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Title: Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases

Abstract

We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the two-dimensional mean-field theory indicates that the quantum fluctuations are much more pronounced than those in three dimensions. In this work, we show that the inclusion of the Gaussian quantum fluctuations naturally recovers the above features in both the BEC and the BCS limits. In the BEC limit, the missing logarithmic dependence on the boson chemical potential is recovered by the quantum fluctuations. Near the quantum phase transition from the vacuum to the BEC phase, we compare our equation of state with the known grand canonical equation of state of two-dimensional Bose gases and determine the ratio of the composite boson scattering length a B to the fermion scattering length a 2D. We find a B ≃ 0.56a 2D, in good agreement with themore » exact four-body calculation. As a result, we compare our equation of state in the BCS-BEC crossover with recent results from the quantum Monte Carlo simulations and the experimental measurements and find good agreements.« less

Authors:
 [1];  [2];  [3];  [4];  [4]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Electronic Science and Technology of China, Chengdu (China)
  3. Tsinghua Univ., Beijing (China)
  4. Swinburne Univ. of Technology, Melbourne (Australia)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1247301
Alternate Identifier(s):
OSTI ID: 1210112
Report Number(s):
LA-UR-15-24447
Journal ID: ISSN 1050-2947; PLRAAN
Grant/Contract Number:  
AC02-05CH11231; 61474018; 11335005; 2013CB922000; 2014CB845400; FT130100815; FT140100003; DP140103231; DP140100637; AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 92; Journal Issue: 2; Journal ID: ISSN 1050-2947
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BCS-BEC crossover; two-dimensional Fermi gas; quantum fluctuation

Citation Formats

He, Lianyi, Lu, Haifeng, Cao, Gaoqing, Hu, Hui, and Liu, Xia -Ji. Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases. United States: N. p., 2015. Web. doi:10.1103/PhysRevA.92.023620.
He, Lianyi, Lu, Haifeng, Cao, Gaoqing, Hu, Hui, & Liu, Xia -Ji. Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases. United States. doi:10.1103/PhysRevA.92.023620.
He, Lianyi, Lu, Haifeng, Cao, Gaoqing, Hu, Hui, and Liu, Xia -Ji. Fri . "Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases". United States. doi:10.1103/PhysRevA.92.023620. https://www.osti.gov/servlets/purl/1247301.
@article{osti_1247301,
title = {Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases},
author = {He, Lianyi and Lu, Haifeng and Cao, Gaoqing and Hu, Hui and Liu, Xia -Ji},
abstractNote = {We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the two-dimensional mean-field theory indicates that the quantum fluctuations are much more pronounced than those in three dimensions. In this work, we show that the inclusion of the Gaussian quantum fluctuations naturally recovers the above features in both the BEC and the BCS limits. In the BEC limit, the missing logarithmic dependence on the boson chemical potential is recovered by the quantum fluctuations. Near the quantum phase transition from the vacuum to the BEC phase, we compare our equation of state with the known grand canonical equation of state of two-dimensional Bose gases and determine the ratio of the composite boson scattering length aB to the fermion scattering length a2D. We find aB ≃ 0.56a2D, in good agreement with the exact four-body calculation. As a result, we compare our equation of state in the BCS-BEC crossover with recent results from the quantum Monte Carlo simulations and the experimental measurements and find good agreements.},
doi = {10.1103/PhysRevA.92.023620},
journal = {Physical Review. A},
number = 2,
volume = 92,
place = {United States},
year = {2015},
month = {8}
}

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Works referenced in this record:

Bose condensation in an attractive fermion gas: From weak to strong coupling superconductivity
journal, May 1985

  • Nozi�res, P.; Schmitt-Rink, S.
  • Journal of Low Temperature Physics, Vol. 59, Issue 3-4
  • DOI: 10.1007/BF00683774

Crossover from BCS to Bose superconductivity: Transition temperature and time-dependent Ginzburg-Landau theory
journal, November 1993

  • Sá de Melo, C. A. R.; Randeria, Mohit; Engelbrecht, Jan R.
  • Physical Review Letters, Vol. 71, Issue 19
  • DOI: 10.1103/PhysRevLett.71.3202

BCS to Bose crossover: Broken-symmetry state
journal, June 1997

  • Engelbrecht, Jan R.; Randeria, Mohit; Sáde Melo, C. A. R.
  • Physical Review B, Vol. 55, Issue 22
  • DOI: 10.1103/PhysRevB.55.15153

BCS–BEC crossover: From high temperature superconductors to ultracold superfluids
journal, June 2005


Resonantly paired fermionic superfluids
journal, January 2007


Theory of ultracold atomic Fermi gases
journal, October 2008

  • Giorgini, Stefano; Pitaevskii, Lev P.; Stringari, Sandro
  • Reviews of Modern Physics, Vol. 80, Issue 4
  • DOI: 10.1103/RevModPhys.80.1215

Emergence of a molecular Bose–Einstein condensate from a Fermi gas
journal, November 2003

  • Greiner, Markus; Regal, Cindy A.; Jin, Deborah S.
  • Nature, Vol. 426, Issue 6966
  • DOI: 10.1038/nature02199

Bose-Einstein Condensation of Molecules
journal, December 2003


Vortices and superfluidity in a strongly interacting Fermi gas
journal, June 2005

  • Zwierlein, M. W.; Abo-Shaeer, J. R.; Schirotzek, A.
  • Nature, Vol. 435, Issue 7045
  • DOI: 10.1038/nature03858

Production of cold molecules via magnetically tunable Feshbach resonances
journal, December 2006

  • Köhler, Thorsten; Góral, Krzysztof; Julienne, Paul S.
  • Reviews of Modern Physics, Vol. 78, Issue 4
  • DOI: 10.1103/RevModPhys.78.1311

Feshbach resonances in ultracold gases
journal, April 2010


BCS-BEC Crossover at Finite Temperature for Superfluid Trapped Fermi Atoms
journal, June 2004


BCS-BEC crossover at finite temperature in the broken-symmetry phase
journal, September 2004


Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
journal, May 2006


Quantum fluctuations in the superfluid state of the BCS-BEC crossover
journal, February 2008


Universal thermodynamics of strongly interacting Fermi gases
journal, April 2007

  • Hu, Hui; Drummond, Peter D.; Liu, Xia-Ji
  • Nature Physics, Vol. 3, Issue 7
  • DOI: 10.1038/nphys598

ϵ Expansion for a Fermi Gas at Infinite Scattering Length
journal, August 2006


Thermodynamics of the BCS-BEC crossover
journal, February 2007


Large- N expansion for unitary superfluid Fermi gases
journal, April 2007


Superfluidity and collective modes in a uniform gas of Fermi atoms with a Feshbach resonance
journal, June 2003


Pairing fluctuations and the superfluid density through the BCS-BEC crossover
journal, December 2006


Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures
journal, March 2007


Exploring the thermodynamics of a universal Fermi gas
journal, February 2010

  • Nascimbène, S.; Navon, N.; Jiang, K. J.
  • Nature, Vol. 463, Issue 7284
  • DOI: 10.1038/nature08814

The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
journal, April 2010


Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
journal, January 2012


Superfluid Fermi Gases with Large Scattering Length
journal, July 2003


Normal State of a Polarized Fermi Gas at Unitarity
journal, November 2006


Resonantly Interacting Fermions in a Box
journal, June 2011


Auxiliary-field quantum Monte Carlo method for strongly paired fermions
journal, December 2011


Fermi Liquid Theory of Dilute Submonolayer 3He on Thin 4He II Film: Dimer Bound State and Cooper Pairs
journal, June 1983


Bound states, Cooper pairing, and Bose condensation in two dimensions
journal, February 1989


Superconductivity in a two-dimensional Fermi gas: Evolution from Cooper pairing to Bose condensation
journal, January 1990


Phase fluctuations and pseudogap phenomena
journal, July 2001


Observation of a Two-Dimensional Fermi Gas of Atoms
journal, July 2010


Ground-State Pressure of Quasi-2D Fermi and Bose Gases
journal, January 2014


Radio-Frequency Spectroscopy of a Strongly Interacting Two-Dimensional Fermi Gas
journal, March 2011


Observation of a pairing pseudogap in a two-dimensional Fermi gas
journal, November 2011

  • Feld, Michael; Fröhlich, Bernd; Vogt, Enrico
  • Nature, Vol. 480, Issue 7375
  • DOI: 10.1038/nature10627

Polaron-to-Polaron Transitions in the Radio-Frequency Spectrum of a Quasi-Two-Dimensional Fermi Gas
journal, June 2012


Spin-Imbalanced Quasi-Two-Dimensional Fermi Gases
journal, March 2015


Observation of Pair Condensation in the Quasi-2D BEC-BCS Crossover
journal, June 2015


Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas
journal, June 2015


Evolution of Fermion Pairing from Three to Two Dimensions
journal, January 2012


Crossover from 2D to 3D in a Weakly Interacting Fermi Gas
journal, March 2011


BCS-BEC Crossover in a Two-Dimensional Fermi Gas
journal, March 2011


Superfluid transition in quasi-two-dimensional Fermi gases
journal, March 2003


Quasi-Two-Dimensional Superfluid Fermionic Gases
journal, October 2005


Imbalanced Fermi superfluid in a one-dimensional optical potential
journal, May 2007


Berezinskii-Kosterlitz-Thouless transition in a trapped quasi-two-dimensional Fermi gas near a Feshbach resonance
journal, October 2008


Superfluidity at the BEC-BCS crossover in two-dimensional Fermi gases with population and mass imbalance
journal, May 2008


Phase diagram of a cold polarized Fermi gas in two dimensions
journal, September 2008


Evolution from BCS to Berezinskii-Kosterlitz-Thouless Superfluidity in One-Dimensional Optical Lattices
journal, October 2009


Density distribution of a trapped two-dimensional strongly interacting Fermi gas
journal, November 2011


Polarons and molecules in a two-dimensional Fermi gas
journal, February 2011


Pairing and radio-frequency spectroscopy in two-dimensional Fermi gases
journal, August 2012


Apparent Low-Energy Scale Invariance in Two-Dimensional Fermi Gases
journal, September 2012


Quantum Anomaly, Universal Relations, and Breathing Mode of a Two-Dimensional Fermi Gas
journal, May 2012


BCS-BEC Crossover in 2D Fermi Gases with Rashba Spin-Orbit Coupling
journal, April 2012


Superfluidity in two-dimensional imbalanced Fermi gases
journal, October 2012

  • Caldas, Heron; Mota, A. L.; Farias, R. L. S.
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 10
  • DOI: 10.1088/1742-5468/2012/10/P10019

Finite-temperature phase diagram of quasi-two-dimensional imbalanced Fermi gases beyond mean field
journal, September 2012


Pseudogap and preformed pairs in the imbalanced Fermi gas in two dimensions
journal, October 2012


Pair Correlations in the Two-Dimensional Fermi Gas
journal, December 2013


Highly polarized Fermi gases in two dimensions
journal, March 2013


Superfluidity, sound velocity, and quasicondensation in the two-dimensional BCS-BEC crossover
journal, November 2013


BCS-BEC crossover in a quasi-two-dimensional Fermi gas
journal, August 2013


Universal Equation of State and Pseudogap in the Two-Dimensional Fermi Gas
journal, April 2014


Pairing effects in the nondegenerate limit of the two-dimensional Fermi gas
journal, January 2014


Pairing effects in the normal phase of a two-dimensional Fermi gas
journal, February 2015


Composite bosons in the two-dimensional BCS-BEC crossover from Gaussian fluctuations
journal, January 2015


Weakly Bound Dimers of Fermionic Atoms
journal, August 2004


On the theory of the superfluidity of two- and one-dimensional bose systems
journal, June 1972

  • Popov, V. N.
  • Theoretical and Mathematical Physics, Vol. 11, Issue 3
  • DOI: 10.1007/BF01028373

Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation
journal, July 2001


Extension of Bogoliubov theory to quasicondensates
journal, May 2003


Variational approach for the two-dimensional trapped Bose-Einstein condensate
journal, July 2004


Equation of state of a weakly interacting two-dimensional Bose gas studied at zero temperature by means of quantum Monte Carlo methods
journal, May 2009


Ground State Energy of the Two-Dimensional Weakly Interacting Bose Gas: First Correction Beyond Bogoliubov Theory
journal, May 2009


Ground-state energy of the interacting Bose gas in two dimensions: An explicit construction
journal, December 2010


Two-dimensional Fermi gas
journal, July 1975


Landau f function for the dilute Fermi gas in two dimensions
journal, May 1992


Functional Integrals for QCD at Nonzero Chemical Potential and Zero Density
journal, November 2003


BCS-BEC crossover in a system of microcavity polaritons
journal, September 2005


Crossover from BCS-superconductivity to Bose-condensation
journal, January 1992


BCS-BEC crossover in three-dimensional Fermi gases with spherical spin-orbit coupling
journal, July 2012


Energy-dependent scattering and the Gross-Pitaevskii equation in two-dimensional Bose-Einstein condensates
journal, April 2002


Exact diagrammatic approach for dimer-dimer scattering and bound states of three and four resonantly interacting particles
journal, March 2006


Energetics of a strongly correlated Fermi gas
journal, December 2008


Large momentum part of a strongly correlated Fermi gas
journal, December 2008


General relations for quantum gases in two and three dimensions: Two-component fermions
journal, July 2012


Superfluid Equation of State of Dilute Composite Bosons
journal, October 2007


    Works referencing / citing this record:

    Effect of weak disorder on the BCS–BEC crossover in a two-dimensional Fermi gas
    journal, April 2017