Journal of Low Temperature Physics

, Volume 183, Issue 3–4, pp 183–190 | Cite as

Strong Coupling Effects on the Specific Heat of an Ultracold Fermi Gas in the Unitarity Limit

  • P. van Wyk
  • H. Tajima
  • R. Hanai
  • Y. Ohashi


We investigate strong-coupling corrections to the specific heat \(C_V\) in the normal state of an ultracold Fermi gas in the BCS–BEC crossover region. A recent experiment on a \(^6\)Li unitary Fermi gas (Ku et. al. in Science 335:563 2012) shows that \(C_V\) is remarkably amplified near the superfluid phase transition temperature \(T_\mathrm{c}\), being similar to the well-known \(\lambda \)-structure observed in liquid \(^4\)He. Including pairing fluctuations within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that strong pairing fluctuations are sufficient to explain the anomalous behavior of \(C_V\) observed in a \(^6\)Li unitary Fermi gas near \(T_\mathrm{c}\). We also show that there is no contribution from stable preformed Cooper pairs to \(C_V\) at the unitarity. This indicates that the origin of the observed anomaly is fundamentally different from the case of liquid \(^{4}\)He, where stable \(^4\)He Bose atoms induce the \(\lambda \)-structure in \(C_V\) near the superfluid instability. Instead, the origin is the suppression of the entropy S, near \(T_\mathrm{c}\), due to the increase of metastable preformed Cooper pairs. Our results indicate that the specific heat is a useful quantity to study the effects of pairing fluctuations on the thermodynamic properties of an ultracold Fermi gas in the BCS–BEC crossover region.


Ultracold Fermi gas Many-body physics Quantum gas BCS–BEC crossover 



We thank D. Inotani and M. Matsumoto for discussions. This work was supported by the KiPAS Project in Keio university. Y.O was supported by Grant-in-Aid for Scientific Research from MEXT and JSPS in Japan (Nos. 25400418, 15H00840).


  1. 1.
    C.A. Regal, M. Greiner, D.S. Jin, Phys. Rev. Lett. 92, 040403 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    J. Kinast, S.L. Hemmer, M.E. Gehm, A. Turlapov, J.E. Thomas, Phys. Rev. Lett. 92, 150402 (2004)ADSCrossRefGoogle Scholar
  3. 3.
    M. Bartenstein, A. Altmeyer, S. Riedl, S. Jochim, C. Chin, J.H. Denschlang, R. Grimm, Phys. Rev. Lett. 92, 203201 (2004)ADSCrossRefGoogle Scholar
  4. 4.
    M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle, Nature 435, 1047 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    W. Ketterle and M.W. Zwierlein, arXiv:0801.2500 [cond-mat] (2008)
  6. 6.
    C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    W. Zwerger, The BCS-BEC Crossover and the Unitary Fermi Gas (Springer, Berlin, 2012)CrossRefGoogle Scholar
  8. 8.
    H. Hu, X.J. Lui, P.D. Drummond, Phys. Rev. A 73, 023617 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    S. Tsuchiya, R. Watanabe, Y. Ohashi, Phys. Rev. A 80, 033613 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    H. Hu, X. Lui, P. Drummond, Phys. Rev. A 77, 061605 (2008)ADSCrossRefGoogle Scholar
  11. 11.
    A. Perali, F. Palestini, P. Pieri, G.C. Strinati, J.T. Stewart, J.P. Gaebler, T.E. Drake, D.S. Jin, Phys. Rev. Lett. 106, 060402 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    J. Kinast, A. Turpalov, J.E. Thomas, Q. Chen, J. Stajic, K. Levin, Science 307, 1296 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    L. Luo, J.E. Thomas, J. Low. Temp. Phys. 154, 1 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    M. Horikoshi, S. Nakajima, M. Ueda, T. Mukaiyama, Science 327, 442 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    S. Nascimbene, N. Navon, K.J. Jiang, F. Chevy, C. Salomon, Nature 463, 1057 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    R. Haussmann, W. Rantner, S. Cerrito, W. Zwerger, Phys. Rev. A 75, 023610 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    M.J.H. Ku, A.T. Sommer, L.W. Cheuk, M.W. Zwierlein, Science 335, 563 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    N.E. Phillips, Phys. Rev. 114, 676 (1959)ADSCrossRefGoogle Scholar
  19. 19.
    O.V. Lounasmaa, J. Cryog. 1, 212 (1961)ADSCrossRefGoogle Scholar
  20. 20.
    P. Nozières, S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985)ADSCrossRefGoogle Scholar
  21. 21.
    D.J. Thouless, Ann. Phys. 10, 553 (1960)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Y. Ohashi, A. Griffin, Phys. Rev. Lett 89, 130402 (2002)ADSCrossRefGoogle Scholar
  23. 23.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (Dover Publications, New York, 2003)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Science and TechnologyKeio UniversityYokohamaJapan

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