Soliton appearing in boson-fermion mixture at the third order of the interaction radius

  • Konstantin V. Zezyulin
  • Pavel A. Andreev
  • Leonid S. Kuz’menkov
Regular Article

Abstract

In this paper we consider an ultra-cold mixture of boson and fermion atoms on the basis of quantum hydrodynamics. Small one-dimensional perturbations in such systems are being analyzed. A possibility is shown for soliton solutions of a new type to appear if the third order of the interaction radius is taken into account in the analysis of interactions. A fermion-fermion interaction occurs in explicit form if this approximation is accepted. The conditions that lead to occurrence of this type of soliton in a mixture of boson and fermion atoms were investigated. Restrictions on the fermion-fermion interaction were found that are necessary for this kind of perturbations to appear in the system. Conditions determining whether perturbances would be a condensed soliton or a rarefied soliton are shown.

Keywords

Cold Matter and Quantum Gas 

References

  1. 1.
    T.P. Billam, S.L. Cornish, S.A. Gardiner, Phys. Rev. A 83, 041602(R) (2011)ADSCrossRefGoogle Scholar
  2. 2.
    J. Abdullaev, A.S. Desyatnikov, E.A. Ostrovskaya, J. Opt. 13, 064023 (2011)ADSCrossRefGoogle Scholar
  3. 3.
    U.A. Khawaja, H.T.C. Stoof, New J. Phys. 13, 085003 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    W.B. Cardosoa, A.T. Avelara, D. Bazeiab, Phys. Lett. A 374, 2640 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    L. Wen, Y. Zhang, J. Feng, J. Phys. B 43, 225302 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    G. Filatrella, B.A. Malomed, L. Salasnich, Phys. Rev. A 79, 045602 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    J. Denschlag et al., Science 287, 97 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    T. Karpiuk et al., Phys. Rev. Lett. 93, 100401 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    T. Tsurumi, M. Wadati, J. Phys. Soc. Jpn 69, 97 (2000)ADSCrossRefGoogle Scholar
  10. 10.
    M. Salerno, Phys. Rev. A 72, 063602 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    B. Ramachandhran, S.G. Bhongale, H. Pu, Phys. Rev. A 83, 033607 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Zeng-Qiang Yu, Shizhong Zhang, Hui Zhai, Phys. Rev. A 83, 041603 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    K.E. Strecker, G.B. Partidge, A.G. Truscott, R.G. Hulet, Nature 417, 9 (2002)CrossRefGoogle Scholar
  14. 14.
    R. Fedele, H. Schamel, Eur. Phys. J. B 27, 313 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, M.K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004)ADSCrossRefGoogle Scholar
  16. 16.
    L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L.D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G.V. Shlyapnikov, M. Lewenstein, Phys. Rev. Lett. 83, 5198 (1999)ADSCrossRefGoogle Scholar
  18. 18.
    B.P. Anderson et al., Phys. Rev. Lett. 86, 2926 (2001)ADSCrossRefGoogle Scholar
  19. 19.
    A.M. Mateo, V. Delgado, B.A. Malomed, Phys. Rev. A 83, 053610 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    J. Cuevas, B.A. Malomed, P.G. Kevrekidis, D.J. Frantzeskakis, Phys. Rev. A 79, 053608 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    G. Csire, D. Schumayer, B. Apagyi, Phys. Rev. A 82, 063608 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    M.A. Hoefer, J.J. Chang, C. Hamner, P. Engels, Phys. Rev. A 84, 041605(R) (2011)ADSCrossRefGoogle Scholar
  23. 23.
    P.A. Andreev, L.S. Kuz’menkov, Mod. Phys. Lett. B 26, 1250152 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    R. Liao, J. Brand, Phys. Rev. A 83, 041604(R) (2011)ADSGoogle Scholar
  25. 25.
    R.G. Scott, F. Dalfovo, L.P. Pitaevskii, S. Stringari, Phys. Rev. Lett. 106, 185301 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    J. Santhanam, V.M. Kenkre, V.V. Konotop, Phys. Rev. A 73, 013612 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    T. Karpiuk, M. Brewczyk, K. Rzewski, Phys. Rev. A 73, 053602 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    S.K. Adhikari, Phys. Rev. A 72, 053608 (2005)ADSCrossRefGoogle Scholar
  29. 29.
    S.K. Adhikari, L. Salasnich, Phys. Rev. A 76, 023612 (2007)ADSCrossRefGoogle Scholar
  30. 30.
    N.G. Parker, D.A. Smith, Phys. Rev. A 85, 013604 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    S.K. Adhikari, J. Phys. B 38, 3607 (2005)ADSCrossRefGoogle Scholar
  32. 32.
    A.G. Truscott, K.E. Strecker, W.I. McAlexander, G.B. Partridge, R.G. Hulet, Science 291, 2570 (2001)ADSCrossRefGoogle Scholar
  33. 33.
    F. Schreck, L. Khaykovich, K.L. Corwin, G. Ferrari, T. Bourdel, J. Cubizolles, C. Salomon, Phys. Rev. Lett. 88, 160401 (2002)CrossRefGoogle Scholar
  34. 34.
    Z. Hadzibabic, C.A. Stan, K. Dieckmann, S. Gupta, M.W. Zwierlein, A. Görlitz, W. Ketterle, Phys. Rev. Lett. 88, 160401 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    G. Roati, F. Riboli, G. Modugno, M. Inguscio, Phys. Rev. Lett. 89, 150403 (2002)ADSCrossRefGoogle Scholar
  36. 36.
    P.A. Andreev, L.S. Kuz’menkov, Phys. Rev. A 78, 053624 (2008)ADSCrossRefGoogle Scholar
  37. 37.
    L.S. Kuz’menkov, S.G. Maksimov, Theor. Math. Phys. 118, 287 (1999)Google Scholar
  38. 38.
    P.A. Andreev, L.S. Kuz’menkov, arXiv:1201.2440Google Scholar
  39. 39.
    P.A. Andreev, M.I. Trukhanova, Russian Phys. J. 53, 912 (2011)MathSciNetCrossRefGoogle Scholar
  40. 40.
    F. Haas, G. Manfredi, M. Feix, Phys. Rev. E 62, 2763 (2000)ADSCrossRefGoogle Scholar
  41. 41.
    L.S. Kuz’menkov, S.G. Maksimov, V.V. Fedoseev, Theor. Math. Fiz. 126, 136 (2001) [Theoretical and Mathematical Physics 126, 110 (2001)]MathSciNetGoogle Scholar
  42. 42.
    M. Marklund, G. Brodin, Phys. Rev. Lett. 98, 025001 (2007)ADSCrossRefGoogle Scholar
  43. 43.
    G. Brodin, M. Marclund, New J. Phys. 9, 277 (2007)CrossRefGoogle Scholar
  44. 44.
    G. Brodin, M. Marklund, J. Zamanian, B. Ericsson, P.L. Mana, Phys. Rev. Lett. 101, 245002 (2008)ADSCrossRefGoogle Scholar
  45. 45.
    P.K. Shukla, B. Eliasson, Rev. Mod. Phys. 83, 885 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    F.A. Asenjo, V. Munoz, J.A. Valdivia, S.M. Mahajan, Phys. Plasmas 18, 012107 (2011)ADSCrossRefGoogle Scholar
  47. 47.
    P.A. Andreev, L.S. Kuz’menkov, M.I. Trukhanova, Phys. Rev. B 84, 245401 (2011)ADSCrossRefGoogle Scholar
  48. 48.
    P.A. Andreev, arXiv:1202.3398Google Scholar
  49. 49.
    P.A. Andreev, arXiv:1201.0779Google Scholar
  50. 50.
    P.A. Andreev, arXiv:1201.6553Google Scholar
  51. 51.
    D.A. Butts, D.S. Rokhsar, Phys. Rev. A 55, 4346 (1997)ADSCrossRefGoogle Scholar
  52. 52.
    S.K. Adhikari, New J. Phys. 8, 258 (2006)CrossRefGoogle Scholar
  53. 53.
    Yu.V. Bludov, J. Santhanam, V.M. Kenkre, V.V. Konotop, Phys. Rev. A 74, 043620 (2006)ADSCrossRefGoogle Scholar
  54. 54.
    M. Rizzi, A. Imambekov, Phys. Rev. A 77, 023621 (2008)ADSCrossRefGoogle Scholar
  55. 55.
    T. Maruyama, G.F. Bertsch, Phys. Rev. A 77, 063611 (2008)ADSCrossRefGoogle Scholar
  56. 56.
    A.M. Belemuk, V.N. Ryzhov, S.-T. Chui, Phys. Rev. A 76, 013609 (2007)ADSCrossRefGoogle Scholar
  57. 57.
    S.K. Adhikari, Phys. Rev. A 70, 043617 (2004)ADSCrossRefGoogle Scholar
  58. 58.
    M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle, Nature 435, 1047 (2005)ADSCrossRefGoogle Scholar
  59. 59.
    H. Washimi, T. Taniuti, Phys. Rev. Lett. 17, 996 (1966)ADSCrossRefGoogle Scholar
  60. 60.
    E. Infeld, G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, 2000)Google Scholar
  61. 61.
    H.-Q. Cai, S.-R. Yang, J.-K. Xue, Commun. Theor. Phys. 55, 583 (2011)ADSMATHCrossRefGoogle Scholar
  62. 62.
    M. Kulkarni, A.G. Abanov, Phys. Rev. A 86, 033614 (2012)ADSCrossRefGoogle Scholar
  63. 63.
    P.A. Andreev, L.S. Kuz’menkov, Russian Phys. J. 52, 912 (2009)MathSciNetADSMATHCrossRefGoogle Scholar
  64. 64.
    N.N. Rosanov, A.G. Vladimirov, D.V. Skryabin, W.J. Firth, Phys. Lett. A 293, 45 (2002)ADSMATHCrossRefGoogle Scholar
  65. 65.
    E. Braaten, H.-W. Hammer, S. Hermans, Phys. Rev. A 63, 063609 (2001)ADSCrossRefGoogle Scholar
  66. 66.
    B.C. Kalita, R. Das, Plasma Phys. 5, 3588 (1998)CrossRefGoogle Scholar
  67. 67.
    Cheng Chin et al., Rev. Mod. Phys. 82, 1225 (2010)ADSCrossRefGoogle Scholar
  68. 68.
    I. Bloch, J. Dalibard, W. Zwerger, Rev. Mod. Phys. 80, 885 (2008)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Konstantin V. Zezyulin
    • 1
  • Pavel A. Andreev
    • 2
  • Leonid S. Kuz’menkov
    • 1
  1. 1.Department of Theoretical Physics, Physics FacultyMoscow State UniversityMoscowRussian Federation
  2. 2.Department of General Physics, Physics FacultyMoscow State UniversityMoscowRussian Federation

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