Quadrupolar matter-wave soliton in two-dimensional free space

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.

Graphical abstract

Keywords

2D matter-wave solitons / quadrupole − quadrupole interaction / anisotropy soliton − soliton interaction / dipole solitons

References

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

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

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

[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)

[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)

[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)

[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)

[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)

[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)

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

[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)

[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)

[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)

[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)

[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)

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

[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)

[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)

[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)

[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)

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

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

[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)

[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)

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

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

[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)

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

[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).

[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)

[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)

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

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

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

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

[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 PT -symmetric defect, Opt. Exp. 22(11), 13927 (2014)

[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)

[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)

[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)

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

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

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg