Polaronic effects in one-dimensional Fermi gas

  • Yadong SongEmail author
  • Huawen Zhang
Regular Article


Using the variational method and exact Bethe ansatz (BA) method, we studied the effects of an impurity immersed in a one-dimensional (1D) Fermi sea. With attractive interactions between them, the impurity is dressed up by surrounding particles in Fermi sea and forms a polaron. For equal masses and heavy polaron systems, we calculated the binding energy, effective mass, momentum distribution and Tan contact. In the strongly attractive limit, the impurity forms a dimer with inner fermion in Fermi sea which just accords with the highly imbalanced 1D Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in experiment. We find that the heavy impurity is dressed more deeply with Fermi sea in whole interaction regime. Furthermore, we explore the complete influence of particle-hole excitation in Fermi polaron system in 1D. We find a shocking phenomenon that the hole term in Fermi sea has a great influence on the Tan relation even in the attractive interaction regime.

Graphical abstract


Cold Matter and Quantum Gas 


  1. 1.
    W. Ketterle, M.W. Zwierlein, in Ultra-Cold Fermi Gases, Proceedings of the International School of Physics Enrico Fermi, SIF, Bologna , edited by M. Inguscio, W. Ketterle, C. Salomon (Amsterdam, IOS Press, 2007), p. 95Google Scholar
  2. 2.
    S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 80, 1215 (2008)ADSCrossRefGoogle Scholar
  3. 3.
    J.H.K. Mark, A.T. Sommer, L.W. Cheuk, M.W. Zwierlein, Science 335, 563 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    X.-W. Guan, M.T. Batchelor, C.-H. Lee, Rev. Mod. Phys. 85, 1633 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    F. Chevy, Phys. Rev. A 74, 063628 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    R. Combescot, A. Recati, C. Lobo, F. Chevy, Phys. Rev. Lett. 98, 180402 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    R. Combescot, S. Giraud, Phys. Rev. Lett. 101, 050404 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    S. Giraud, R. Combescot, Phys. Rev. A 79, 043615 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    R.S. Christensen, J. Levinsen, G.M. Bruun, Phys. Rev. Lett. 115, 160401 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    F. Grusdt, M. Fleischhauer, Phys. Rev. Lett. 116, 053602 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    R. Schmidt, M. Knap, D.A. Ivanov, J.S. You, M. Cetina, E. Demler, Rep. Prog. Phys. 81, 024401 (2018)ADSCrossRefGoogle Scholar
  12. 12.
    P. Fulde, R.A. Ferrell, Phys. Rev. 135, A550 (1964)ADSCrossRefGoogle Scholar
  13. 13.
    A.I. Larkin, Y.N. Ovchinnikov, ZhETF 47, 1136 (1964)Google Scholar
  14. 14.
    M.M. Parish, Phys. Rev. A 83, 051603 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    P. Massignan, M. Zaccanti, G.M. Bruun, Rep. Prog. Phys. 77, 034401 (2014)ADSCrossRefGoogle Scholar
  16. 16.
    X.-W. Guan, Front. Phys. 7, 8 (2012)CrossRefGoogle Scholar
  17. 17.
    J.B. McGuire, J. Math. Phys. 6, 432 (1965)ADSCrossRefGoogle Scholar
  18. 18.
    R.X. Mao, X.W. Guan, B. Wu, Phys. Rev. A 94, 043645 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    Y.A. Liao, A.S.C. Rittner, T. Paprotta, W. Li, G.B. Partridge, R.G. Hulet, S.K. Baur, E.J. Mueller, Nature (London) 467, 567 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen, U. Sen, Adv. Phys. 56, 243 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    R. Schmidt, H.R. Sadeghpour, E. Demler, Phys. Rev. Lett. 116, 105302 (2016)ADSCrossRefGoogle Scholar
  22. 22.
    P. Massignan, G.M. Bruun, Eur. Phys. J. D 65, 83 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    W. Yi, X. Cui, Phys. Rev. A 92, 013620 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    M. Koschorreck, D. Pertot, E. Vogt, B. Fröhlich, M. Feld, M. Köhl, Nature (London) 485, 619 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    S. Tan, Ann. Phys. 323, 2952A (2008)ADSCrossRefGoogle Scholar
  26. 26.
    S. Tan, Ann. Phys. 323, 2971A (2008)ADSCrossRefGoogle Scholar
  27. 27.
    S. Tan, Ann. Phys. 323, 2987A (2008)ADSCrossRefGoogle Scholar
  28. 28.
  29. 29.
    M. Barth, W. Zwerger, Ann. Phys. 326, 2544 (2011)ADSCrossRefGoogle Scholar
  30. 30.
    E.V.H. Doggen, J.J. Kinnunen, Phys. Rev. Lett. 111, 025302 (2013)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of SciencesWuhanP.R. China
  2. 2.School of Physical Sciences, University of Chinese Academy of SciencesBeijingP.R. China
  3. 3.School of Computer Science and Technology, Huazhong University of Science and TechnologyWuhanP.R. China

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