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Compared with the scalar Bose-Einstein condensate, the spinor Bose-Einstein condensate, in which internal degrees of freedom are essentially free, has aroused the great interest in the study of topological excitations. In particular, the spinor Bose-Einstein condensate with rotation provides a new opportunity for studying novel quantum states including a coreless vortex and vortex lattice. To date, in the presence of rotation, a great many of studies on the topological excitations have focused on the Bose-Einstein condensate system with the uniform Zeeman field or without external magnetic field. However, the ground state structure of a rotating Bose-Einstein condensate in the presence of in-plane gradient-magnetic-field remains an open question. In this work, by using the imaginary-time propagation method, we study the ground state structure of a rotating Bose-Einstein condensate with in-plane quadrupole field. We first examine the effect of in-plane quadrupole field on trapped spinor Bose-Einstein condensate. The numerical results show that Mermin-Ho vortex can be induced only by the cooperation between quadrupole field and rotation. When magnetic field gradient is increased, the vortices around Mermin-Ho vortex display the symmetrical arrangement. For an even larger magnetic field gradient strength, the system only presents the Mermin-Ho vortex because the in-plane quadrupole field can prevent the vortices around Mermin-Ho vortex from occurring. Next, we examine the effect of the rotation on trapped spinor Bose-Einstein condensate. A phase transition from a polar-core vortex to a Mermin-Ho vortex is found through applying a rotational potential, which is caused by the cooperation between the in-plane quadrupole field and the rotation. We further study the combined effects of spin exchange interaction and density-density interaction. The results confirm that in the presence of the quadrupole field both spin exchange interaction and density-density interaction, acting as controllable parameters, can control the number of the vortices around Mermin-Ho vortex. The corresponding number of the vortices shows step behavior with increasing the ratio between spin exchange interaction and density-density interaction, which behaves as hexagon, pentagon, square and triangle. It is found that two types of topology structures, i.e., the hyperbolic meron and half-skyrmion, can occur in the present system. These vortex structures can be realized via time-of-flight absorption imaging technique. Our results not only provide an opportunity to investigate the exotic vortex structures and the corresponding phase transitions in a controlled platform, but also lay the foundation for the study of topological defect subjected to gauge field and dipolar interaction in future.
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Keywords:
- rotating Bose-Einstein condensate /
- in-plane quadrupole field /
- spin-exchange interaction /
- spin texture
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[1] Stenger J, Inouye S, Stamper-Kurn D M, Miesner H J, Chikkatur A P, Ketterle W 1998 Nature 396 345
[2] Ho T L 1998 Phys. Rev. Lett. 81 742
[3] Görlitz A, Gustavson T L, Leanhardt A E, Löw R, Chikkatur A P, Gupta S, Inouye S, Pritchard D E, Ketterle W 2003 Phys. Rev. Lett. 90 090401
[4] Klausen N N, Bohn J L, Greene C H 2001 Phys. Rev. A 64 053602
[5] Isoshima T, Machida K, Ohmi T 2001 J. Phys. Soc. Jpn. 70 1604
[6] Kasamatsu K, Tsubota M, Ueda M 2005 Int. J. Mod. Phys. B 19 1835
[7] Tuchiya S, Kurihara S 2001 J. Phys. Soc. Jpn. 70 1182
[8] Raman C, Abo-Shaeer J R, Vogels J M, Xu K, Ketterle W 2001 Phys. Rev. Lett. 87 210402
[9] Williams R A, Al-Assam S, Foot C J 2010 Phys. Rev. Lett. 104 050404
[10] Schweikhard V, Coddington I, Engels P, Tung S, Cornell E A 2004 Phys. Rev. Lett. 93 210403
[11] Chevy F, Madison K W, Dalibard J 2000 Phys. Rev. Lett. 85 2223
[12] Martikainen J P, Collin A, Suominen K A 2002 Phys. Rev. A 66 053604
[13] Mizushima T, Kobayashi N, Machida K 2004 Phys. Rev. A 70 043613
[14] Mizushima T, Machida K, Kita T 2002 Phys. Rev. Lett. 89 030401
[15] Mizushima T, Machida K, Kita T 2002 Phys. Rev. A 66 053610
[16] Anderson B M, Spielman I B, Juzeliūnas G 2013 Phys. Rev. Lett. 111 125301
[17] Xu Z F, You L, Ueda M 2013 Phys. Rev. A 87 063634
[18] Aidelsburger M, Atala M, Lohse M, Barreiro J T, Paredes B, Bloch I 2013 Phys. Rev. Lett. 111 185301
[19] Kennedy J C, Siviloglou G A, Miyake H, Burton W C, Ketterle W 2013 Phys. Rev. Lett. 111 225301
[20] Ray M W, Ruokokoski E, Kandel S, Möttönen M, Hall D S 2014 Nature 505 657
[21] Ray M W, Ruokokoski E, Tiurev K, Möttönen M, Hall D S 2015 Science 348 544
[22] Hall D S, Ray M W, Tiurev K, Ruokokoski E, Gheorghe A H, Möttönen M 2015 Nature Phys. 12 478
[23] Ji A C, Liu W M, Song J L, Zhou F 2008 Phys. Rev. Lett. 101 010402
[24] Bulgakov E N, Sadreev A F 2003 Phys. Rev. Lett. 90 200401
[25] Lovegrove J, Borgh M O, Ruostekoski J 2012 Phys. Rev. A 86 013613
[26] Pritchard D E 1983 Phys. Rev. Lett. 51 1336
[27] Leanhardt A E, Shin Y, Kielpinski D, Pritchard D E, Ketterle W 2003 Phys. Rev. Lett. 90 140403
[28] Leanhardt A E, Görlitz A, Chikkatur A P, Kielpinski D, Shin Y, Pritchard D E, Ketterle W 2002 Phys. Rev. Lett. 89 190403
[29] Stamper-Kurn D M, Ueda M 2013 Rev. Mod. Phys. 85 1191
[30] Dalfovo F, Stringari S 1996 Phys. Rev. A 53 2477
[31] Zhang X F, Dong R F, Liu T, Liu W M, Zhang S G 2012 Phys. Rev. A 86 063628
[32] Bao W Z, Du Q 2004 SIAM J. Sci. Comput. 25 1674
[33] Kasamatsu K, Tsubota M 2009 Phys. Rev. A 79 023606
[34] Sadler L E, Higbie J M, Leslie S R, Vengalattore M, Stamper-Kurn D M 2006 Nature 443 312
[35] Fetter A L 2009 Rev. Mod. Phys. 81 647
[36] Su S W, Hsueh C H, Liu I K, Horng T L, Tsai Y C, Gou S C, Liu W M 2011 Phys. Rev. A 84 023601
[37] Liu C F, Liu W M 2012 Phys. Rev. A 86 033602
[38] Volovik G E 2003 The Universe in a Helium Droplet (Oxford:Oxford University Press)
[39] Liu C F, Wan W J, Zhang G Y 2013 Acta Phys. Sin. 62 200306 (in Chinese)[刘超飞, 万文娟, 张赣源 2013 62 200306]
[40] Song S W, Sun R, Zhao H, Wang X, Han B Z 2016 Chin. Phys. B 25 040305
[41] Zhang X F, Zhang P, Chen G P, Dong B, Tan R B, Zhang S G 2015 Acta Phys. Sin. 64 060302 (in Chinese)[张晓斐, 张培, 陈光平, 董彪, 谭仁兵, 张首刚 2015 64 060302]
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