High Temperature Superfluid and Feshbach Resonance

We study an effective field theory describing cold fermionic atoms near a Feshbach resonance. The theory gives a unique description of the dynamics in the limit that the energy of the Feshbach resonance is tuned to be twice that of the Fermi surface. We show that in this limit the zero temperature superfluid condensate is of order the Fermi energy, and obtain a critical temperature TC ≃ 0.43 TF PACS numbers: 03.75.Ss, 64.60.-i, 74.20.-z Typeset using REVTEX 1 After the successful achievement of Bose-Einstein condensation in ultracold atomic gases, a natural question is whether one can achieve superfluidity in a degenerate fermion gas. Samples of fermionic alkali atoms have already been cooled below their Fermi temperature of several hundreds nano-Kelvin [1], where quantum degeneracy phenomena such as Cooperpairing of atoms are potentially important [2]. It was suggested that the superfluidity gap may be made as large as of order the Fermi energy in the alkali atomic gases [3,4,5], using a Feshbach resonance [6], at which the scattering length becomes very large. For weak coupling, the scattering length away from resonance is usually much smaller than the typical wavelength of fermions near the Fermi surface, |a| ≪ k F and the Cooper pairing gap is then given in terms of scattering length as ∆ ≃ 2EFe , (1) where EF is the Fermi energy and h̄kF = pF is the Fermi momentum. The effective strength of attraction is related to the scattering length as V = 4πh̄an/m, where n is the number density and m is the fermion mass. Therefore, a weakly bound Cooper-pair gap is typically much smaller than the Fermi energy. However, if the scattering of fermions occurs at the Feshbach resonance, whose energy is nearly equal to twice that of the Fermi surface, the effective scattering length becomes quite large and so does the gap. In this paper we analyze this enhancement at the Feshbach resonance in detail. At ultralow temperature, the atomic gas can be described by a Fermi liquid à la Landau, whose (effective) Lagrangian density is given as, suppressing the spin indices, Leff = ψ (