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Nonlinear Dynamics

, Volume 88, Issue 4, pp 2957–2967 | Cite as

Tunneling dynamics between atomic bright solitons

  • Li-Chen Zhao
  • Liming Ling
  • Zhan-Ying Yang
  • Wen-Li Yang
Original Paper

Abstract

We investigate tunneling behavior between two bright solitons in a Bose–Einstein condensate with attractive contact interactions between atoms. The explicit tunneling properties including tunneling particles and oscillation period are described analytically, which indicates that the periodic tunneling form is a nonlinear Josephson type oscillation. The results suggest that the breathing behavior of solitons comes from the tunneling mechanism in an effective double-well potential, which is quite different from the modulational instability mechanism for Akhmediev breather and K-M breather. The relative phase between the two solitons has no effects on the tunneling period and particle exchanging rate. Furthermore, we obtain a phase diagram for two-soliton interaction which admits tunneling property, particle-like property, interference property, and a resonant interaction case. The explicit conditions for them are clarified based on the defined critical distance \(d_c\) and spatial interference period D.

Keywords

Soliton tunneling Wave properties Particle properties 

Notes

Acknowledgements

This work is supported by National Natural Science Foundation of China (Contact No. 11405129, 11404259), and Shaanxi Province Science association of colleges and universities (Contact No. 20160216).

References

  1. 1.
    Zabusky, N.J., Kruskal, M.D.: Interaction of solitrons in a collisionless plasma and the recurrence of initial state. Phys. Rev. Lett. 15, 240 (1965)CrossRefMATHGoogle Scholar
  2. 2.
    Stegeman, G.I., Segev, M.: Optical spatial solitons and their interactions: universality and diversity. Science 286, 1518–1523 (1999)CrossRefGoogle Scholar
  3. 3.
    Serkin, V.N., Hasegawa, A.: Novel soliton solutions of the nonlinear Schrdinger equation model. Phys. Rev. Lett. 85, 4502–4505 (2000)CrossRefGoogle Scholar
  4. 4.
    Serkin, V.N., Hasegawa, A.: Nonautonomous solitons in external potentials. Phys. Rev. Lett. 98, 074102 (2007)CrossRefGoogle Scholar
  5. 5.
    Zhao, L.C., Yang, Z.Y., Ling, L.M., et al.: Precisely controllable bright nonautonomous solitons in Bose–Einstein condensate. Phys. Lett. A 375, 1839–1842 (2011)CrossRefGoogle Scholar
  6. 6.
    Akhmediev, N., Ankiewicz, A.: Spatial soliton X-junctions and couplers. Opt. Commun. 100, 186–192 (1993)CrossRefMATHGoogle Scholar
  7. 7.
    Kevrekidis, P.G., Frantzeskakis, D., Carretero-Gonzalez, R.: Emergent Nonlinear Phenomena in Bose–Einstein Condensates: Theory and Experiment. Springer, Berlin (2009)MATHGoogle Scholar
  8. 8.
    Snyder, A.W., John, D.: Mitchell. Access. Solitons, Sci. 276, 1538–1541 (1997)Google Scholar
  9. 9.
    Kumar, V.R., Radha, R., Panigrahi, P.K.: Matter wave interference pattern in the collision of bright solitons. Phys. Lett. A 373, 4381–4385 (2009)CrossRefMATHGoogle Scholar
  10. 10.
    Helm, J.L., Cornish, S.L., Gardiner, S.A.: Sagnac interferometry using bright matter-wave solitons. Phys. Rev. Lett. 114, 134101 (2015)CrossRefGoogle Scholar
  11. 11.
    McDonald, G.D., Kuhn, C.C.N., Hardman, K.S., et al.: Bright solitonic matter-wave interferometer. Phys. Rev. Lett. 113, 013002 (2014)CrossRefGoogle Scholar
  12. 12.
    Polo, J., Ahufinger, V.: Soliton-based matter-wave interferometer. Phys. Rev. A 88, 053628 (2013)CrossRefGoogle Scholar
  13. 13.
    Sakaguchi, H., Malomed, B.A.: Matter-wave soliton interferometer based on a nonlinear splitter. New J. Phys. 18, 025020 (2016)CrossRefGoogle Scholar
  14. 14.
    Zhao, L.C., Ling, L., Yang, Z.Y., et al.: Properties of the temporalspatial interference pattern during soliton interaction. Nonlinear Dyn. 83, 659–665 (2016)CrossRefGoogle Scholar
  15. 15.
    Nguyen, J.H.V., Dyke, P., Luo, D., Malomed, B.A., Hulet, R.G.: Collisions of matter-wave solitons. Nat. Phys. 10, 918–922 (2014)CrossRefGoogle Scholar
  16. 16.
    Billam, T.P., Weiss, C.: Atomic solitons: these crashing waves. Nat. Phys. 10, 902–903 (2014)CrossRefGoogle Scholar
  17. 17.
    Kuznetsov, E.: Solitons in a parametrically unstable plasma. Sov. Phys. Dokl. 22, 507–508 (1977)Google Scholar
  18. 18.
    Ma, Y.C.: The perturbed plane-wave solution of the cubic Schrodinger equation. Stud. Appl. Math. 60, 43–58 (1979)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: GeigerNuttall law for Schrdinger solitons. J. Mod. Opt. 60, 116–127 (2013)CrossRefMATHGoogle Scholar
  20. 20.
    Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Soliton selfinduced sub-barrier transparency and the controllable shooting out effect. J. Mod. Opt. 60, 444–451 (2013)CrossRefGoogle Scholar
  21. 21.
    Martin, A.D., Ruostekoski, J.: Quantum dynamics of atomic bright solitons under splitting and re-collision, and implications for interferometry. New J. Phys. 14, 043040 (2012)CrossRefGoogle Scholar
  22. 22.
    Tkeshelashvili, L.: Tunneling of optical lattice solitons at interfaces. Phys. Rev. A 86, 033836 (2012)CrossRefGoogle Scholar
  23. 23.
    Karamatskos, E.T., Stockhofe, J., Kevrekidis, P.G., Schmelcher, P.: Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap. Phys. Rev. A 91, 043637 (2015)CrossRefGoogle Scholar
  24. 24.
    Salasnich, L., Parola, A., Reatto, L.: Modulational instability and complex dynamics of confined matter-wave solitons. Phys. Rev. Lett. 91, 080405 (2003)CrossRefGoogle Scholar
  25. 25.
    Leggett, A.J.: Bose–Einstein condensation in the alkali gases: some fundamental concepts. Rev. Mod. Phys. 73, 307 (2001)CrossRefGoogle Scholar
  26. 26.
    Billam, T.P., Cornish, S.L., Gardiner, S.A.: Realizing bright matter-wave soliton collisions with controlled relative phase. Phys. Rev. A 83, 041602(R) (2011)CrossRefGoogle Scholar
  27. 27.
    Becker, C., Stellmer, S., Panahi, P.S., et al.: Oscillations and interactions of dark and dark-bright solitons in Bose–Einstein condensates. Nat. Phys. 4, 496–501 (2008)CrossRefGoogle Scholar
  28. 28.
    Khaykovich, L., Schreck, F., Ferrari, G., et al.: Formation of a matter-wave bright soliton. Science 296, 1290 (2002)CrossRefGoogle Scholar
  29. 29.
    Matveev, V.B., Salle, M.A.: Darboux Transformation and Solitons. Springer, Berlin (1991)CrossRefMATHGoogle Scholar
  30. 30.
    Guo, B.L., Ling, L.M., Liu, Q.P.: Nonlinear Schrdinger equation: generalized Darboux transformation and rogue wave solutions. Phys. Rev. E 85, 026607 (2012)CrossRefGoogle Scholar
  31. 31.
    Josephson, B.D.: Possible new effects in superconductive tunnelling. Phys. Lett. 1, 251 (1962)CrossRefMATHGoogle Scholar
  32. 32.
    Belyaeva, T.L., Serkin, V.N.: Wave-particle duality of solitons and solitonic analog of the Ramsauer–Townsend effect. Eur. Phys. J. D 66, 153 (2012)CrossRefGoogle Scholar
  33. 33.
    Jisha, C.P., Alberucci, A., Lee, R.K., Assanto, G.: Deflection and trapping of spatial solitons in linear photonic potentials. Opt. Express 21, 18646 (2013)CrossRefGoogle Scholar
  34. 34.
    Wang, C.H., Hong, T.M., Lee, R.K., et al.: Particle-wave duality in quantum tunneling of a bright soliton. Opt. Express 20, 22675 (2012)CrossRefGoogle Scholar
  35. 35.
    Williams, J., Walser, R., Cooper, J., Cornell, E., Holland, M.: Nonlinear Josephson-type oscillations of a driven, two-component Bose–Einstein condensate. Phys. Rev. A 59, R31 (1999)Google Scholar
  36. 36.
    Williams, J.: Optimal conditions for observing Josephson oscillations in a double-well Bose-gas condensate. Phys. Rev. A 64, 013610 (2001)CrossRefGoogle Scholar
  37. 37.
    Zhao, L.C., He, S.L.: Matter wave solitons in coupled system with external potentials. Phys. Lett. A 375, 3017–3020 (2011)CrossRefGoogle Scholar
  38. 38.
    Zhao, L.C., Liu, J.: Localized nonlinear waves in a two-mode nonlinear fiber. J. Opt. Soc. Am. B 29, 3119–3127 (2012)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Bludov, Y.V., Konotop, V.V., Akhmediev, N.: Vector rogue waves in binary mixtures of Bose–Einstein condensates. Eur. Phys. J. Spec. Top. 185, 169–180 (2010)CrossRefGoogle Scholar
  40. 40.
    Law, K.J.H., Kevrekidis, P.G., Tuckerman, Laurette S.: Stable vortexbright-soliton structures in two-component Bose–Einstein condensates. Phys. Rev. Lett. 105, 160405 (2010)CrossRefGoogle Scholar
  41. 41.
    Blow, K.J., Doran, N.J.: Multiple dark soliton solutions of the nonlinear Schrdinger equation. Phys. Lett. A 107, 55–58 (1985)MathSciNetCrossRefMATHGoogle Scholar
  42. 42.
    Middelkamp, S., Chang, J.J., Hamner, C., et al.: Dynamics of darkbright solitons in cigar-shaped Bose–Einstein condensates. Phys. Lett. A 375, 642–646 (2011)CrossRefGoogle Scholar
  43. 43.
    Negretti, A., Henkel, C.: Enhanced phase sensitivity and soliton formation in an integrated BEC interferometer. J. Phys. B 37, L385–L390 (2004)CrossRefGoogle Scholar
  44. 44.
    Robins, N., Altin, P., Debs, J., Close, J.: Atom lasers: production, properties and prospects for precision inertial measurement. Phys. Rep. 529, 265 (2013)CrossRefGoogle Scholar
  45. 45.
    Debs, J.E., Altin, P.A., Barter, T.H., et al.: Cold atom gravimetry with a Bose–Einstein Condensate. Phys. Rev. A 84, 033610 (2011)CrossRefGoogle Scholar
  46. 46.
    Cuevas, J., Kevrekidis, P.G., Malomed, B.A., Dyke, P., Hulet, R.G.: Interactions of solitons with a Gaussian barrier: splitting and recombination in quasi-1D and 3D. New J. Phys. 15, 063006 (2013)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Gertjierenken, B.: Bright-soliton quantum superpositions: signatures of high- and low-fidelity states. Phys. Rev. A 88, 053623 (2013)CrossRefGoogle Scholar
  48. 48.
    Gertjerenken, B., Billam, T.P., Blackley, C.L., et al.: Generating mesoscopic Bell states via collisions of distinguishable quantum bright solitons. Phys. Rev. Lett. 111, 100406 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.School of PhysicsNorthwest UniversityXi’anChina
  2. 2.Shaanxi Key Laboratory for Theoretical Physics FrontiersXi’anChina
  3. 3.School of MathematicsSouth China University of TechnologyGuangzhouChina
  4. 4.Institute of Modern PhysicsNorthwest UniversityXianChina

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