Exotic complexes in two-component one-dimensional Bose-Einstein condensates

  • D. Belobo BeloboEmail author
Regular Article


Novel explicit solutions of two-component Bose gases slightly in touch with a reservoir of cold atoms, with time-dependent two- and three-body interactions and under the influence of linear fields are constructed. Using a relatively simple method, complexes made of “solitons-generalized Jacobi elliptic functions”, “solitons-triangular periodic” waves, and others, are unveiled. The mean dynamics, relative phase, the miscibility-immiscibility transition are fully controlled by the geometry of linear fields and the mass ration of the atomic species. Our analytical predictions are confirmed by intensive numerical simulations with a good accuracy.


  1. 1.
    Y.S. Kivshar, G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003)Google Scholar
  2. 2.
    C.B. Tabi, A. Mohamadou, T.C. Kofané, Solitons in DNA and Biological Implications (Scholar’ Press, USA, 2014)Google Scholar
  3. 3.
    P.G. Kevrekidis, D.J. Frantzeskakis, R. Carretero-Gonzalez, Emergent Nonlinear Phenomena in Bose-Einstein Condensates (Springer-Verlag, Berlin, 2008)Google Scholar
  4. 4.
    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
  5. 5.
    J. Denschlag, J.E. Simsarian, D.L. Feder, C.W. Clark, L.A. Collins, J. Cubizolles, L. Deng, E.W. Hagley, K. Helmerson, W.P. Reinhardt, S.L. Rolston, B.I. Schneider, W.D. Phillips, Science 287, 97 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L.D. Carr, Y. Castin, C. Salomon, Science 296, 1290 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    R.W. Pattinson, Two-Component Bose-Einstein Condensates: Equilibria and Dynamics at Zero Temperature and Beyond, PhD thesis, Newcastle University (2014) and references thereinGoogle Scholar
  8. 8.
    Th. Busch, J.R. Anglin, Phys. Rev. Lett. 87, 010401 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    C. Becker, S. Stellmer, P. Soltan-Panahi, S. Dörscher, M. Baumert, E.M. Richter, J. Kronjäger, K. Bongs, K. Sengstock, Nat. Phys. 4, 496 (2008)CrossRefGoogle Scholar
  10. 10.
    C. Hamner, J.J. Chang, P. Engels, M.A. Hoefer, Phys. Rev. Lett. 106, 065302 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    C. Hamner, Y. Zhang, J.J. Chang, C. Zhang, P. Engels, Phys. Rev. Lett. 111, 264101 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    M.A. Hoefer, J.J. Chang, C. Hamner, P. Engels, Phys. Rev. A 84, 041605(R) (2011)ADSCrossRefGoogle Scholar
  13. 13.
    A.M. Kamchatnov, V.V. Sokolov, Phys. Rev. A 91, 043621 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    P. Öhberg, L. Santos, Phys. Rev. Lett. 86, 2918 (2001)ADSCrossRefGoogle Scholar
  15. 15.
    Yao Shu-Fang, Li Qiu-Yan, Li Zai-Dong, Chin. Phys. B 20, 110307 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    K. Manikandan, P. Muruganandam, M. Senthilvelan, M. Lakshmanan, Phys. Rev. E 93, 032212 (2016)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    C. Qu, L.P. Pitaevskii, S. Stringari, Phys. Rev. Lett. 116, 160402 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    D. Belobo Belobo, Dynamics of Matter-Wave Condensates: Effects of quantum fluctuations and three-body interatomic interactions, PhD thesis, University of Yaounde I (2015)Google Scholar
  19. 19.
    D. Belobo Belobo, G.H. Ben-Bolie, T.C. Kofané, Phys. Rev. E 89, 042913 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    D. Belobo Belobo, G.H. Ben-Bolie, T.C. Kofané, Phys. Rev. E 91, 042902 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    S. Knoop, T. Schuster, R. Scelle, A. Trautmann, J. Appmeier, M.K. Oberthaler, E. Tiesinga, E. Tiemann, Phys. Rev. A 83, 042704 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    V.S. Filho, S.M. Holz, L. Tomio, Phys. Lett. A 372, 6778 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    R. Labouvie, B. Santra, S. Heun, S. Wimberger, H. Ott, Phys. Rev. Lett. 115, 050601 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    G. Kordas, D. Witthaut, P. Buonsante, A. Vezzani, R. Burioni, A.I. Karanikas, S. Wimberger, Eur. Phys. J. ST 224, 2127 (2015)CrossRefGoogle Scholar
  25. 25.
    H. Ott, Rep. Prog. Phys. 79, 054401 (2016)ADSCrossRefGoogle Scholar
  26. 26.
    D. Witthaut, F. Trimborn, H. Hennig, G. Kordas, T. Geisel, S. Wimberger, Phys. Rev. A 83, 063608 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    N.N. Rozanov, J. Opt. Technol. 76, 187 (2009)CrossRefGoogle Scholar
  28. 28.
    Z. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, F. Lederer, J. Opt. Soc. Am. B 19, 487 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    E. Ultanir, G.I. Stegeman, D. Michaelis, C.H. Lange, F. Lederer, Phys. Rev. Lett. 90, 253903 (2003)ADSCrossRefGoogle Scholar
  30. 30.
    R. Kuszelewicz, S. Barbay, G. Tissoni, G. Almuneau, Eur. Phys. J. D 59, 1 (2010) and references thereinADSCrossRefGoogle Scholar
  31. 31.
    K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, P. Grelu, Phys. Rev. Lett. 118, 243901 (2017)ADSCrossRefGoogle Scholar
  32. 32.
    M. Wimmer, A. Regensburger, M.-A. Miri, C. Bersch, D.N. Christodoulides, U. Peschel, Nat. Commun. 6, 7782 (2015)CrossRefGoogle Scholar
  33. 33.
    Y. Lumer, Y. Plotnik, M.C. Rechtman, M. Segev, Phys. Rev. Lett. 111, 263901 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    Li-Hua Zhang, Appl. Math. Comput. 208, 144 (2009)MathSciNetGoogle Scholar
  35. 35.
    Emad A.-B. Abdel-Salam, Z. Naturforsch. 64a, 639 (2009)ADSGoogle Scholar
  36. 36.
    G. Modugno, M. Modugno, F. Riboli, G. Roati, M. Inguscio, Phys. Rev. Lett. 89, 190404 (2002)ADSCrossRefGoogle Scholar
  37. 37.
    G.D. Telles, A.R.L. Caires, V.S. Bagnato, L.G. Marcassa, Phys. Rev. Lett. 92, 133203 (2004)ADSCrossRefGoogle Scholar
  38. 38.
    S.B. Papp, C.E. Wieman, Phys. Rev. Lett. 97, 180404 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    D.T. Son, M.A. Stephanov, Phys. Rev. A 65, 063621 (2002)ADSCrossRefGoogle Scholar
  40. 40.
    M. Saba, T.A. Pasquini, C. Sanner, Y. Shin, W. Ketterle, D.E. Pritchard, Science 307, 1945 (2005)ADSCrossRefGoogle Scholar
  41. 41.
    D.S. Hall, M.R. Matthews, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 81, 1543 (1998)ADSCrossRefGoogle Scholar
  42. 42.
    P. Treutlein, P. Hommelhoff, T. Steinmetz, T.W. Hänsch, J. Reichel, Phys. Rev. Lett. 92, 203005 (2004)ADSCrossRefGoogle Scholar
  43. 43.
    P. Rosenbusch, Appl. Phys. B 95, 227 (2009)ADSCrossRefGoogle Scholar
  44. 44.
    R.P. Anderson, C. Ticknor, A.I. Sidorov, B.V. Hall, Phys. Rev. A 80, 023603 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    Y. Li, Y. Castin, A. Sinatra, Phys. Rev. Lett. 100, 210401 (2008)ADSCrossRefGoogle Scholar
  46. 46.
    A.M. Rey, L. Jiang, M.D. Lukin, Phys. Rev. A 76, 053617 (2007)ADSCrossRefGoogle Scholar
  47. 47.
    G.-R. Jin, S.W. Kim, Phys. Rev. Lett. 99, 170405 (2007)ADSCrossRefGoogle Scholar
  48. 48.
    A. Sørensen, L.-M. Duan, J.I. Cirac, P. Zoller, Nature (London) 409, 63 (2001)ADSCrossRefGoogle Scholar
  49. 49.
    X. Ma, R. Driben, B.A. Malomed, T. Meier, S. Schumacher, Sci. Rep. 6, 34847 (2016)ADSCrossRefGoogle Scholar
  50. 50.
    A. Roeksabutr, T. Mayteevarunyoo, B.A. Malomed, Opt. Express 20, 24559 (2012)ADSCrossRefGoogle Scholar
  51. 51.
    V.M. Pérez-García, J. Belmonte Beitia, Phys. Rev. A 72, 033620 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    S. Coen, M. Haelterman, Phys. Rev. Lett. 87, 140401 (2001)ADSCrossRefGoogle Scholar
  53. 53.
    N. Dror, B.A. Malomed, J. Zeng, Phys. Rev. E 84, 046602 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.African Centre for Advanced StudiesYaoundeCameroon
  2. 2.PREPAVOGTYaoundeCameroon

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