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Title: 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 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.

Authors:
; ;  [1];  [2];  [1]
  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)
Publication Date:
OSTI Identifier:
21546850
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 83; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.83.053637; (c) 2011 American Institute of Physics; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; ATOMS; BOSE-EINSTEIN CONDENSATION; BOSE-EINSTEIN GAS; CORRECTIONS; FERMI GAS; FERMIONS; INTERACTIONS; MEAN-FIELD THEORY; SPIN; VARIATIONAL METHODS; ANGULAR MOMENTUM; CALCULATION METHODS; PARTICLE PROPERTIES

Citation Formats

Mihaila, Bogdan, Chien, Chih-Chun, Timmermans, Eddy, Dawson, John F, Cooper, Fred, and Santa Fe Institute, Santa Fe, New Mexico 87501. Auxiliary field formalism for dilute fermionic atom gases with tunable interactions. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.053637.
Mihaila, Bogdan, Chien, Chih-Chun, Timmermans, Eddy, Dawson, John F, Cooper, Fred, & Santa Fe Institute, Santa Fe, New Mexico 87501. Auxiliary field formalism for dilute fermionic atom gases with tunable interactions. United States. https://doi.org/10.1103/PHYSREVA.83.053637
Mihaila, Bogdan, Chien, Chih-Chun, Timmermans, Eddy, Dawson, John F, Cooper, Fred, and Santa Fe Institute, Santa Fe, New Mexico 87501. Sun . "Auxiliary field formalism for dilute fermionic atom gases with tunable interactions". United States. https://doi.org/10.1103/PHYSREVA.83.053637.
@article{osti_21546850,
title = {Auxiliary field formalism for dilute fermionic atom gases with tunable interactions},
author = {Mihaila, Bogdan and Chien, Chih-Chun and Timmermans, Eddy and Dawson, John F and Cooper, Fred and Santa Fe Institute, Santa Fe, New Mexico 87501},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.83.053637},
url = {https://www.osti.gov/biblio/21546850}, journal = {Physical Review. A},
issn = {1050-2947},
number = 5,
volume = 83,
place = {United States},
year = {2011},
month = {5}
}