Journal of Low Temperature Physics

, Volume 196, Issue 1–2, pp 119–125 | Cite as

Isothermal Compressibility of an Ultracold Fermi Gas in the BCS–BEC Crossover

  • R. SatoEmail author
  • D. Kagamihara
  • K. Manabe
  • D. Inotani
  • Y. Ohashi


We theoretically investigate the isothermal compressibility \(\kappa _{\mathrm{T}}\) in the normal state of an ultracold Fermi gas with a tunable attractive interaction. We calculate this thermodynamic quantity by considering fluctuations in the Cooper channel, within the framework of the self-consistent T-matrix approximation (SCTMA). For comparison, we also evaluate this quantity in a “non”-self-consistent T-matrix approximation (TMA). We show that the calculated \(\kappa _{\mathrm{T}}\) diverges at \(T_{\mathrm{c}}\) in the BCS–BEC crossover region. On the other hand, such a singular behavior is absent when we deal with this quantity in SCTMA. We point out that the origin of this difference is the neglect of an effective inter-pair interaction in the former approximation. We also explicitly show how such an interaction is involved in the theory when one deals with pairing fluctuations in SCTMA. Our results indicate that the isothermal compressibility is a useful quantity in considering how preformed Cooper pairs interact with one another in the BCS–BEC crossover regime of an ultracold Fermi gas.


Isothermal compressibility Ultracold Fermi gas Repulsive inter-pair interaction 



This work was supported by KiPAS project in Keio University. DI was supported by Grant-in-aid for Scientific Research from JSPS in Japan (No. JP16K17773). YO was supported by Grant-in-aid for Scientific Research from MEXT and JSPS in Japan (No. JP16K05503).


  1. 1.
    S. Giorgini, L. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008)CrossRefGoogle Scholar
  2. 2.
    I. Bloch, J. Dalobard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)CrossRefGoogle Scholar
  3. 3.
    C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 80, 1215 (2008)CrossRefGoogle Scholar
  4. 4.
    P. Nozières, S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985)CrossRefGoogle Scholar
  5. 5.
    C.A.R. Sá de Melo, M. Randeria, J.R. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993)CrossRefGoogle Scholar
  6. 6.
    Y. Ohashi, A. Griffin, Phys. Rev. Lett. 89, 130402 (2002)CrossRefGoogle Scholar
  7. 7.
    C.A. Regal, M. Greiner, D.S. Jin, Phys. Rev. Lett. 92, 040403 (2004)CrossRefGoogle Scholar
  8. 8.
    M.W. Zwierlein, C.A. Stan, C.H. Shunck, S.M.F. Raupach, A.J. Kerman, W. Ketterle, Phys. Rev. Lett. 92, 120403 (2004)CrossRefGoogle Scholar
  9. 9.
    M.J.H. Ku, A.T. Sommer, L.W. Cheuk, M.W. Zwierlein, Science 335, 563 (2012)CrossRefGoogle Scholar
  10. 10.
    A. Sommer, M. Ku, G. Roati, M.W. Zwierlein, Nature 472, 201 (2011)CrossRefGoogle Scholar
  11. 11.
    L. Luo, B. Clancy, J. Joseph, J. Kinast, J.E. Thomas, Phys. Rev. Lett. 98, 080402 (2007)CrossRefGoogle Scholar
  12. 12.
    R. Haussmann, W. Rantner, S. Cerrito, W. Zwerger, Phys. Rev. A 75, 023610 (2007)CrossRefGoogle Scholar
  13. 13.
    F. Palestini, P. Pieri, G.C. Strinati, Phys. Rev. Lett. 108, 080401 (2012)CrossRefGoogle Scholar
  14. 14.
    R. Hausmann, Z. Phys. B 91, 291 (1993)CrossRefGoogle Scholar
  15. 15.
    P. Pieri, G.C. Strinati, Phys. Rev. B 61, 15370 (2000)CrossRefGoogle Scholar
  16. 16.
    R. Haussmann, Phys. Rev. B 49, 12975 (1994)CrossRefGoogle Scholar
  17. 17.
    D.J. Thouless, Ann. Phys. 10, 553 (1960)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • R. Sato
    • 1
    Email author
  • D. Kagamihara
    • 1
  • K. Manabe
    • 1
  • D. Inotani
    • 1
  • Y. Ohashi
    • 1
  1. 1.Department of PhysicsKeio UniversityYokohamaJapan

Personalised recommendations