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

[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

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

[1]	谢轲, 罗继红, 姚星灿. 基于退磁冷却的镝原子玻色-爱因斯坦凝聚制备. , 2024, 73(21): 216701. doi: 10.7498/aps.73.20241299
[2]	邢健崇, 张文静, 杨涛. 玻色-爱因斯坦凝聚中的非正则涡旋态及其动力学. , 2023, 72(10): 100306. doi: 10.7498/aps.72.20222289
[3]	贺丽, 张天琪, 李可芯, 余增强. 双组分玻色-爱因斯坦凝聚体的混溶性. , 2023, 72(11): 110302. doi: 10.7498/aps.72.20230001
[4]	贾瑞煜, 方乒乒, 高超, 林机. 玻色-爱因斯坦凝聚体中的淬火孤子与冲击波. , 2021, 70(18): 180303. doi: 10.7498/aps.70.20210564
[5]	郭慧, 王雅君, 王林雪, 张晓斐. 玻色-爱因斯坦凝聚中的环状暗孤子动力学. , 2020, 69(1): 010302. doi: 10.7498/aps.69.20191424
[6]	贺丽, 余增强. 自旋-轨道耦合作用下玻色-爱因斯坦凝聚在量子相变附近的朗道临界速度. , 2017, 66(22): 220301. doi: 10.7498/aps.66.220301
[7]	袁都奇. 三维简谐势阱中玻色-爱因斯坦凝聚的边界效应. , 2014, 63(17): 170501. doi: 10.7498/aps.63.170501
[8]	李志, 王建忠. 自旋-轨道耦合玻色-爱因斯坦凝聚势垒散射特性的研究. , 2013, 62(10): 100306. doi: 10.7498/aps.62.100306
[9]	赵文垒, 豆福全, 王建忠. 玻色-爱因斯坦凝聚体中非线性相互作用对量子共振棘流的影响. , 2012, 61(22): 220503. doi: 10.7498/aps.61.220503
[10]	王建忠, 曹辉, 豆福全. 玻色-爱因斯坦凝聚体Rosen-Zener跃迁中的多体量子涨落效应. , 2012, 61(22): 220305. doi: 10.7498/aps.61.220305
[11]	宋立军, 严冬, 刘烨. 玻色-爱因斯坦凝聚系统的量子Fisher信息与混沌. , 2011, 60(12): 120302. doi: 10.7498/aps.60.120302
[12]	曲春雷, 赵清. 周期驱动玻色-爱因斯坦凝聚系统的棘齿效应. , 2009, 58(7): 4390-4395. doi: 10.7498/aps.58.4390
[13]	宗丰德, 杨阳, 张解放. 外势场作用下的玻色-爱因斯坦凝聚啁啾孤子的演化与操控. , 2009, 58(6): 3670-3678. doi: 10.7498/aps.58.3670
[14]	严冬, 宋立军, 陈殿伟. 两分量玻色-爱因斯坦凝聚系统的自旋压缩. , 2009, 58(6): 3679-3684. doi: 10.7498/aps.58.3679
[15]	王海雷, 杨世平. 三势阱中玻色-爱因斯坦凝聚的开关特性. , 2008, 57(8): 4700-4705. doi: 10.7498/aps.57.4700
[16]	王志霞, 张喜和, 沈柯. 玻色-爱因斯坦凝聚中的混沌反控制. , 2008, 57(12): 7586-7590. doi: 10.7498/aps.57.7586
[17]	房永翠, 杨志安, 杨丽云. 对称双势阱玻色-爱因斯坦凝聚系统在周期驱动下的动力学相变及其量子纠缠熵表示. , 2008, 57(2): 661-666. doi: 10.7498/aps.57.661
[18]	刘泽专, 杨志安. 噪声对双势阱玻色-爱因斯坦凝聚体系自俘获现象的影响. , 2007, 56(3): 1245-1252. doi: 10.7498/aps.56.1245
[19]	王冠芳, 傅立斌, 赵鸿, 刘杰. 双势阱玻色-爱因斯坦凝聚体系的自俘获现象及其周期调制效应. , 2005, 54(11): 5003-5013. doi: 10.7498/aps.54.5003
[20]	崔海涛, 王林成, 衣学喜. 低维俘获原子的玻色-爱因斯坦凝聚中的有限粒子数效应. , 2004, 53(4): 991-995. doi: 10.7498/aps.53.991

计量

文章访问数: 7498
PDF下载量: 450
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板