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

He, Lianyi; Lu, Haifeng; Cao, Gaoqing; Hu, Hui; Liu, Xia -Ji

doi:10.1103/PhysRevA.92.023620

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

Journal Article · Fri Aug 14 00:00:00 EDT 2015 · Physical Review A - Atomic, Molecular, and Optical Physics

DOI:https://doi.org/10.1103/PhysRevA.92.023620· OSTI ID:1247301

He, Lianyi ^[1]; Lu, Haifeng ^[2]; Cao, Gaoqing ^[3]; Hu, Hui ^[4]; Liu, Xia -Ji ^[4]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Electronic Science and Technology of China, Chengdu (China)
Tsinghua Univ., Beijing (China)
Swinburne Univ. of Technology, Melbourne (Australia)

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 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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-05CH11231; 61474018; 11335005; 2013CB922000; 2014CB845400; FT130100815; FT140100003; DP140103231; DP140100637; AC52-06NA25396

OSTI ID:: 1247301

Alternate ID(s):: OSTI ID: 1210112

Report Number(s):: LA-UR-15-24447; PLRAAN

Journal Information:: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 92, Issue 2; ISSN 1050-2947

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 74 works

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Weakly bound dimers of fermionic atoms Petrov, D. S.; Salomon, C.; Shlyapnikov, G. V. arXiv https://doi.org/10.48550/arxiv.cond-mat/0309010	text	January 2003
Variational approach for the two-dimensional trapped Bose Einstein condensate Pricoupenko, Ludovic arXiv https://doi.org/10.48550/arxiv.cond-mat/0309212	text	January 2003
BCS-BEC crossover at finite temperature in the broken-symmetry phase Pieri, P.; Pisani, L.; Strinati, G. C. arXiv https://doi.org/10.48550/arxiv.cond-mat/0406099	text	January 2004
Energetics of a strongly correlated Fermi gas Tan, Shina arXiv https://doi.org/10.48550/arxiv.cond-mat/0505200	text	January 2005
Quasi two-dimensional superfluid Fermi gases Martikainen, J. -P.; Torma, Paivi arXiv https://doi.org/10.48550/arxiv.cond-mat/0505275	text	January 2005
Thermodynamics of the BCS-BEC crossover Haussmann, R.; Rantner, W.; Cerrito, S. arXiv https://doi.org/10.48550/arxiv.cond-mat/0608282	text	January 2006
Pairing fluctuations and the superfluid density through the BCS-BEC crossover Taylor, E.; Griffin, A.; Fukushima, N. arXiv https://doi.org/10.48550/arxiv.cond-mat/0609187	text	January 2006
Large-N expansion for unitary superfluid Fermi gases Veillette, M. Y.; Sheehy, D. E.; Radzihovsky, L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0610798	text	January 2006
Resonantly-paired fermionic superfluids Gurarie, V.; Radzihovsky, L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0611022	text	January 2006
Imbalanced Fermi superfluid in a one-dimensional optical potential Tempere, J.; Wouters, M.; Devreese, J. T. arXiv https://doi.org/10.48550/arxiv.cond-mat/0701272	text	January 2007
Functional integrals for QCD at nonzero chemical potential and zero density Cohen, Thomas D. . arXiv https://doi.org/10.48550/arxiv.hep-ph/0307089	text	January 2003

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Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms Turlapov, A. V.; Yu Kagan, M. Journal of Physics: Condensed Matter, Vol. 29, Issue 38 https://doi.org/10.1088/1361-648x/aa7ad9	journal	August 2017
Quantum fluctuations in a strongly interacting Bardeen-Cooper-Schrieffer polariton condensate at thermal equilibrium Hu, Hui; Liu, Xia-Ji Physical Review A, Vol. 101, Issue 1 https://doi.org/10.1103/physreva.101.011602	journal	January 2020
Chiral two-dimensional $p$ -wave superfluid from $s$ -wave pairing in the Bose-Einstein-condensate regime Thompson, K.; Brand, J.; Zülicke, U. Physical Review A, Vol. 101, Issue 1 https://doi.org/10.1103/physreva.101.013613	journal	January 2020
Theory of strongly paired fermions with arbitrary short-range interactions Hu, Jianshen; Wu, Fan; He, Lianyi Physical Review A, Vol. 101, Issue 1 https://doi.org/10.1103/physreva.101.013615	journal	January 2020
Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases Galea, Alexander; Dawkins, Hillary; Gandolfi, Stefano Physical Review A, Vol. 93, Issue 2 https://doi.org/10.1103/physreva.93.023602	journal	February 2016
Strongly correlated Fermi superfluid near an orbital Feshbach resonance: Stability, equation of state, and Leggett mode He, Lianyi; Wang, Jia; Peng, Shi-Guo Physical Review A, Vol. 94, Issue 4 https://doi.org/10.1103/physreva.94.043624	journal	October 2016
Dimensional crossover in a strongly interacting ultracold atomic Fermi gas Toniolo, Umberto; Mulkerin, Brendan C.; Vale, Chris J. Physical Review A, Vol. 96, Issue 4 https://doi.org/10.1103/physreva.96.041604	journal	October 2017
Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations Vitali, Ettore; Shi, Hao; Qin, Mingpu Physical Review A, Vol. 96, Issue 6 https://doi.org/10.1103/physreva.96.061601	journal	December 2017
Strongly interacting Sarma superfluid near orbital Feshbach resonances Zou, Peng; He, Lianyi; Liu, Xia-Ji Physical Review A, Vol. 97, Issue 4 https://doi.org/10.1103/physreva.97.043616	journal	April 2018
Effect of weak disorder on the BCS–BEC crossover in a two-dimensional Fermi gas Khan, Ayan; Tanatar, B. International Journal of Modern Physics B, Vol. 31, Issue 09 https://doi.org/10.1142/s0217979217500667	journal	April 2017
Going beyond the BCS level in the superfluid path integral: A consistent treatment of electrodynamics and thermodynamics Anderson, Brandon M.; Boyack, Rufus; Wu, Chien-Te Physical Review B, Vol. 93, Issue 18 https://doi.org/10.1103/physrevb.93.180504	journal	May 2016
Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region Boettcher, I.; Bayha, L.; Kedar, D. arXiv https://doi.org/10.48550/arxiv.1509.03610	text	January 2015
Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases Galea, Alexander; Dawkins, Hillary; Gandolfi, Stefano arXiv https://doi.org/10.48550/arxiv.1511.05123	text	January 2015
Strongly correlated Fermi superfluid near an orbital Feshbach resonance: Stability, equation of state and Leggett mode He, Lianyi; Wang, Jia; Peng, Shi-Guo arXiv https://doi.org/10.48550/arxiv.1606.00188	text	January 2016
Pressure profiles of nonuniform two-dimensional atomic Fermi gases Martiyanov, Kirill; Barmashova, Tatiana; Makhalov, Vasiliy arXiv https://doi.org/10.48550/arxiv.1609.00550	text	January 2016
Effect of Weak Disorder on the BCS-BEC crossover in a two-dimensional Fermi Gas Khan, Ayan; Tanatar, B. arXiv https://doi.org/10.48550/arxiv.1611.06854	text	January 2016
Dimensional crossover in a strongly interacting ultracold atomic Fermi gas Toniolo, Umberto; Mulkerin, Brendan C.; Vale, Chris J. arXiv https://doi.org/10.48550/arxiv.1701.08477	text	January 2017
Visualizing the BEC-BCS crossover in the two-dimensional Fermi gas: pairing gaps and dynamical response functions from ab initio computations Vitali, Ettore; Shi, Hao; Qin, Mingpu arXiv https://doi.org/10.48550/arxiv.1705.07929	text	January 2017
A strongly interacting Sarma superfluid near orbital Feshbach resonances Zou, Peng; He, Lianyi; Liu, Xia-Ji arXiv https://doi.org/10.48550/arxiv.1802.02703	text	January 2018
Theory of strongly paired fermions with arbitrary short-range interactions Hu, Jianshen; Wu, Fan; He, Lianyi arXiv https://doi.org/10.48550/arxiv.1907.12527	text	January 2019

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