Contact in the Unitary Fermi Gas across the Superfluid Phase Transition

Jensen, S.; Gilbreth, C. N.; Alhassid, Y.

doi:10.1103/physrevlett.125.043402

Contact in the Unitary Fermi Gas across the Superfluid Phase Transition

Journal Article · Wed Jul 22 00:00:00 EDT 2020 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.125.043402· OSTI ID:1644301

^[1]; ^[2]; ^[3]

Yale University, New Haven, CT (United States); Yale University, CT (United States)
Central Washington University, Ellensburg, WA (United States); Honeywell Quantum Solutions, Broomfield, CO (United States)
Yale University, New Haven, CT (United States)

A quantity known as the contact is a fundamental thermodynamic property of quantum many-body systems with short-range interactions. Determination of the temperature dependence of the contact for the unitary Fermi gas of infinite scattering length has been a major challenge, with different calculations yielding qualitatively different results. Here we use finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods on the lattice within the canonical ensemble to calculate the temperature dependence of the contact for the homogeneous spin-balanced unitary Fermi gas. We extrapolate to the continuum limit for 40, 66, and 114 particles, eliminating systematic errors due to finite-range effects. We observe a dramatic decrease in the contact as the superfluid critical temperature is approached from below, followed by a gradual weak decrease as the temperature increases in the normal phase. Our theoretical results are in excellent agreement with the most recent precision ultracold atomic gas experiments. Here, we also present results for the energy as a function of temperature in the continuum limit.

View Accepted Manuscript (DOE)

Research Organization:: Yale University, New Haven, CT (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-05CH11231; FG02-00ER41132; FG02-91ER40608; SC0019521

OSTI ID:: 1644301

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 4 Vol. 125; ISSN 1079-7114; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (65)

Superfluid Pairing in Neutrons and Cold Atoms Carlson, J.; Gandolfi, S.; Gezerlis, A. arXiv https://doi.org/10.48550/arxiv.1204.2596	text	January 2012
Thermodynamic Measurements in a Strongly Interacting Fermi Gas Luo, Le; Thomas, J. E. Journal of Low Temperature Physics, Vol. 154, Issue 1-2 https://doi.org/10.1007/s10909-008-9850-2	journal	November 2008
Generalized virial theorem and pressure relation for a strongly correlated Fermi gas Tan, Shina Annals of Physics, Vol. 323, Issue 12 https://doi.org/10.1016/j.aop.2008.03.003	journal	December 2008
Energetics of a strongly correlated Fermi gas Tan, Shina Annals of Physics, Vol. 323, Issue 12 https://doi.org/10.1016/j.aop.2008.03.004	journal	December 2008
Large momentum part of a strongly correlated Fermi gas Tan, Shina Annals of Physics, Vol. 323, Issue 12 https://doi.org/10.1016/j.aop.2008.03.005	journal	December 2008
Viscosity and scale invariance in the unitary Fermi gas Enss, Tilman; Haussmann, Rudolf; Zwerger, Wilhelm Annals of Physics, Vol. 326, Issue 3 https://doi.org/10.1016/j.aop.2010.10.002	journal	March 2011
Stabilizing canonical-ensemble calculations in the auxiliary-field Monte Carlo method Gilbreth, C. N.; Alhassid, Y. Computer Physics Communications, Vol. 188 https://doi.org/10.1016/j.cpc.2014.09.002	journal	March 2015
Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases Liu, Xia-Ji Physics Reports, Vol. 524, Issue 2 https://doi.org/10.1016/j.physrep.2012.10.004	journal	March 2013
Exploring the thermodynamics of a universal Fermi gas Nascimbène, S.; Navon, N.; Jiang, K. J. Nature, Vol. 463, Issue 7284 https://doi.org/10.1038/nature08814	journal	February 2010
Enhanced paraconductivity-like fluctuations in the radiofrequency spectra of ultracold Fermi atoms Pieri, Pierbiagio; Perali, Andrea; Strinati, Giancarlo Calvanese Nature Physics, Vol. 5, Issue 10 https://doi.org/10.1038/nphys1345	journal	August 2009
Pre-pairing for condensation Randeria, Mohit Nature Physics, Vol. 6, Issue 8 https://doi.org/10.1038/nphys1748	journal	August 2010
Review of pseudogaps in strongly interacting Fermi gases Mueller, Erich J. Reports on Progress in Physics, Vol. 80, Issue 10 https://doi.org/10.1088/1361-6633/aa7e53	journal	September 2017
Universal contact of strongly interacting fermions at finite temperatures Hu, Hui; Liu, Xia-Ji; Drummond, Peter D. New Journal of Physics, Vol. 13, Issue 3 https://doi.org/10.1088/1367-2630/13/3/035007	journal	March 2011
The Fermi–Hubbard model at unitarity Burovski, Evgeni; Prokof'ev, Nikolay; Svistunov, Boris New Journal of Physics, Vol. 8, Issue 8 https://doi.org/10.1088/1367-2630/8/8/153	journal	August 2006
Three fermions in a box at the unitary limit: universality in a lattice model Pricoupenko, L.; Castin, Y. Journal of Physics A: Mathematical and Theoretical, Vol. 40, Issue 43 https://doi.org/10.1088/1751-8113/40/43/003	journal	October 2007
Quantum Monte Carlo approaches to nuclear and atomic physics Carlson, J.; Gandolfi, Stefano; Gezerlis, Alexandros Progress of Theoretical and Experimental Physics, Vol. 2012, Issue 1 https://doi.org/10.1093/ptep/pts031	journal	January 2012
Sum-rule analysis of radio-frequency spectroscopy of ultracold Fermi gas Zhang, Shizhong; Leggett, Anthony J. Physical Review A, Vol. 77, Issue 3 https://doi.org/10.1103/PhysRevA.77.033614	journal	March 2008
Quantum Monte Carlo simulations of the BCS-BEC crossover at finite temperature Bulgac, Aurel; Drut, Joaquín E.; Magierski, Piotr Physical Review A, Vol. 78, Issue 2 https://doi.org/10.1103/PhysRevA.78.023625	journal	August 2008
Universal relations for a strongly interacting Fermi gas near a Feshbach resonance Braaten, Eric; Kang, Daekyoung; Platter, Lucas Physical Review A, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevA.78.053606	journal	November 2008
Universal properties of the ultracold Fermi gas Zhang, Shizhong; Leggett, Anthony J. Physical Review A, Vol. 79, Issue 2 https://doi.org/10.1103/PhysRevA.79.023601	journal	February 2009
Particle distribution tail and related energy formula Combescot, R.; Alzetto, F.; Leyronas, X. Physical Review A, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevA.79.053640	journal	May 2009
Viscosity of strongly interacting quantum fluids: Spectral functions and sum rules Taylor, Edward; Randeria, Mohit Physical Review A, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevA.81.053610	journal	May 2010
Short-distance and short-time structure of a unitary Fermi gas Son, Dam T.; Thompson, Ethan G. Physical Review A, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevA.81.063634	journal	June 2010
Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas Palestini, F.; Perali, A.; Pieri, P. Physical Review A, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevA.82.021605	journal	August 2010
Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity Goulko, Olga; Wingate, Matthew Physical Review A, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevA.82.053621	journal	November 2010
BEC-BCS crossover and universal relations in unitary Fermi gases Gandolfi, S.; Schmidt, K. E.; Carlson, J. Physical Review A, Vol. 83, Issue 4 https://doi.org/10.1103/PhysRevA.83.041601	journal	April 2011
Virial expansion with Feynman diagrams Leyronas, X. Physical Review A, Vol. 84, Issue 5 https://doi.org/10.1103/PhysRevA.84.053633	journal	November 2011
Auxiliary-field quantum Monte Carlo method for strongly paired fermions Carlson, J.; Gandolfi, Stefano; Schmidt, Kevin E. Physical Review A, Vol. 84, Issue 6 https://doi.org/10.1103/PhysRevA.84.061602	journal	December 2011
Equation of state of the unitary Fermi gas: An update on lattice calculations Drut, Joaquín E.; Lähde, Timo A.; Wlazłowski, Gabriel Physical Review A, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevA.85.051601	journal	May 2012
Probing strongly interacting atomic gases with energetic atoms Nishida, Yusuke Physical Review A, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevA.85.053643	journal	May 2012
General relations for quantum gases in two and three dimensions: Two-component fermions Werner, Félix; Castin, Yvan Physical Review A, Vol. 86, Issue 1 https://doi.org/10.1103/PhysRevA.86.013626	journal	July 2012
Lattice Monte Carlo calculations for unitary fermions in a finite box Endres, Michael G.; Kaplan, David B.; Lee, Jong-Wan Physical Review A, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevA.87.023615	journal	February 2013
Pair condensation in a finite trapped Fermi gas Gilbreth, C. N.; Alhassid, Y. Physical Review A, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevA.88.063643	journal	December 2013
High-temperature expansion for interacting fermions Sun, Mingyuan; Leyronas, Xavier Physical Review A, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevA.92.053611	journal	November 2015
Numerical study of the unitary Fermi gas across the superfluid transition Goulko, Olga; Wingate, Matthew Physical Review A, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevA.93.053604	journal	May 2016
Diagrammatic Monte Carlo algorithm for the resonant Fermi gas Van Houcke, K.; Werner, F.; Ohgoe, T. Physical Review B, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevB.99.035140	journal	January 2019
Exact Relations for a Strongly Interacting Fermi Gas from the Operator Product Expansion Braaten, Eric; Platter, Lucas Physical Review Letters, Vol. 100, Issue 20 https://doi.org/10.1103/PhysRevLett.100.205301	journal	May 2008
Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly Interacting Fermi Gas Braaten, Eric; Kang, Daekyoung; Platter, Lucas Physical Review Letters, Vol. 104, Issue 22 https://doi.org/10.1103/PhysRevLett.104.223004	journal	June 2010
Verification of Universal Relations in a Strongly Interacting Fermi Gas Stewart, J. T.; Gaebler, J. P.; Drake, T. E. Physical Review Letters, Vol. 104, Issue 23 https://doi.org/10.1103/PhysRevLett.104.235301	journal	June 2010
Universal Behavior of Pair Correlations in a Strongly Interacting Fermi Gas Kuhnle, E. D.; Hu, H.; Liu, X. -J. Physical Review Letters, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevLett.105.070402	journal	August 2010
Temperature Dependence of the Universal Contact Parameter in a Unitary Fermi Gas Kuhnle, E. D.; Hoinka, S.; Dyke, P. Physical Review Letters, Vol. 106, Issue 17 https://doi.org/10.1103/PhysRevLett.106.170402	journal	April 2011
Momentum Distribution and Contact of the Unitary Fermi Gas Drut, Joaquín E.; Lähde, Timo A.; Ten, Timour Physical Review Letters, Vol. 106, Issue 20 https://doi.org/10.1103/PhysRevLett.106.205302	journal	May 2011
Resonantly Interacting Fermions in a Box Forbes, Michael McNeil; Gandolfi, Stefano; Gezerlis, Alexandros Physical Review Letters, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevLett.106.235303	journal	June 2011
Measurement of the Homogeneous Contact of a Unitary Fermi Gas Sagi, Yoav; Drake, Tara E.; Paudel, Rabin Physical Review Letters, Vol. 109, Issue 22 https://doi.org/10.1103/PhysRevLett.109.220402	journal	November 2012
Precise Determination of the Structure Factor and Contact in a Unitary Fermi Gas Hoinka, Sascha; Lingham, Marcus; Fenech, Kristian Physical Review Letters, Vol. 110, Issue 5 https://doi.org/10.1103/PhysRevLett.110.055305	journal	January 2013
Homogeneous Atomic Fermi Gases Mukherjee, Biswaroop; Yan, Zhenjie; Patel, Parth B. Physical Review Letters, Vol. 118, Issue 12 https://doi.org/10.1103/PhysRevLett.118.123401	journal	March 2017
Contact and Momentum Distribution of the Unitary Fermi Gas Rossi, R.; Ohgoe, T.; Kozik, E. Physical Review Letters, Vol. 121, Issue 13 https://doi.org/10.1103/PhysRevLett.121.130406	journal	September 2018
Contact and Sum Rules in a Near-Uniform Fermi Gas at Unitarity Carcy, C.; Hoinka, S.; Lingham, M. G. Physical Review Letters, Vol. 122, Issue 20 https://doi.org/10.1103/PhysRevLett.122.203401	journal	May 2019
Spectral Response and Contact of the Unitary Fermi Gas Mukherjee, Biswaroop; Patel, Parth B.; Yan, Zhenjie Physical Review Letters, Vol. 122, Issue 20 https://doi.org/10.1103/PhysRevLett.122.203402	journal	May 2019
Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas Jensen, S.; Gilbreth, C. N.; Alhassid, Y. Physical Review Letters, Vol. 124, Issue 9 https://doi.org/10.1103/PhysRevLett.124.090604	journal	March 2020
Equation of State of a Fermi Gas in the BEC-BCS Crossover: A Quantum Monte Carlo Study Astrakharchik, G. E.; Boronat, J.; Casulleras, J. Physical Review Letters, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevLett.93.200404	journal	November 2004
Momentum Distribution of a Fermi Gas of Atoms in the BCS-BEC Crossover Regal, C. A.; Greiner, M.; Giorgini, S. Physical Review Letters, Vol. 95, Issue 25 https://doi.org/10.1103/PhysRevLett.95.250404	journal	December 2005
Spin 1 / 2 Fermions in the Unitary Regime: A Superfluid of a New Type Bulgac, Aurel; Drut, Joaquín E.; Magierski, Piotr Physical Review Letters, Vol. 96, Issue 9 https://doi.org/10.1103/PhysRevLett.96.090404	journal	March 2006
Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity Burovski, Evgeni; Prokof’ev, Nikolay; Svistunov, Boris Physical Review Letters, Vol. 96, Issue 16 https://doi.org/10.1103/PhysRevLett.96.160402	journal	April 2006
Theory of rf-Spectroscopy of Strongly Interacting Fermions Punk, M.; Zwerger, W. Physical Review Letters, Vol. 99, Issue 17 https://doi.org/10.1103/PhysRevLett.99.170404	journal	October 2007
Coherence and Clock Shifts in Ultracold Fermi Gases with Resonant Interactions Baym, Gordon; Pethick, C. J.; Yu, Zhenhua Physical Review Letters, Vol. 99, Issue 19 https://doi.org/10.1103/PhysRevLett.99.190407	journal	November 2007
Deep Inelastic Scattering on Ultracold Gases Hofmann, Johannes; Zwerger, Wilhelm Physical Review X, Vol. 7, Issue 1 https://doi.org/10.1103/PhysRevX.7.011022	journal	March 2017
The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions Navon, N.; Nascimbene, S.; Chevy, F. Science, Vol. 328, Issue 5979 https://doi.org/10.1126/science.1187582	journal	April 2010
Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas Ku, M. J. H.; Sommer, A. T.; Cheuk, L. W. Science, Vol. 335, Issue 6068 https://doi.org/10.1126/science.1214987	journal	January 2012
Number of closed-channel molecules in the BEC-BCS crossover Werner, F.; Tarruell, L.; Castin, Y. The European Physical Journal B, Vol. 68, Issue 3 https://doi.org/10.1140/epjb/e2009-00040-8	journal	February 2009
The pseudogap regime in the unitary Fermi gas Jensen, S.; Gilbreth, C. N.; Alhassid, Y. The European Physical Journal Special Topics, Vol. 227, Issue 15-16 https://doi.org/10.1140/epjst/e2019-800105-y	journal	March 2019
Neutron Matter from Low to High Density Gandolfi, Stefano; Gezerlis, Alexandros; Carlson, J. Annual Review of Nuclear and Particle Science, Vol. 65, Issue 1 https://doi.org/10.1146/annurev-nucl-102014-021957	journal	October 2015
Static structure factor of a strongly correlated Fermi gas at large momenta Hu, H.; Liu, X. -J.; Drummond, P. D. EPL (Europhysics Letters), Vol. 91, Issue 2 https://doi.org/10.1209/0295-5075/91/20005	journal	July 2010
Molecular signatures in the structure factor of an interacting Fermi gas Combescot, R.; Giorgini, S.; Stringari, S. Europhysics Letters (EPL), Vol. 75, Issue 5 https://doi.org/10.1209/epl/i2006-10165-x	journal	September 2006
Making, probing and understanding ultracold Fermi gases Ketterle, W.; Zwierlein, M. W. La Rivista del Nuovo Cimento, Vol. 2008, Issue 5-6, 247-422 https://doi.org/10.1393/ncr/i2008-10033-1	journal	July 2008

Cited By (3)

Reducing the complexity of finite-temperature auxiliary-field quantum Monte Carlo Gilbreth, C. N.; Jensen, S.; Alhassid, Y. arXiv https://doi.org/10.48550/arxiv.1907.10596	preprint	January 2019
Tunneling transport of unitary fermions across the superfluid transition Del Pace, G.; Kwon, W. J.; Zaccanti, M. arXiv https://doi.org/10.48550/arxiv.2010.00582	text	January 2020
Beyond-mean-field description of a trapped unitary Fermi gas with mass and population imbalance Pini, M.; Pieri, P.; Grimm, R. arXiv https://doi.org/10.48550/arxiv.2012.01833	text	January 2020

Similar Records

Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas

Journal Article · Sun Mar 01 19:00:00 EST 2020 · Physical Review Letters · OSTI ID:1799991

The pseudogap regime in the unitary Fermi gas

Journal Article · Mon Mar 04 19:00:00 EST 2019 · European Physical Journal. Special Topics · OSTI ID:1530857

Reducing the complexity of finite-temperature auxiliary-field quantum Monte Carlo

Journal Article · Tue Mar 16 20:00:00 EDT 2021 · Computer Physics Communications · OSTI ID:1849345

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
Cold atoms
Cold atoms & matter waves
Critical phenomena
Fermi gases
Fermionic condensates
Superfluidity
Thermodynamics

Contact in the Unitary Fermi Gas across the Superfluid Phase Transition

Citation Formats

References (65)

Cited By (3)

Similar Records

Related Subjects