Journal of Low Temperature Physics

, Volume 187, Issue 5–6, pp 661–667 | Cite as

Single-Particle Properties of a Strongly Interacting Bose–Fermi Mixture Above the BEC Phase Transition Temperature



We theoretically investigate the normal state properties of a Bose–Fermi mixture with a strong attractive interaction between Fermi and Bose atoms. We extend the ordinary T-matrix approximation (TMA) with respect to Bose–Fermi pairing fluctuations, to include the Hugenholtz–Pines’ relation for all Bose Green’s functions appearing in TMA self-energy diagrams. This extension is shown to be essentially important to correctly describe the physical properties of the Bose–Fermi mixture, especially near the Bose–Einstein condensation instability. Using this improved TMA, we clarify how the formation of composite fermions affects Bose and Fermi single-particle excitation spectra, over the entire interaction strength.


Bose–Fermi mixture BEC Single-particle excitations Strong-coupling effects 



D. K. thanks Keio Leading-edge Laboratory of Science and Technology (KLL) for supporting this research. This work was supported by KiPAS project in Keio University. D. I. was supported by Grant-in-Aid for Young Scientists (B) (No. 16K17773) from JSPS and R. H. was supported by Grant-in-Aid for JSPS fellows. Y. O. was supported by Grand-in-Aid for Scientific Research from MEXT and JSPS in Japan (No. 15K00178, No. 15H00840, No. 16K05503). We would like to thank H. Tajima and P. van Wyk for useful discussions.


  1. 1.
    I. Ferrier-Barbut, M. Delehaye, S. Laurent, A.T. Grier, M. Pierce, B.S. Rem, F. Chevy, S. Salomon, Science 345, 1035 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, New York, 2002)Google Scholar
  3. 3.
    M. Delehaye, S. Laurent, I. Ferrier-Barbut, S. Jin, F. Chevy, C. Salomon, arXiv:1510.06709
  4. 4.
    C.A. Regal, M. Greiner, D.S. Jin, Phys. Rev. Lett. 92, 040403 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    M.W. Zwierlein, C.A. Stan, C.H. Schunck, S.M.F. Raupach, A.J. Kerman, W. Ketterle, Phys. Rev. Lett. 92, 120403 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    C.A.R. Sá de Melo, M. Randeria, J.R. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993)ADSCrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    J.R. Engelbrecht, M. Randeria, C.A.R. Sá de Melo, Phys. Rev. B 55, 15153 (1997)ADSCrossRefGoogle Scholar
  10. 10.
    P. Pieri, G.C. Strinati, Phys. Rev. B 61, 15370 (2000)ADSCrossRefGoogle Scholar
  11. 11.
    S. Tsuchiya, R. Watanabe, Y. Ohashi, Phys. Rev. A 80, 033613 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    A. Perali, P. Pieri, G.C. Strinati, C. Castellani, Phys. Rev. B 66, 024510 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    P. Pieri, L. Pisani, G.C. Strinati, Phys. Rev. Lett. 92, 110401 (2004)ADSCrossRefGoogle Scholar
  14. 14.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-particle Systems (Dover Publications, New York, 2003)MATHGoogle Scholar
  15. 15.
    E. Fratini, P. Pieri, Phys. Rev. A 81, 051606(R) (2010)ADSCrossRefGoogle Scholar
  16. 16.
    E. Fratini, P. Pieri, Phys. Rev. A 85, 063618 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    E. Fratini, P. Pieri, Phys. Rev. A 88, 013627 (2013)ADSCrossRefGoogle Scholar
  18. 18.
    A. Storozhenko, P. Schuck, T. Suzuki, H. Yabu, J. Dukelsky, Phys. Rev. A 71, 063617 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    T. Watanabe, T. Suzuki, P. Schuck, Phys. Rev. A 78, 033601 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    T. Sogo, P. Schuck, M. Urban, Phys. Rev. A 88, 023613 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    N.M. Hugenholtz, D. Pines, Phys. Rev. 116, 489 (1959)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    J. Goldstone, A. Salam, S. Weinberg, Phys. Rev. 127, 965 (1962)ADSMathSciNetCrossRefGoogle Scholar

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Physics, Faculty of Science and TechnologyKeio UniversityKohoku-ku, YokohamaJapan

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