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


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.

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  1. 1.

    S. Giorgini, L. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008)

    ADS  Article  Google Scholar 

  2. 2.

    I. Bloch, J. Dalobard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)

    ADS  Article  Google Scholar 

  3. 3.

    C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Rev. Mod. Phys. 80, 1215 (2008)

    Article  Google Scholar 

  4. 4.

    P. Nozières, S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985)

    ADS  Article  Google Scholar 

  5. 5.

    C.A.R. Sá de Melo, M. Randeria, J.R. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993)

    ADS  Article  Google Scholar 

  6. 6.

    Y. Ohashi, A. Griffin, Phys. Rev. Lett. 89, 130402 (2002)

    ADS  Article  Google Scholar 

  7. 7.

    C.A. Regal, M. Greiner, D.S. Jin, Phys. Rev. Lett. 92, 040403 (2004)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  9. 9.

    M.J.H. Ku, A.T. Sommer, L.W. Cheuk, M.W. Zwierlein, Science 335, 563 (2012)

    ADS  Article  Google Scholar 

  10. 10.

    A. Sommer, M. Ku, G. Roati, M.W. Zwierlein, Nature 472, 201 (2011)

    ADS  Article  Google Scholar 

  11. 11.

    L. Luo, B. Clancy, J. Joseph, J. Kinast, J.E. Thomas, Phys. Rev. Lett. 98, 080402 (2007)

    ADS  Article  Google Scholar 

  12. 12.

    R. Haussmann, W. Rantner, S. Cerrito, W. Zwerger, Phys. Rev. A 75, 023610 (2007)

    ADS  Article  Google Scholar 

  13. 13.

    F. Palestini, P. Pieri, G.C. Strinati, Phys. Rev. Lett. 108, 080401 (2012)

    ADS  Article  Google Scholar 

  14. 14.

    R. Hausmann, Z. Phys. B 91, 291 (1993)

    ADS  Article  Google Scholar 

  15. 15.

    P. Pieri, G.C. Strinati, Phys. Rev. B 61, 15370 (2000)

    ADS  Article  Google Scholar 

  16. 16.

    R. Haussmann, Phys. Rev. B 49, 12975 (1994)

    ADS  Article  Google Scholar 

  17. 17.

    D.J. Thouless, Ann. Phys. 10, 553 (1960)

    ADS  Article  Google Scholar 

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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).

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Correspondence to R. Sato.

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Sato, R., Kagamihara, D., Manabe, K. et al. Isothermal Compressibility of an Ultracold Fermi Gas in the BCS–BEC Crossover. J Low Temp Phys 196, 119–125 (2019).

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  • Isothermal compressibility
  • Ultracold Fermi gas
  • Repulsive inter-pair interaction