自由膨胀准二维玻色-爱因斯坦凝聚中的密度-密度关联

徐岩; 樊炜; 陈兵; 南向红; 陈达; 周强; 张鲁殷

doi:10.7498/aps.62.216701

摘要

利用Madelung变换, 考虑密度和相位涨落, 给出了准二维玻色-爱因斯坦凝聚体的有效拉格朗日密度函数和波函数量子涨落的算符化表示, 计算了凝聚体在去除约束势场自由膨胀时两点之间的密度-密度关联函数, 结果表明在长波极限下, 两点之间的密度关联函数正比于波数k, 而在短波极限下, 密度关联函数趋近于一个常数.

关键词:

The effective Lagrangian density function and the quantum fluctuation of the wave function in the form of quantized operators are presented for a quasi two-dimensional Bose-Einstein condensate by means of Madelung transformation. This paper calculates the two-point density-density correlation function of the condensate during its free expansion after its confinement potential is removed. Results show that the two-point density-density correlation function in the long-wave limit is proportional to the wave number k and it tends to be a constant in the short-wave limit.

Keywords:

作者及机构信息

1.
山东科技大学理学院, 青岛 266510

基金项目: 国家自然科学基金(批准号: 11105086)、山东省中青年科学家奖励基金(批准号: BS2011DX029)、青岛市科技计划(批准号: 11-2-4-4-(6)-jch)和山东科技大学杰出青年基金(2011KYJQ101)资助的课题.

Authors and contacts

1.
College of Science, Shandong University of Science & Technology, Qingdao 266510, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No.11105086), the Natural Science Foundation of Shandong Province, China (Grant No. BS2011DX029), the basic scientific research project of Qingdao, China (Grant No.11-2-4-4-(6)-jch), and the SDUST research fund (2011KYJQ101).

参考文献

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[2]	Levy S, Lahoud E, Shoroni I, Steinhauer J 2007 Nature 449 579
[3]	Liu B, Fu L B, Yang S P, Liu J 2007 Phys. Rev. A 75 033601
[4]	Zhang J N, Sun C P, Yi S, Nori F 2011 Phys. Rev. A 83 033614
[5]	Wang W Y, Meng H J, Yang Y, Qi P T, Ma Y Y, Ma Y, Wang S J, Duan W S 2012 Acta Phys. Sin. 61 087302 (in Chinese) [王文元, 蒙红娟, 杨阳, 祁鹏堂, 马云云, 马莹, 王善进, 段文山 2012 61 087302]
[6]	Meng H J, Yang Y, Wang W Y, Qi P T, Ma Y Y, Ma Y, Wang S J, Duan W S 2012 Acta Phys. Sin. 61 060303 (in Chinese) [蒙红娟, 杨阳, 王文元, 祁鹏堂, 马云云, 马莹, 王善进, 段文山 2012 61 060303]
[7]	Wang J Z, Cao H, Dou F Q 2012 Acta Phys. Sin. 61 220305 (in Chinese) [王建忠, 曹辉, 豆福全 2012 61 220305]
[8]	Liu J, Zhang C W, Raizen M G, Niu Q 2006 Phys. Rev. A 73 013601
[9]	Teng F, Xie Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 62 026701]
[10]	Cui B, Wang L C, Yi X X 2010 Phys. Rev. A 82 062105
[11]	Wuster S, Dabrowska-Wuster B J, Davis M J 2012 Phys. Rev. Lett. 109 080401
[12]	Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 (in Chinese) [王冠芳, 傅立斌, 赵鸿, 刘杰 2005 54 5003]
[13]	Tozzo C, Dalfovo F 2004 Phys. Rev. A 69 05360 Liu S J, Xiong H W 2009 Physica B-Condensed Matter 404 3510 Wu M Z, Zhou XJ, Liu W M, Chen X Z 2010 Phys. Rev. A 81 033625
[14]	Xu Y, Xiong Z Z, Li Z X, Chen B, Tan L 2009 Chin. Phys. B 18 4734
[15]	Imambekov A, Mazets I E, Petrov D S, Gritsev V, Manz S, Hofferberth S, Schumm T, Demler E, Schmiedmayer J 2009 Phys. Rev. A 80 033604
[16]	Salasnich L, Manini N, Bonelli F, Korbman M, Parola A 2007 Phys. Rev. A 75 043616
[17]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[18]	Castin Y, Dum R, 1996 Phys. Rev. Lett. 77 5315 Ohberg P, Santos L 2002 Phys. Rev. Lett. 89 240402
[19]	Kagan Yu, Surkov E L, Shlyapnikov G V 1996 Phys. Rev. A 54 R1753 Kagan Yu, Surkov E L, Shlyapnikov G V 1997 Phys. Rev. A 55 R18
[20]	Salasnich L, Parola A, Reatto L, 2005 Phys. Rev. A 72 025602 Diana G, Manini N, Salasnich L 2006 Phys. Rev. A 73 065601
[21]	Prain A, Fagnocchi S, Liberati S 2010 Phys. Rev. D 82 105018
[22]	Carusotto I, Fagnocchi S, Recati A, Balbinot R, Fabbri A, 2008 New J. Phys. 10 103001
[23]	Balbinot R, Fabbri A, Fagnocchi S, Recati A, Carusotto I 2008 Phys. Rev. A 78 021603
[24]	Recati A, Pavloff N, Carusotto I 2009 Phys. Rev. A 80 043603
[25]	Zapata I, Albert M, Parentani R, Sols F 2011 New J. Phys. 13 063048
[26]	Carusotto I, Balbinot R, Fabbri A, Recati A 2010 Eur. Phys. J. D 56 391
[27]	Larre P E, Recati A, Carusotto I, Pavloff N 2012 Phys. Rev. A 85 013621
[28]	Gorlitz A, Vogels J M, Leanhardt A E, Raman C, Gustavson T L, Abo-Shaeer J R, Chikkatur A P, Gupta S, Inouye S, Rosenband T, Ketterle W 2001 Phys. Rev. Lett. 87 130402

施引文献

[1]	Yasunaga M, Tsubota M 2010 Phys. Rev. A 81 023624 Yasunaga M, Tsubota M 2011 Phys. Rev. A 83 013618
[2]	Levy S, Lahoud E, Shoroni I, Steinhauer J 2007 Nature 449 579
[3]	Liu B, Fu L B, Yang S P, Liu J 2007 Phys. Rev. A 75 033601
[4]	Zhang J N, Sun C P, Yi S, Nori F 2011 Phys. Rev. A 83 033614
[5]	Wang W Y, Meng H J, Yang Y, Qi P T, Ma Y Y, Ma Y, Wang S J, Duan W S 2012 Acta Phys. Sin. 61 087302 (in Chinese) [王文元, 蒙红娟, 杨阳, 祁鹏堂, 马云云, 马莹, 王善进, 段文山 2012 61 087302]
[6]	Meng H J, Yang Y, Wang W Y, Qi P T, Ma Y Y, Ma Y, Wang S J, Duan W S 2012 Acta Phys. Sin. 61 060303 (in Chinese) [蒙红娟, 杨阳, 王文元, 祁鹏堂, 马云云, 马莹, 王善进, 段文山 2012 61 060303]
[7]	Wang J Z, Cao H, Dou F Q 2012 Acta Phys. Sin. 61 220305 (in Chinese) [王建忠, 曹辉, 豆福全 2012 61 220305]
[8]	Liu J, Zhang C W, Raizen M G, Niu Q 2006 Phys. Rev. A 73 013601
[9]	Teng F, Xie Z W 2013 Acta Phys. Sin. 62 026701 (in Chinese) [藤斐, 谢征微 2013 62 026701]
[10]	Cui B, Wang L C, Yi X X 2010 Phys. Rev. A 82 062105
[11]	Wuster S, Dabrowska-Wuster B J, Davis M J 2012 Phys. Rev. Lett. 109 080401
[12]	Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 (in Chinese) [王冠芳, 傅立斌, 赵鸿, 刘杰 2005 54 5003]
[13]	Tozzo C, Dalfovo F 2004 Phys. Rev. A 69 05360 Liu S J, Xiong H W 2009 Physica B-Condensed Matter 404 3510 Wu M Z, Zhou XJ, Liu W M, Chen X Z 2010 Phys. Rev. A 81 033625
[14]	Xu Y, Xiong Z Z, Li Z X, Chen B, Tan L 2009 Chin. Phys. B 18 4734
[15]	Imambekov A, Mazets I E, Petrov D S, Gritsev V, Manz S, Hofferberth S, Schumm T, Demler E, Schmiedmayer J 2009 Phys. Rev. A 80 033604
[16]	Salasnich L, Manini N, Bonelli F, Korbman M, Parola A 2007 Phys. Rev. A 75 043616
[17]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[18]	Castin Y, Dum R, 1996 Phys. Rev. Lett. 77 5315 Ohberg P, Santos L 2002 Phys. Rev. Lett. 89 240402
[19]	Kagan Yu, Surkov E L, Shlyapnikov G V 1996 Phys. Rev. A 54 R1753 Kagan Yu, Surkov E L, Shlyapnikov G V 1997 Phys. Rev. A 55 R18
[20]	Salasnich L, Parola A, Reatto L, 2005 Phys. Rev. A 72 025602 Diana G, Manini N, Salasnich L 2006 Phys. Rev. A 73 065601
[21]	Prain A, Fagnocchi S, Liberati S 2010 Phys. Rev. D 82 105018
[22]	Carusotto I, Fagnocchi S, Recati A, Balbinot R, Fabbri A, 2008 New J. Phys. 10 103001
[23]	Balbinot R, Fabbri A, Fagnocchi S, Recati A, Carusotto I 2008 Phys. Rev. A 78 021603
[24]	Recati A, Pavloff N, Carusotto I 2009 Phys. Rev. A 80 043603
[25]	Zapata I, Albert M, Parentani R, Sols F 2011 New J. Phys. 13 063048
[26]	Carusotto I, Balbinot R, Fabbri A, Recati A 2010 Eur. Phys. J. D 56 391
[27]	Larre P E, Recati A, Carusotto I, Pavloff N 2012 Phys. Rev. A 85 013621
[28]	Gorlitz A, Vogels J M, Leanhardt A E, Raman C, Gustavson T L, Abo-Shaeer J R, Chikkatur A P, Gupta S, Inouye S, Rosenband T, Ketterle W 2001 Phys. Rev. Lett. 87 130402

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