Auxiliary field formalism for dilute fermionic atom gases with tunable interactions

Journal Article · Sun May 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.053637· OSTI ID:21546850

Mihaila, Bogdan; Chien, Chih-Chun; Timmermans, Eddy ^[1]; Dawson, John F ^[2]; Cooper, Fred ^[1]

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1. Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2. Department of Physics, University of New Hampshire, Durham, New Hampshire 03824 (United States)

We develop the auxiliary field formalism corresponding to a dilute system of spin-1/2 fermions. This theory represents the Fermi counterpart of the Bose-Einstein condensation (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 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 obtained in the standard BCS variational picture. At finite temperature, LOAF leads to the theory discussed 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 on by calculating the one-particle irreducible action corrections, order by order.

• OSTI ID: 21546850
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ANGULAR MOMENTUM
APPROXIMATIONS
ATOMS
BOSE-EINSTEIN CONDENSATION
BOSE-EINSTEIN GAS
CALCULATION METHODS
CORRECTIONS
FERMI GAS
FERMIONS
INTERACTIONS
MEAN-FIELD THEORY
PARTICLE PROPERTIES
SPIN
VARIATIONAL METHODS