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Title: Universality in phase transitions for ultracold fermionic atoms

Abstract

We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from Bose-Einstein condensation (BEC) to BCS-type superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit, and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance and BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond mean-field theory we include the fluctuations of the molecule field and the renormalization effects for the atom-molecule coupling. We find excellent agreement with the observed fraction of bare molecules in {sup 6}Li and qualitative agreement with the condensate fraction in {sup 6}Li and {sup 40}K. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms, and the sound velocity.

Authors:
;  [1]
  1. Institut fuer Theoretische Physik, Philosophenweg 16, 69120 Heidelberg (Germany)
Publication Date:
OSTI Identifier:
20786973
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.033615; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BINDING ENERGY; BOSE-EINSTEIN CONDENSATION; CORRELATIONS; COUPLING; FERMIONS; FLUCTUATIONS; INTERATOMIC DISTANCES; LITHIUM 6; MAGNETIC FIELDS; MEAN-FIELD THEORY; MOLECULES; PHASE DIAGRAMS; PHASE TRANSFORMATIONS; POTASSIUM 40; RENORMALIZATION; RESONANCE; SCATTERING; SCATTERING LENGTHS; SOUND WAVES; SUPERFLUIDITY; YUKAWA POTENTIAL

Citation Formats

Diehl, S., and Wetterich, C. Universality in phase transitions for ultracold fermionic atoms. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Diehl, S., & Wetterich, C. Universality in phase transitions for ultracold fermionic atoms. United States. doi:10.1103/PHYSREVA.73.0.
Diehl, S., and Wetterich, C. Wed . "Universality in phase transitions for ultracold fermionic atoms". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786973,
title = {Universality in phase transitions for ultracold fermionic atoms},
author = {Diehl, S. and Wetterich, C.},
abstractNote = {We describe the gas of ultracold fermionic atoms by a functional integral for atom and molecule fields. The crossover from Bose-Einstein condensation (BEC) to BCS-type superfluidity shows universal features in terms of a concentration parameter for the ratio between scattering length and average interatomic distance. We discuss the relevance of the Yukawa coupling between atoms and molecules, establish an exact narrow resonance limit, and show that renormalized quantities are independent of the Yukawa coupling for the broad resonance and BCS and BEC limits. Within our functional integral formalism we compute the atom scattering in vacuum and the molecular binding energy. This connects the universal concentration parameter to the magnetic field of a given experiment. Beyond mean-field theory we include the fluctuations of the molecule field and the renormalization effects for the atom-molecule coupling. We find excellent agreement with the observed fraction of bare molecules in {sup 6}Li and qualitative agreement with the condensate fraction in {sup 6}Li and {sup 40}K. In addition to the phase diagram and condensate fraction we compute the correlation length for molecules, the in-medium scattering length for molecules and atoms, and the sound velocity.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 3,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}