Vortex-pair states in spin-orbit-coupled Bose–Einstein condensates with coherent coupling

Abstract

Three types of vortex-pair are identified in two-component Bose–Einstein condensates (BEC) of different kinds of spin-orbit coupling. One type holds the two vortices in one component of the twocomponent condensates. Both the other two types hold a vortex in each component of the twocomponent condensates, and exhibit meron-pair textures that have either null or unit topological charge, respectively. The cores of the two vortices are connected by a string of the relative phase jump. These vortex pairs can be generated from a vortex-free wave packet by incorporating different non- Abelian gauge field into the BEC. When a Rabi coupling is introduced, the distance between the two cores is effectively controlled by the Rabi coupling strength and a transition of vortex configurations is observed.

Keywords

Bose–Einstein condensates / spin-orbit coupling / vortex-pair states

References

[1] D. C. Tsui, H. L. Stormer, and A. C. Gossard, Twodimensional magnetotransport in the extreme quantum limit, Phys. Rev. Lett. 48(22), 1559 (1982)

[2] I. Zutic, J. Fabian, and S. Das Sarma, Spintronics: Fundamentals and applications, Rev. Mod. Phys. 76(2), 323 (2004)

[3] M. Z. Hasan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)

[4] X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)

[5] F. Wilczek, Majorana returns, Nat. Phys. 5(9), 614 (2009)

[6] X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83(20), 205101 (2011)

[7] Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Spin-orbit-coupled Bose–Einstein condensates, Nature 471(7336), 83 (2011)

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

[9] Y. Li and J. K. Xue, Stationary and moving solitons in spin-orbit-coupled spin-1 Bose–Einstein condensates, Front. Phys. 13(2), 130307 (2018)

[10] L. Huang, Z. Meng, P. Wang, P. Peng, S. Zhang, L. Chen, D. Li, Q. Zhou, and J. Zhang, Experimental realization of two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases, Nat. Phys. 12(6), 540 (2016)

[11] Z. Wu, L. Zhang, W. Sun, X. Xu, B. Wang, S. Ji, Y. Deng, S. Chen, X. Liu, and J. Pan, Realization of twodimensional spin-orbit coupling for Bose–Einstein condensates, Science 354(6308), 83 (2016)

[12] W. Sun, B. Wang, X. Xu, C. Yi, L. Zhang, Z. Wu, Y. Deng, X. Liu, S. Chen, and J. Pan, Long-lived 2D Spin- Orbit coupled Topological Bose Gas, arXiv: 1710.00717 (2017)

[13] S. Sinha, R. Nath, and L. Santos, Trapped twodimensional condensates with synthetic spin-orbit coupling, Phys. Rev. Lett. 107(27), 270401 (2011)

[14] H. Hu, B. Ramachandhran, H. Pu, and X. J. Liu, Spinorbit coupled weakly interacting Bose–Einstein condensates in harmonic traps, Phys. Rev. Lett. 108(1), 010402 (2012)

[15] B. Ramachandhran, B. Opanchuk, X. J. Liu, H. Pu, P. D. Drummond, and H. Hu, Half-quantum vortex state in a spin-orbit-coupled Bose–Einstein condensate, Phys. Rev. A 85(2), 023606 (2012)

[16] C. Wang, C. Gao, C. M. Jian, and H. Zhai, Spin-orbit coupled spinor Bose–Einstein condensates, Phys. Rev. Lett. 105(16), 160403 (2010)

[17] X. Zhou, Y. Li, Z. Cai, and C. Wu, Unconventional states of bosons with the synthetic spin-orbit coupling, J. Phys. At. Mol. Opt. Phys. 46(13), 134001 (2013)

[18] Y. Kawaguchi and M. Ueda, Spinor Bose–Einstein condensates, Phys. Rep. 520(5), 253 (2012)

[19] H. Mäkelä, Explicit expressions for the topological defects of spinor Bose–Einstein condensates,J. Phys. Math. Gen. 39(23), 7423 (2006)

[20] K. Kasamatsu, H. Takeuchi, M. Tsubota, and M. Nitta, Wall-vortex composite solitons in two-component Bose– Einstein condensates, Phys. Rev. A 88(1), 013620 (2013)

[21] T. A. Skyrme, A unified field theory of mesons and baryons, Nucl. Phys. 31, 556 (1962)

[22] Y. M. Cho, Monopoles and knots in Skyrme theory, Phys. Rev. Lett. 87(25), 252001 (2001)

[23] S. L. Sondhi, A. Karlhede, S. A. Kivelson, and E. H. Rezayi, Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies, Phys. Rev. B 47(24), 16419 (1993)

[24] N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Writing and deleting single magnetic skyrmions, Science 341(6146), 636 (2013)

[25] Y. Kawaguchi, M. Kobayashi, M. Nitta, and M. Ueda, Topological excitations in spinor Bose–Einstein condensates, Prog. Theor. Phys. Suppl. 186, 455 (2010)

[26] K. Kasamatsu, M. Tsubota, and M. Ueda, Spin textures in rotating two-component Bose–Einstein condensates, Phys. Rev. A 71(4), 043611 (2005)

[27] K. Kasamatsu, M. Tsubota, and M. Ueda, Vortex molecules in coherently coupled two-component Bose– Einstein condensates, Phys. Rev. Lett. 93(25), 250406 (2004)

[28] T. D. Stanescu, C. Zhang, and V. Galitski, Nonequilibrium spin dynamics in a trapped fermi gas with effective spin-orbit interactions, Phys. Rev. Lett. 99(11), 110403 (2007)

[29] J. Ruseckas, G. Juzeliunas, P. Ohberg, and M. Fleischhauer, Non-Abelian gauge potentials for ultracold atoms with degenerate dark states, Phys. Rev. Lett. 95(1), 010404 (2005)

[30] T. Stanescu, B. Anderson, and V. Galitski, Spin-orbit coupled Bose–Einstein condensates, Phys. Rev. A 78(2), 023616 (2008)

[31] J. Radić, T. A. Sedrakyan, I. B. Spielman, and V. Galitski, Vortices in spin-orbit-coupled Bose–Einstein condensates, Phys. Rev. A 84(6), 063604 (2011)

[32] K. Kasamatsu, H. Takeuchi, M. Tsubota, and M. Nitta, Wall-vortex composite solitons in two-component Bose– Einstein condensates, Phys. Rev. A 88(1), 013620 (2013)

[33] H. Wang, L. Wen, H. Yang, C. Shi, and J. Li, Vortex states and spin textures of rotating spin-orbit-coupled Bose–Einstein condensates in a toroidal trap, J. Phys. At. Mol. Opt. Phys. 50(15), 155301 (2017)

[34] W. Bao, D. Jaksch, and P. A. Markowich, Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation, J. Comput. Phys. 187(1), 318 (2003)

[35] W. Bao and H. Wang, An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose–Einstein condensates, J. Comput. Phys. 217(2), 612 (2006)

[36] T. Kawakami, T. Mizushima, M. Nitta, and K. Machida, Stable skyrmions in SU(2) gauged Bose– Einstein condensates, Phys. Rev. Lett. 109(1), 015301 (2012)

[37] T. Kawakami, T. Mizushima, and K. Machida, Textures of F= 2 spinor Bose–Einstein condensates with spinorbit coupling, Phys. Rev. A 84, 011607(R) (2011)

[38] Y. K. Liu and S. J. Yang, Three-dimensional dimeron as a stable topological object, Phys. Rev. A 91(4), 043616 (2015)

[39] M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, Watching a superfluid untwist itself: Recurrence of Rabi oscillations in a Bose–Einstein condensate, Phys. Rev. Lett. 83(17), 3358 (1999)

RIGHTS & PERMISSIONS

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature