzihovsky, L. (2007). Large- N expansion for unitary superfluid Fermi gases. Physical Review A - Atomic, Molecular, and Optical Physics, 75 (4) https://doi.org/10.1103/PhysRevA.75.043614