具有面内四极磁场的旋转玻色-爱因斯坦凝聚体的基态结构研究

刘静思; 李吉; 刘伍明

doi:10.7498/aps.66.130305

摘要

通过虚时演化方法研究了具有面内四极磁场的旋转玻色-爱因斯坦凝聚体的基态结构.结果发现：面内四极磁场和旋转双重作用可导致中央Mermin-Ho涡旋的产生；随着磁场梯度增强，Mermin-Ho涡旋周围环绕的涡旋趋向对称化排布；在四极磁场下，密度相互作用和自旋交换相互作用作为体系的调控参数，可以控制Mermin-Ho涡旋周围的涡旋数目；该体系自旋结构中存在双曲型meron和half-skyrmion两种拓扑结构.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
中国科学院物理研究所, 北京凝聚态物理国家实验室, 北京 100190;

2.
中国科学院大学物理学院, 北京 100190

通信作者: 李吉, liji2015@iphy.ac.cn

基金项目: 国家重点研发计划量子调控与量子信息重点专项（批准号：2016YFA0301500）和国家自然科学基金（批准号：11434015，KZ201610005011）资助的课题.

Authors and contacts

1.
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;

2.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Li Ji, liji2015@iphy.ac.cn

Funds: Project supported by the NKRDP (Grant No.2016YFA0301500),and the National Natural Science Foundation of China (Grant Nos.1143401,KZ201610005011).

参考文献

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[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 物理学报 64 060302]

施引文献

[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 物理学报 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 物理学报 64 060302]

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