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Title: Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance

Abstract

We address the thermodynamics, density profiles, and superfluid density of trapped fermions undergoing BCS-BEC crossover. We consider the case of zero and finite population imbalance and apply the local density approximation (LDA) to include the trap potential. Our approach represents a fully self-consistent treatment of 'pseudogap effects'. These effects reflect the distinction between the pair formation temperature T* and the pair condensation temperature T{sub c}. As a natural corollary, this temperature difference must be accommodated in the fermionic excitation spectrum E{sub k} to reflect the fact that fermions are paired at and above T{sub c}. It is precisely this natural corollary which has been omitted from all other many body approaches in the literature. At a formal level, we show how enforcing this corollary implies that pairing fluctuation or self-energy contributions enter into both the gap and the number equations; this is necessary in order to be consistent with a generalized Ward identity. At a less formal level, we demonstrate that we obtain physical results for the superfluid density n{sub s}(T) at all temperatures. In contrast, previous work in the literature has led to nonmonotonic, or multivalued or discontinuous behavior for n{sub s}(T). Because it reflects the essence of themore » superfluid state, we view the superfluid density as a critical measure of the physicality of a given crossover theory. In a similarly unique fashion, we emphasize that in order to properly address thermodynamic properties of a trapped Fermi gas, a necessary first step is to demonstrate that the particle density profiles are consistent with experiment. Without a careful incorporation of the distinction between the pairing gap and the order parameter, the LDA-derived density profiles (of the unpolarized gas) tend to exhibit sharp features at the condensate edge, which are never seen experimentally in the crossover regime. The lack of demonstrable consistency between theoretical and experimental density profiles, along with problematic behavior found for the superfluid density, casts doubt on previous claims in the literature concerning quantitative agreement between thermodynamical calculations and experiment.« less

Authors:
; ; ;  [1]
  1. James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637 (United States)
Publication Date:
OSTI Identifier:
21052820
Resource Type:
Journal Article
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 76; Journal Issue: 22; Other Information: DOI: 10.1103/PhysRevB.76.224516; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BCS THEORY; BOSE-EINSTEIN CONDENSATION; DENSITY FUNCTIONAL METHOD; EXCITATION; FERMI GAS; FERMIONS; FLUCTUATIONS; MANY-BODY PROBLEM; ORDER PARAMETERS; SELF-ENERGY; SUPERFLUIDITY; THERMODYNAMIC PROPERTIES; THERMODYNAMICS; TRAPPING; WARD IDENTITY

Citation Formats

Yan, He, Chien, C -C, Qijin, Chen, and Levin, K. Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance. United States: N. p., 2007. Web. doi:10.1103/PHYSREVB.76.224516.
Yan, He, Chien, C -C, Qijin, Chen, & Levin, K. Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance. United States. https://doi.org/10.1103/PHYSREVB.76.224516
Yan, He, Chien, C -C, Qijin, Chen, and Levin, K. Sat . "Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance". United States. https://doi.org/10.1103/PHYSREVB.76.224516.
@article{osti_21052820,
title = {Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance},
author = {Yan, He and Chien, C -C and Qijin, Chen and Levin, K},
abstractNote = {We address the thermodynamics, density profiles, and superfluid density of trapped fermions undergoing BCS-BEC crossover. We consider the case of zero and finite population imbalance and apply the local density approximation (LDA) to include the trap potential. Our approach represents a fully self-consistent treatment of 'pseudogap effects'. These effects reflect the distinction between the pair formation temperature T* and the pair condensation temperature T{sub c}. As a natural corollary, this temperature difference must be accommodated in the fermionic excitation spectrum E{sub k} to reflect the fact that fermions are paired at and above T{sub c}. It is precisely this natural corollary which has been omitted from all other many body approaches in the literature. At a formal level, we show how enforcing this corollary implies that pairing fluctuation or self-energy contributions enter into both the gap and the number equations; this is necessary in order to be consistent with a generalized Ward identity. At a less formal level, we demonstrate that we obtain physical results for the superfluid density n{sub s}(T) at all temperatures. In contrast, previous work in the literature has led to nonmonotonic, or multivalued or discontinuous behavior for n{sub s}(T). Because it reflects the essence of the superfluid state, we view the superfluid density as a critical measure of the physicality of a given crossover theory. In a similarly unique fashion, we emphasize that in order to properly address thermodynamic properties of a trapped Fermi gas, a necessary first step is to demonstrate that the particle density profiles are consistent with experiment. Without a careful incorporation of the distinction between the pairing gap and the order parameter, the LDA-derived density profiles (of the unpolarized gas) tend to exhibit sharp features at the condensate edge, which are never seen experimentally in the crossover regime. The lack of demonstrable consistency between theoretical and experimental density profiles, along with problematic behavior found for the superfluid density, casts doubt on previous claims in the literature concerning quantitative agreement between thermodynamical calculations and experiment.},
doi = {10.1103/PHYSREVB.76.224516},
url = {https://www.osti.gov/biblio/21052820}, journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 22,
volume = 76,
place = {United States},
year = {2007},
month = {12}
}