玻色-爱因斯坦凝聚体中的双孤子相互作用操控

何章明; 张志强

doi:10.7498/aps.65.110502

摘要

考虑周期性驱动线性势, 利用Darboux变换法解析地研究了玻色-爱因斯坦凝聚体(BEC)中的双孤子相互作用, 得到了S-波散射长度的临界值. 结果表明: 当S-波散射长度高于临界值时, BEC中的两个亮孤子相互吸引并融合; 而当S-波散射长度低于临界值时, 两个亮孤子保持局域稳定. 此外, 在外部势阱的驱动下, 两个稳定的亮孤子产生周期性振荡行为.

关键词:

Considering the periodically driving linear potential, we study the interactions between two solitons in Bose-Einstein condensate (BEC). By using Darboux transformation, the double bright soliton solution of Gross-Pitaevskii equation is obtained. Then we numerically calculate the properties of interaction between the two bright solitons in BEC, and obtain a critical value of the S-wave scattering length (SL). It is shown that, when the SL is more than the critical value, the attractive interaction and the atom transfer between two bright solitons can be observed. While the SL is less than the critical value, two bright solitons can keep stable and localized. Furthermore, the stable periodic oscillations of two solitons can be observed by slowly changing the potential. These results will be conducive to the BEC soliton experiments.

Keywords:

作者及机构信息

何章明¹,
张志强²

1.
湖南工业大学理学院, 株洲 412007;

2.
郑州科技学院基础部, 郑州 450064

通信作者: 何章明, hezm1982@163.com

基金项目: 国家自然科学基金(批准号: 11447223, 11505054)、湖南省教育厅一般项目(批准号: 14C0348), 理论物理国家重点实验室开放课题(批准号: Y4KF211CJ1)和河南省教育厅科学技术研究重点项目 (批准号: 14B140014)资助的课题.

Authors and contacts

1.
College of Science, Hunan University of Technology, Zhuzhou 412007, China;

2.
Department of Basic Course, Zhengzhou College of Science and Technology, Zhengzhou 450064, China

Corresponding author: He Zhang-Ming, hezm1982@163.com

Funds: Project supported by the National Nature Science Foundation of China (Grant Nos. 11447223, 11505054), the Research Foundation of Education Bureau of Hunan Province of China (Grant No. 14 C0348), the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences (Grant No. Y4KF211CJ1), and the Research Foundation of Education Bureau of Henan Province of China (Grant No. 14B140014).

参考文献

[1]	Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150
[2]	Zhang X F, Hu X H, Liu X X, Liu W M 2009 Phys. Rev. A 79 033630
[3]	Liu X X, Pu H, Xiong B, Liu W M, Gong J B 2009 Phys. Rev. A 79 013423
[4]	Pu H, Bigelow N P 1998 Phys. Rev. Lett. 80 1134
[5]	Huang G X, Li X Q, Szeftel J 2004 Phys. Rev. A 69 065601
[6]	Wang D S, Hu X H, Liu W M 2010 Phys. Rev. A 82 023612
[7]	Yu H Y, Pan L X, Yan J R, Tang J Q 2009 J. Phys. B: At. Mol. Opt. Phys. 42 025301
[8]	Luo M, Bao C G, Li Z B 2008 J. Phys. B: At. Mol. Opt. Phys. 41 245301
[9]	Sun Z Y, Gao Y T, Yu X, Liu W J, Liu Y 2009 Phys. Rev. E 80 066608
[10]	Liang Z X, Zhang Z D, Liu W M 2005 Phys. Rev. Lett. 94 050402
[11]	Bettina G, Billam T P, Blackley C L, Ruth L S C, Lev K, Cornish S L, Weiss C 2013 Phys. Rev. Lett. 111 100406
[12]	Helm J L, Billam T P, Gardiner S A 2012 Phys. Rev. A 85 053621
[13]	Helm J L, Rooney S J, Weiss Christoph, Gardiner S A 2014 Phys. Rev. A 89 033610
[14]	Helm J L, Cornish S L, Gardiner S A 2015 Phys. Rev. Lett. 114 134101
[15]	Polo J Ahufinger V 2013 Phys. Rev. A 88 053628
[16]	Li S C, Fu L B, Duan W S, Liu J 2008 Phys. Rev.A 78 063621
[17]	He Z M, Wang D L, Ding J W, Yan X H 2012 Commun. Theor. Phys. 58 381
[18]	Liu X X, Zhang X F, Zhang P 2010 Chin. Phys. Lett. 27 070306
[19]	Yan J R, Pan L X, Yu H Y, Ao S M 2009 Chin. Phys. Lett. 26 090301
[20]	Li L, Malomed B A, Mihalache D, Liu W M 2006 Phys. Rev.E 73 066610
[21]	Cheng Y S 2009 J. Phys. B: At. Mol. Opt. Phys. 42 205005
[22]	Xiong B, Gong J B 2010 Phys. Rev.A 81 033618
[23]	Xuan H N, Zuo M 2011 Commun. Theor. Phys. 56 1035
[24]	He Z M, Wang D L, Ding J W, Yan X H 2012 Acta Phys. Sin. 61 230508 (in Chinese) [何章明, 王登龙, 丁建文, 颜晓红 2012 61 230508]
[25]	Li L, Li Z D, Malomed B A, Mihalache D, Liu W M 2005 Phys. Rev. A 72 033611
[26]	Zhao L C, He S L 2011 Phys. Lett.A 375 3017
[27]	Wen L, Liu W M, Cai Y, Zhang J M, Hu J 2012 Phys. Rev.A 85 043602
[28]	Chen Z, Wu B 2010 Phys. Rev. A 81 043611
[29]	Wu L, Li L, Zhang J F 2009 Phys. Rev. A 80 013617
[30]	Xue J K, Peng P 2006 Chin. Phys.B 15 1149
[31]	Zhang C W, Liu J, Raizen M G, Niu Q 2004 Phys. Rev. Lett. 92 054101
[32]	Huang G X, Velarde M G, Makarov V A 2001 Phys. Rev.A 64 013617
[33]	Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod. Phys. 82 1225
[34]	Li B, Zhang X F, Li Y Q, Liu W M 2011 J. Phys. B: At. Mol. Opt. Phys. 44 175301
[35]	Zhang H Q, Tian Bo, Lu Xing, Li He, Meng X H 2009 Phys. Lett.A 373 4315
[36]	Belmonte-Beitia J, Cuevas J 2009 J. Phys. A: Math. Theor. 42 165201
[37]	Zhang X F, Yang Q, Zhang J F, Chen X Z, Liu W M 2008 Phys. Rev.A 77 023613
[38]	Li S C, Dou F Q 2015 Europhys. Lett. 111 30005
[39]	Yang Q, Zhang J F 2006 Opt. Commun. 258 35
[40]	Yang Z Y, Zhao L C, Zhang T, Li Y H, Yue R H 2010 Phys. Rev.A 81 043826
[41]	He X G, Zhao D, Li L, Luo H G 2009 Phys. Rev.E 79 056610
[42]	Tian Q, Wu L, Zhang J F, Malomed B A, Mihalache D, Liu W M 2011 Phys. Rev.E 83 016602
[43]	Wang S J, Jia C L, Zhao D, Luo H G, An J H 2003 Phys. Rev.A 68 015601
[44]	Zong F D, Zhang J F 2008 Acta Phys. Sin. 57 2658 (in Chinese) [宗丰德, 张解放 2008 57 2658]
[45]	Yan Z Y 2010 Phys. Lett.A 374 4838
[46]	Li Z D, Li QY, Li L, Liu W M 2007 Phys. Rev.E 76 026605
[47]	Xia T C, Chen X H, Chen D Y 2005 Chaos Soliton. Fract. 26 889
[48]	Zhao D, He X G, Luo H G 2009 Eur. Phys. J.D 53 213
[49]	Guo B L, Ling Li M, Liu Q P 2012 Phys. Rev. E 85 026607
[50]	Tao Y S, He J S 2012 Phys. Rev. E 85 026601
[51]	Yang G Y, Li Lu, Jia S T 2012 Phys. Rev. E 85 046608
[52]	Qin Z Y, Mu G 2012 Phys. Rev. E 86 036601
[53]	Wang L H, Porsezian K, He J S 2013 Phys. Rev. E 87 053202
[54]	Ling L M, Zhao L C 2013 Phys. Rev. E 88 043201

施引文献

[1]	Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150
[2]	Zhang X F, Hu X H, Liu X X, Liu W M 2009 Phys. Rev. A 79 033630
[3]	Liu X X, Pu H, Xiong B, Liu W M, Gong J B 2009 Phys. Rev. A 79 013423
[4]	Pu H, Bigelow N P 1998 Phys. Rev. Lett. 80 1134
[5]	Huang G X, Li X Q, Szeftel J 2004 Phys. Rev. A 69 065601
[6]	Wang D S, Hu X H, Liu W M 2010 Phys. Rev. A 82 023612
[7]	Yu H Y, Pan L X, Yan J R, Tang J Q 2009 J. Phys. B: At. Mol. Opt. Phys. 42 025301
[8]	Luo M, Bao C G, Li Z B 2008 J. Phys. B: At. Mol. Opt. Phys. 41 245301
[9]	Sun Z Y, Gao Y T, Yu X, Liu W J, Liu Y 2009 Phys. Rev. E 80 066608
[10]	Liang Z X, Zhang Z D, Liu W M 2005 Phys. Rev. Lett. 94 050402
[11]	Bettina G, Billam T P, Blackley C L, Ruth L S C, Lev K, Cornish S L, Weiss C 2013 Phys. Rev. Lett. 111 100406
[12]	Helm J L, Billam T P, Gardiner S A 2012 Phys. Rev. A 85 053621
[13]	Helm J L, Rooney S J, Weiss Christoph, Gardiner S A 2014 Phys. Rev. A 89 033610
[14]	Helm J L, Cornish S L, Gardiner S A 2015 Phys. Rev. Lett. 114 134101
[15]	Polo J Ahufinger V 2013 Phys. Rev. A 88 053628
[16]	Li S C, Fu L B, Duan W S, Liu J 2008 Phys. Rev.A 78 063621
[17]	He Z M, Wang D L, Ding J W, Yan X H 2012 Commun. Theor. Phys. 58 381
[18]	Liu X X, Zhang X F, Zhang P 2010 Chin. Phys. Lett. 27 070306
[19]	Yan J R, Pan L X, Yu H Y, Ao S M 2009 Chin. Phys. Lett. 26 090301
[20]	Li L, Malomed B A, Mihalache D, Liu W M 2006 Phys. Rev.E 73 066610
[21]	Cheng Y S 2009 J. Phys. B: At. Mol. Opt. Phys. 42 205005
[22]	Xiong B, Gong J B 2010 Phys. Rev.A 81 033618
[23]	Xuan H N, Zuo M 2011 Commun. Theor. Phys. 56 1035
[24]	He Z M, Wang D L, Ding J W, Yan X H 2012 Acta Phys. Sin. 61 230508 (in Chinese) [何章明, 王登龙, 丁建文, 颜晓红 2012 61 230508]
[25]	Li L, Li Z D, Malomed B A, Mihalache D, Liu W M 2005 Phys. Rev. A 72 033611
[26]	Zhao L C, He S L 2011 Phys. Lett.A 375 3017
[27]	Wen L, Liu W M, Cai Y, Zhang J M, Hu J 2012 Phys. Rev.A 85 043602
[28]	Chen Z, Wu B 2010 Phys. Rev. A 81 043611
[29]	Wu L, Li L, Zhang J F 2009 Phys. Rev. A 80 013617
[30]	Xue J K, Peng P 2006 Chin. Phys.B 15 1149
[31]	Zhang C W, Liu J, Raizen M G, Niu Q 2004 Phys. Rev. Lett. 92 054101
[32]	Huang G X, Velarde M G, Makarov V A 2001 Phys. Rev.A 64 013617
[33]	Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod. Phys. 82 1225
[34]	Li B, Zhang X F, Li Y Q, Liu W M 2011 J. Phys. B: At. Mol. Opt. Phys. 44 175301
[35]	Zhang H Q, Tian Bo, Lu Xing, Li He, Meng X H 2009 Phys. Lett.A 373 4315
[36]	Belmonte-Beitia J, Cuevas J 2009 J. Phys. A: Math. Theor. 42 165201
[37]	Zhang X F, Yang Q, Zhang J F, Chen X Z, Liu W M 2008 Phys. Rev.A 77 023613
[38]	Li S C, Dou F Q 2015 Europhys. Lett. 111 30005
[39]	Yang Q, Zhang J F 2006 Opt. Commun. 258 35
[40]	Yang Z Y, Zhao L C, Zhang T, Li Y H, Yue R H 2010 Phys. Rev.A 81 043826
[41]	He X G, Zhao D, Li L, Luo H G 2009 Phys. Rev.E 79 056610
[42]	Tian Q, Wu L, Zhang J F, Malomed B A, Mihalache D, Liu W M 2011 Phys. Rev.E 83 016602
[43]	Wang S J, Jia C L, Zhao D, Luo H G, An J H 2003 Phys. Rev.A 68 015601
[44]	Zong F D, Zhang J F 2008 Acta Phys. Sin. 57 2658 (in Chinese) [宗丰德, 张解放 2008 57 2658]
[45]	Yan Z Y 2010 Phys. Lett.A 374 4838
[46]	Li Z D, Li QY, Li L, Liu W M 2007 Phys. Rev.E 76 026605
[47]	Xia T C, Chen X H, Chen D Y 2005 Chaos Soliton. Fract. 26 889
[48]	Zhao D, He X G, Luo H G 2009 Eur. Phys. J.D 53 213
[49]	Guo B L, Ling Li M, Liu Q P 2012 Phys. Rev. E 85 026607
[50]	Tao Y S, He J S 2012 Phys. Rev. E 85 026601
[51]	Yang G Y, Li Lu, Jia S T 2012 Phys. Rev. E 85 046608
[52]	Qin Z Y, Mu G 2012 Phys. Rev. E 86 036601
[53]	Wang L H, Porsezian K, He J S 2013 Phys. Rev. E 87 053202
[54]	Ling L M, Zhao L C 2013 Phys. Rev. E 88 043201

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