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Quadrupolar matter-wave soliton in two-dimensional free space

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Abstract

We study two-dimensional (2D) matter-wave solitons in the mean-field models formed by electric quadrupole particles with long-range quadrupole–quadrupole interaction (QQI) in 2D free space. The existence of 2D matter-wave solitons in the free space was predicted using the 2D Gross–Pitaevskii Equation (GPE). We find that the QQI solitons have a higher mass (smaller size and higher intensity) and stronger anisotropy than the dipole–dipole interaction (DDI) solitons under the same environmental parameters. Anisotropic soliton–soliton interaction between two identical QQI solitons in 2D free space is studied. Moreover, stable anisotropic dipole solitons are observed, to our knowledge, for the first time in 2D free space under anisotropic nonlocal cubic nonlinearity.

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References

  1. L. P. Pitaevskii and S. Sandro, Bose–Einstein Condensation, No. 116, Oxford University Press, 2003

    MATH  Google Scholar 

  2. S. Burger, K. Bongs, S. Dettmer, W. Ertmer, and K. Sengstock, Dark solitons in Bose-Einstein condensates, Phys. Rev. Lett. 83(25), 5198 (1999)

    Article  ADS  Google Scholar 

  3. S. Song, L. Wen, C. Liu, S. Gou, and W. Liu, Ground states, solitons and spin textures in spin-1 Bose–Einstein condensates, Front. Phys. 8(3), 302 (2013)

    Article  Google Scholar 

  4. B. P. Anderson, P. C. Haljan, C. A. Regal, D. L. Feder, L. A. Collins, C. W. Clark, and E. A. Cornell, Watching dark solitons decay into vortex rings in a Bose–Einstein condensate, Phys. Rev. Lett. 86(14), 2926 (2001)

    Article  ADS  Google Scholar 

  5. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, Observation of vortex lattices in Bose–Einstein condensates, Science 292(5516), 476 (2001)

    Article  ADS  Google Scholar 

  6. F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, Josephson junction arrays with Bose-Einstein condensates, Science 293(5531), 843 (2001)

    Article  ADS  Google Scholar 

  7. C. Lee, W. Hai, L. Shi, X. Zhu, and K. Gao, Chaotic and frequency-locked atomic population oscillations between two coupled Bose-Einstein condensates, Phys. Rev. A 64(5), 053604 (2001)

    Article  ADS  Google Scholar 

  8. C. Lee, J. Huang, H. Deng, H. Dai, and J. Xu, Nonlinear quantum interferometry with Bose condensed atoms, Front. Phys. 7(1), 109 (2012)

    Article  Google Scholar 

  9. C. Lee, Universality and anomalous mean-field breakdown of symmetry-breaking transitions in a coupled two-component Bose–Einstein condensate, Phys. Rev. Lett. 102(7), 070401 (2009)

    Article  ADS  Google Scholar 

  10. H. Zheng and Q. Gu, Dynamics of Bose–Einstein condensates in a one-dimensional optical lattice with double-well potential, Front. Phys. 8(4), 375 (2013)

    Article  Google Scholar 

  11. Y. Li, J. Liu, W. Pang, and B. A. Malomed, Symmetry breaking in dipolar matter-wave solitons in dual-core couplers, Phys. Rev. A 87(1), 013604 (2013)

    Article  ADS  Google Scholar 

  12. Y. Li, W. Pang, and B. A. Malomed, Nonlinear modes and symmetry breaking in rotating double-well potentials, Phys. Rev. A 86(2), 023832 (2012)

    Article  ADS  Google Scholar 

  13. J. Denschlag, Generating solitons by phase engineering of a Bose–Einstein condensate, Science 287, 97 (2000)

    Article  ADS  Google Scholar 

  14. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cubizolles, L. D. Carr, Y. Castin, and C. Salomon, Formation of a matter-wave bright soliton, Science 296, 1290 (2002)

    Article  ADS  Google Scholar 

  15. Ph. Courteille, R. S. Freeland, D. J. Heinzen, F. A. van Abeelen, and B. J. Verhaar, Observation of a Feshbach resonance in cold atom scattering, Phys. Rev. Lett. 81, 69 (1998)

    Article  ADS  Google Scholar 

  16. M. Theis, G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. Hecker Denschlag, Tuning the scattering length with an optically induced Feshbach resonance, Phys. Rev. Lett. 93(1), 123001 (2004)

    Article  ADS  Google Scholar 

  17. X. Zhang, X. Hu, D. Wang, X. Liu, and W. Liu, Dynamics of Bose-Einstein condensates near Feshbach resonance in external potential, Front. Phys. China 6(1), 46 (2011)

    ADS  Google Scholar 

  18. S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn and W. Ketterle, Observation of Feshbach resonances in a Bose–Einstein condensate, Nature 293(6672), 151 (1998)

    ADS  Google Scholar 

  19. P. Courteille, R. S. Freeland, D. J. He inzen, F. A. van Abeelen and B. J. Verhaar, Observation of Feshbach resonances in cold atom scattering, Phys. Rev. Lett. 81, 69 (1998)

    Article  ADS  Google Scholar 

  20. J. Huang, H. Li, X. Zhang, and Y. Li, Transmission, reflection, scattering, and trapping of traveling discrete solitons by Ƈ and Ʋ point defects, Front. Phys. 10(2), 104201 (2015)

    Article  MathSciNet  Google Scholar 

  21. Z. Chen, J. Huang, J. Chai, X. Zhang, Y. Li, and B. A. Malomed, Discrete solitons in self-defocusing systems with PT -symmetric defects, Phys. Rev. A 91(5), 053821 (2015)

    Article  ADS  Google Scholar 

  22. M. Saha, A. K. Sarma, Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects, Opt. Commun. 291, 321 (2013)

    Article  ADS  Google Scholar 

  23. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices, Nature 422(6928), 147 (2003)

    Article  ADS  Google Scholar 

  24. G. Chen, Z. Hong, and Z. Mai, Two-dimensional discrete Anderson location in waveguide matrix, J. Nonlinear Optic. Phys. Mat. 23(03), 1450033 (2014)

    Article  ADS  Google Scholar 

  25. X. Zhang, J. Chai, D. Ou, and Y. Li, Antisymmetry breaking of discrete dipole gap solitons induced by a phase-slip defect, Mod. Phys. Lett. B 28(12), 1450097 (2014)

    Article  ADS  Google Scholar 

  26. N. K. Efremidis and D. N. Christodoulides, Lattice solitons in Bose–Einstein condensates, Phys. Rev. A 67(6), 063608 (2003).

    Article  ADS  Google Scholar 

  27. N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Two-dimensional optical lattice solitons, Phys. Rev. Lett. 91(21), 213906 (2003)

    Article  ADS  Google Scholar 

  28. W. Pang, J. Wu, Z. Yuan, Y. Liu, and G. Chen, Lattice solitons in optical lattice controlled by electromagnetically induced transparency, J. Phys. Soc. Jpn. 80(11), 113401 (2011)

    Article  ADS  Google Scholar 

  29. J. T. Cole and Z. H. Musslimani, Band gaps and lattice solitons for the higher-order nonlinear Schrödinger equation with a periodic potential, Phys. Rev. A 90(1), 013815 (2014)

    Article  ADS  Google Scholar 

  30. X. Gan, P. Zhang, S. Liu, F. Xiao, and J. Zhao, Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton, Phys. Rev. A 89(1), 013844 (2014)

    Article  ADS  Google Scholar 

  31. G. Chen, H. Huang, and M. Wu, Solitary vortices in twodimensional waveguide matrix, J. Nonlinear Optic. Phys. Mat. 24(01), 1550012 (2015)

    Article  ADS  Google Scholar 

  32. G. Chen, H. Huang, and M. Wu, Discrete vortices on anisotropic lattices, Front. Phys. 10, 104206 (2015)

    Google Scholar 

  33. R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Low, and T. Pfau, Rydberg excitation of Bose–Einstein condensates, Phys. Rev. Lett. 100(3), 033601 (2008)

    Article  ADS  Google Scholar 

  34. M. Viteau, M. G. Bason, J. Radogostowicz, N. Malossi, D. Ciampini, O. Morsch, and E. Arimondo, Rydberg excitations in Bose–Einstein condensates in quasi-one-dimensional potentials and optical lattices, Phys. Rev. Lett. 107(6), 060402 (2011)

    Article  ADS  Google Scholar 

  35. S. Giovanazzi, A. Gorlitz, and T. Pfau, Tuning the dipolar interaction in quantum gases, Phys. Rev. Lett. 89(13), 130401 (2002)

    Article  ADS  Google Scholar 

  36. P. Pedri and L. Santos, Two-dimensional bright solitons in dipolar Bose–Einstein condensates, Phys. Rev. Lett. 95(20), 200404 (2005)

    Article  ADS  Google Scholar 

  37. T. Koch, T. Lahaye, J. Metz, B. Frohlich, A. Griesmaier, and T. Pfau, Stabilization of a purely dipolar quantum gas against collapse, Nat. Phys. 4(3), 218 (2008)

    Article  Google Scholar 

  38. I. Tikhonenkov, B. A. Malomed, and A. Vardi, Anisotropic solitons in dipolar Bose–Einstein condensates, Phys. Rev. Lett. 100(9), 090406 (2008)

    Article  ADS  Google Scholar 

  39. Y. Li, J. Liu, W. Pang, and B. A. Malomed, Matter-wave solitons supported by field-induced dipole–dipole repulsion with spatially modulated strength, Phys. Rev. A 88(5), 053630 (2013).

    Article  ADS  Google Scholar 

  40. Z. Luo, Y. Li, W. Pang, and Y. Liu, Dipolar matter-wave soliton in one-dimensional optical lattice with tunable local and nonlocal nonlinearities, J. Phys. Soc. Jpn. 82(9), 094401 (2013)

    Article  ADS  Google Scholar 

  41. S. E. Pollack, D. Dries, M. Junker, Y. P. Chen, T. A. Corcovilos, and R. G. Hulet, Extreme tunability of interactions in a Li7 Bose–Einstein condensate, Phys. Rev. Lett. 102(9), 090402 (2009)

    Article  ADS  Google Scholar 

  42. L. P. Pitaevskii and A. Stringari, Bose–Einstein condensation, Clarendon Press, Oxford, 2003

    MATH  Google Scholar 

  43. Y. Li, J. Liu, W. Pang, and B. A. Malomed, Lattice solitons with quadrupolar intersite interactions, Phys. Rev. A 88(6), 063635 (2013)

    Article  ADS  Google Scholar 

  44. L. D. Landau and E. M. Lifshitz, The Field Theory, Nauka-Publishers, Moscow, 1988

    Google Scholar 

  45. H. Sakaguchi and B. A. Malomed, Solitons in combined linear and nonlinear lattice potentials, Phys. Rev. A 81(1), 013624 (2010)

    Article  ADS  Google Scholar 

  46. X. Zhang, J. Chai, J. Huang, Z. Chen, Y. Li, and B. A. Malomed, Discrete solitons and scattering of lattice waves in guiding arrays with a nonlinear ƤƬ -symmetric defect, Opt. Exp. 22(11), 13927 (2014)

    Article  ADS  Google Scholar 

  47. M. L. Chiofalo, S. Succi, and M. P. Tosi, Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm, Phys. Rev. E 62(5), 7438 (2000)

    Article  ADS  Google Scholar 

  48. J. Yang and T. I. Lakoba, Accelerated imaginary-time evolution methods for the computation of solitary waves, Stud. Appl. Math. 120(3), 265 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  49. J. Yang and T. I. Lakoba, Universally-convergent squaredoperator iteration methods for solitary waves in general nonlinear wave equations, Stud. Appl. Math. 118(2), 153 (2007)

    Article  MathSciNet  Google Scholar 

  50. G. P. Agrawal, Nonlinear Fiber Optics, Academic Press, 2007

    Google Scholar 

  51. Z. Chen, J. Liu, S. Fu, Y. Li, and B. A. Malomed, Discrete solitons and vortices on two-dimensional lattices of ƤƬ -symmetric couplers, Opt. Exp. 22(24), 029679 (2014)

    Article  Google Scholar 

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Huang, JS., Jiang, XD., Chen, HY. et al. Quadrupolar matter-wave soliton in two-dimensional free space. Front. Phys. 10, 1–7 (2015). https://doi.org/10.1007/s11467-015-0501-1

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