Auxiliary field formalism for dilute fermionic atom gases with tunable interactions

Abstract

We develop the auxiliary field formalism corresponding to a dilute system of spin-1/2 fermions. This theory represents the Fermi counterpart of the BEC theory developed recently by F. Cooper et al. [Phys. Rev. Lett. 105, 240402 (2010)] to describe a dilute gas of Bose particles. Assuming tunable interactions, this formalism is appropriate for the study of the crossover from the regime of Bardeen-Cooper-Schriffer (BCS) pairing to the regime of Bose-Einstein condensation (BEC) in ultracold fermionic atom gases. We show that when applied to the Fermi case at zero temperature, the leading-order auxiliary field (LOAF) approximation gives the same equations as those obtained in the standard BCS variational picture. At finite temperature, LOAF leads to the theory discussed by by Sa de Melo, Randeria, and Engelbrecht [Phys. Rev. Lett. 71, 3202(1993); Phys. Rev. B 55, 15153(1997)]. As such, LOAF provides a unified framework to study the interacting Fermi gas. The mean-field results discussed here can be systematically improved upon by calculating the one-particle irreducible (1-PI) action corrections, order by order.

12 pages, 5 figures

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• The explicit expression of the fugacity for weakly interacting Bose and Fermi gases
• The Josephson relation for the superfluid density and the connection to the Goldstone theorem in dilute Bose atomic gasses
• Quantum Many-Body Calculations using Body-Centered Cubic Lattices
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Fundamental Constraints on Linear Response Theories of Fermi Superfluids Above and Below $T_c$
• Density and Spin Linear Response of Atomic Fermi Superfluids with Population Imbalance in BCS-BEC Crossover
• Shear Viscosity of Uniform Fermi Gases with Population Imbalance
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Neutrino condensation from a New Higgs Interaction
• BCS thermal vacuum of fermionic superfluids and its perturbation theory
• Weighted Hartree-Fock-Bogoliubov method for interacting fermions: An application to ultracold Fermi superfluids