Fermi super-Tonks-Girardeau state for attractive Fermi gases in an optical lattice

  • L. Wang
  • Z. H. Xu
  • S. ChenEmail author
Regular Article


We demonstrate that a kind of highly excited state of strongly attractive Hubbard model, named of Fermi super-Tonks-Girardeau state, can be realized in the spin-1/2 Fermi optical lattice system by a sudden switch of interaction from the strongly repulsive regime to the strongly attractive regime. In contrast to the ground state of the attractive Hubbard model, such a state is the lowest scattering state with no pairing between attractive fermions. With the aid of Bethe-ansatz method, we calculate energies of both the Fermi Tonks-Girardeau gas and the Fermi super-Tonks-Girardeau state of spin-1/2 ultracold fermions and show that both energies approach to the same limit as the strength of the interaction goes to infinity. By exactly solving the quench dynamics of the Hubbard model, we demonstrate that the Fermi super-Tonks-Girardeau state can be transferred from the initial repulsive ground state very efficiently. This allows the experimental study of properties of Fermi super-Tonks-Girardeau gas in optical lattices.


Cold Matter and Quantum Gas 


  1. 1.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)CrossRefADSGoogle Scholar
  2. 2.
    B. Paredes et al., Nature 429, 277 (2004)CrossRefADSGoogle Scholar
  3. 3.
    T. Kinoshita, T. Wenger, D.S. Weiss, Science 305, 1125 (2004)CrossRefADSGoogle Scholar
  4. 4.
    G.E. Astrakharchik, J. Boronat, J. Casulleras, S. Giorgini, Phys. Rev. Lett. 95, 190407 (2005)CrossRefADSGoogle Scholar
  5. 5.
    E. Haller et al., Science 325, 1224 (2009)CrossRefADSGoogle Scholar
  6. 6.
    J.B. McGuire, J. Math. Phys. 5, 622 (1964)MathSciNetzbMATHCrossRefADSGoogle Scholar
  7. 7.
    M.T. Batchelor, M. Bortz, X.W. Guan, N. Oelkers, J. Stat. Mech.: Theory Exp., L10001 (2005)Google Scholar
  8. 8.
    E. Tempfli, S. Zöllner, P. Schmelcher, New J. Phys. 10, 103021 (2008)CrossRefADSGoogle Scholar
  9. 9.
    S. Chen, L. Guan, X. Yin, Y. Hao, X.-W. Guan, Phys. Rev. A 81, 031609(R) (2010)ADSGoogle Scholar
  10. 10.
    M.D. Girardeau, G.E. Astrakhachik, Phys. Rev. A 81, 061601(R) (2010)ADSGoogle Scholar
  11. 11.
    M. Valiente, Europhys. Lett. 98, 10010 (2012)CrossRefADSGoogle Scholar
  12. 12.
    L. Wang, Y. Hao, S. Chen, Phys. Rev. A 81, 063637 (2010)CrossRefADSGoogle Scholar
  13. 13.
    M.D. Girardeau, Phys. Rev. A 82, 011607(R) (2010)ADSGoogle Scholar
  14. 14.
    L. Guan, S. Chen, Phys. Rev. Lett. 105, 175301 (2010)CrossRefADSGoogle Scholar
  15. 15.
    S. Chen, X.-W. Guan, X. Yin, L. Guan, M.T. Batchelor, Phys. Rev. A 81, 031608(R) (2010)ADSGoogle Scholar
  16. 16.
    X. Yin, X.W. Guan, M.T. Batchelor, S. Chen, Phys. Rev. A 83, 013602 (2011)CrossRefADSGoogle Scholar
  17. 17.
    M.D. Girardeau, Phys. Rev. A 83, 011601(R) (2011)CrossRefADSGoogle Scholar
  18. 18.
    D. Muth, M. Fleischhauer, Phys. Rev. Lett. 105, 150403 (2010)CrossRefADSGoogle Scholar
  19. 19.
    M. Kormos, G. Mussardo, A. Trombettoni, Phys. Rev. A 83, 013617 (2011)CrossRefADSGoogle Scholar
  20. 20.
    A. Rosch, D. Rasch, B. Binz, M. Vojta, Phys. Rev. Lett. 101, 265301 (2008)CrossRefADSGoogle Scholar
  21. 21.
    A. Kantian, A.J. Daley, P. Zoller, Phys. Rev. Lett. 104, 240406 (2010)CrossRefADSGoogle Scholar
  22. 22.
    E.H. Lieb, F.Y. Wu, Phys. Rev. Lett. 20, 1443 (1968)CrossRefADSGoogle Scholar
  23. 23.
    C.N. Yang, Phys. Rev. Lett. 19, 1312 (1967)MathSciNetzbMATHCrossRefADSGoogle Scholar
  24. 24.
    M. Gaudin, Phys. Lett. A 24, 55 (1967)CrossRefADSGoogle Scholar
  25. 25.
    M. Ogata, H. Shiba, Phys. Rev. B 41, 2326 (1990)CrossRefADSGoogle Scholar
  26. 26.
    F. Woynarovich, K. Penc, Z. Phys. B 85, 269 (1991)CrossRefADSGoogle Scholar
  27. 27.
    C.N. Yang, Phys. Rev. Lett. 63, 2144 (1989)CrossRefADSGoogle Scholar
  28. 28.
    L. Guan, S. Chen, Y. Wang, Z.Q. Ma, Phys. Rev. Lett. 102, 160402 (2009)CrossRefADSGoogle Scholar
  29. 29.
    M.D. Girardeau, A. Minguizzi, Phys. Rev. Lett. 99, 230402 (2007)CrossRefADSGoogle Scholar
  30. 30.
    F. Deuretzbacher et al., Phys. Rev. Lett. 100, 160405 (2008)CrossRefADSGoogle Scholar
  31. 31.
    E.H. Lieb, D. Mattis, Phys. Rev. 125, 164 (1962)zbMATHCrossRefADSGoogle Scholar
  32. 32.
    L.-M. Duan, E. Demler, M.D. Lukin, Phys. Rev. Lett. 91, 090402 (2003)CrossRefADSGoogle Scholar
  33. 33.
    A.B. Kuklov, B.V. Svistunov, Phys. Rev. Lett. 90, 100401 (2003)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Beijing National Laboratory for Condensed Matter Physics, Institute of PhysicsChinese Academy of SciencesBeijingP.R. China

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