Auxiliary field formalism for dilute fermionic atom gases with tunable interactions
Abstract
We develop the auxiliary field formalism corresponding to a dilute system of spin1/2 fermions. This theory represents the Fermi counterpart of the BoseEinstein 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 BardeenCooperSchriffer (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 leadingorder 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 meanfield results discussed here can be systematically improved on by calculating the oneparticle irreducible action corrections, order by order.
 Authors:

 Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
 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 10502947
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; ATOMS; BOSEEINSTEIN CONDENSATION; BOSEEINSTEIN GAS; CORRECTIONS; FERMI GAS; FERMIONS; INTERACTIONS; MEANFIELD THEORY; SPIN; VARIATIONAL METHODS; ANGULAR MOMENTUM; CALCULATION METHODS; PARTICLE PROPERTIES
Citation Formats
Mihaila, Bogdan, Chien, ChihChun, 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, ChihChun, 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, ChihChun, 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, ChihChun 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 spin1/2 fermions. This theory represents the Fermi counterpart of the BoseEinstein 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 BardeenCooperSchriffer (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 leadingorder 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 meanfield results discussed here can be systematically improved on by calculating the oneparticle irreducible action corrections, order by order.},
doi = {10.1103/PHYSREVA.83.053637},
url = {https://www.osti.gov/biblio/21546850},
journal = {Physical Review. A},
issn = {10502947},
number = 5,
volume = 83,
place = {United States},
year = {2011},
month = {5}
}