玻色-爱因斯坦凝聚体Rosen-Zener跃迁中的多体量子涨落效应

王建忠; 曹辉; 豆福全

doi:10.7498/aps.61.220305

摘要

研究了处于对称双势阱中玻色-爱因斯坦凝聚体Rosen-Zener跃迁过程的多体量子涨落效应, 分析了末态平均布居数差与扫描周期的关系. 线性情况下, 得到了末态平均布居数差关于扫描周期的解析表达式, 该结果与平均场下的结果完全一致, 并利用数值方法进行了验证.非线性情况下, 通过数值计算发现, 快速扫描时末态平均布居数差与平均场情况下的结果符合比较好; 然而绝热扫描时与平均场情况却有着很大的不同: 末态平均布居数差随扫描周期的变化不再是平均场情况下的方波形式而是类似于正弦型的振荡, 而且振荡周期会随着粒子数N以及非线性参数c的增加而增大.

关键词:

Abstract

We investigate many-body quantum fluctuation effects of Rosen-Zener transition of Bose-Einstein condensate (BEC) in a symmetric double-well potential through the relation between the average population imbalance of the final state (APIFS) and scanning period. In the linear case, we deduce the analytical expression of the APIFS which has the same behavior as in the mean-field level. We also employ numerical calculation to demonstrate it. In the nonlinear case, numerical results show that the APIFS in the sudden limit also accords with that in the mean-field level whereas in the adiabatic limit the many-body result is quite different from that of the mean-field case: the behavior of APIFS with respect to scanning period is similar to sinusoidal rather than rectangular oscillation, besides the oscillation period increases with both the total number N and the nonlinear parameter c increasing.

Keywords:

作者及机构信息

1.
北京理工大学物理学院, 北京 100081;

2.
北京应用物理与计算数学研究所, 计算物理国家重点实验室, 北京 100088;

3.
北京大学应用物理与技术研究中心, 高能量密度物理数值模拟教育部重点实验室, 北京 100084

基金项目: 国家高技术研究发展计划(863计划)(批准号: 2011AA120101)资助的课题.

Authors and contacts

1.
School of Physics Beijing Institute of Technology, Beijing 100081, China;

2.
National Key Laboratory of Science and Technology on Computation Physics Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;

3.
HEDPS Center for Applied Physics and Technology Peking University, Beijing 100084, China

Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2011AA120101).

参考文献

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[2]	Rabi I I 1937 Phys. Rev. 51 652
[3]	Thomas G F 1983 Phys. Rev. A 27 2744
[4]	Osherov V I, Voronin A I 1994 Phys. Rev. A 49 265
[5]	Robiscoe R T 1978 Phys. Rev. A 17 247
[6]	Bambini A, Berman P R 1981 Phys. Rev. A 23 2496
[7]	Robiscoe R T 1983 Phys. Rev. A 27 1365
[8]	Vitanov N V 1993 J. Phys. B: At. Mol. Opt. Phys. 26 L53
[9]	Liu J, Hu B, Li B W 1998 Phys. Rev. Lett. 81 1749
[10]	Osherov V I, Nakamura H 1999 Phys. Rev. A 59 2486
[11]	Robinson E J, Berman P R 1983 Phys. Rev. A 27 1022
[12]	Bava E, Godone A, Novero C, Rocco H O D 1992 Phys. Rev. A 45 1967
[13]	Fu L B 2004 Phys. Rev. Lett. 92 130404
[14]	Olson R E 1972 Phys. Rev. A 6 1822
[15]	Suominen K A, Garraway B M, Stenholm S. 1992 Phys. Rev. A 45 3060
[16]	Fu L B, Xin G G, Ye D F, Liu J 2012 Phys. Rev. Lett. 108 103601
[17]	Robinson E J 1993 J. Phys.: Condens. Matter 5 13
[18]	Kirillov A S 2004 Advances in Space Research 33 993
[19]	Anderson M H, Ensher J R, Mattews M R, Wieman C E, Cornell E A 1995 Science 269 198
[20]	Davis K B, Mcwes M O, Andrews M R, Druten N J, Durfee D S, Kurn D M, Kerrerle W 1995 Phys. Rev. Lett. 75 3969
[21]	Bradley C C, Sackett C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687
[22]	Anderson M R, Townsend C G, Mienser H J, Durfee D S, Kurn D M, Ketterle W 1997 Science 275 637
[23]	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]
[24]	Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 013609
[25]	Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623
[26]	Liu J, Zhang C W, Raizen M G, Niu Q 2006 Phys. Rev. A 73 013601
[27]	Ye D F, Fu L B, Liu J 2008 Phys. Rev. A 77 013402
[28]	Jiang X, Duan W S, Li S C, Shi Y R 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185001
[29]	Fu L B, Ye D F, Lee C H, Zhang W P, Liu J 2009 Phys. Rev. A 80 013619
[30]	Li S C, Fu L B, Duan W S, Liu J 2008 Phys. Rev. A 78 063621
[31]	Ishkhanyan A, Sokhoyan R, Joulakian B, Suominen K A 2009 Optics Communications 282 218
[32]	Xu X Q, Lu L H, Li Y Q 2008 Phys. Rev. A 78 043609
[33]	Torosov B T, Vitanov N V 2007 Phys. Rev. A 76 053404
[34]	Lu L H, Xu X Q, Li Y Q 2011 J. Phys. B: At. Opt. Phys. 44 145301
[35]	Klich I, Lannert C, Refael G 2007 Phys. Rev. Lett 99 205303
[36]	Franco D, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys 71 463
[37]	Anthony L 2001 Rev. Mod. Phys 73 307
[38]	Steel M J, Collett M J 1998 Phys. Rev. A 57 2920
[39]	Cirac J I, Lewenstein M, Momer K, Zoller P 1998 Phys. Rev. A 57 1208

施引文献

[1]	Rosen N, Zener C 1932 Phys. Rev. 40 502
[2]	Rabi I I 1937 Phys. Rev. 51 652
[3]	Thomas G F 1983 Phys. Rev. A 27 2744
[4]	Osherov V I, Voronin A I 1994 Phys. Rev. A 49 265
[5]	Robiscoe R T 1978 Phys. Rev. A 17 247
[6]	Bambini A, Berman P R 1981 Phys. Rev. A 23 2496
[7]	Robiscoe R T 1983 Phys. Rev. A 27 1365
[8]	Vitanov N V 1993 J. Phys. B: At. Mol. Opt. Phys. 26 L53
[9]	Liu J, Hu B, Li B W 1998 Phys. Rev. Lett. 81 1749
[10]	Osherov V I, Nakamura H 1999 Phys. Rev. A 59 2486
[11]	Robinson E J, Berman P R 1983 Phys. Rev. A 27 1022
[12]	Bava E, Godone A, Novero C, Rocco H O D 1992 Phys. Rev. A 45 1967
[13]	Fu L B 2004 Phys. Rev. Lett. 92 130404
[14]	Olson R E 1972 Phys. Rev. A 6 1822
[15]	Suominen K A, Garraway B M, Stenholm S. 1992 Phys. Rev. A 45 3060
[16]	Fu L B, Xin G G, Ye D F, Liu J 2012 Phys. Rev. Lett. 108 103601
[17]	Robinson E J 1993 J. Phys.: Condens. Matter 5 13
[18]	Kirillov A S 2004 Advances in Space Research 33 993
[19]	Anderson M H, Ensher J R, Mattews M R, Wieman C E, Cornell E A 1995 Science 269 198
[20]	Davis K B, Mcwes M O, Andrews M R, Druten N J, Durfee D S, Kurn D M, Kerrerle W 1995 Phys. Rev. Lett. 75 3969
[21]	Bradley C C, Sackett C A, Tollett J J, Hulet R G 1995 Phys. Rev. Lett. 75 1687
[22]	Anderson M R, Townsend C G, Mienser H J, Durfee D S, Kurn D M, Ketterle W 1997 Science 275 637
[23]	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]
[24]	Wang G F, Fu L B, Liu J 2006 Phys. Rev. A 73 013609
[25]	Liu J, Wang W G, Zhang C W, Niu Q, Li B W 2005 Phys. Rev. A 72 063623
[26]	Liu J, Zhang C W, Raizen M G, Niu Q 2006 Phys. Rev. A 73 013601
[27]	Ye D F, Fu L B, Liu J 2008 Phys. Rev. A 77 013402
[28]	Jiang X, Duan W S, Li S C, Shi Y R 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185001
[29]	Fu L B, Ye D F, Lee C H, Zhang W P, Liu J 2009 Phys. Rev. A 80 013619
[30]	Li S C, Fu L B, Duan W S, Liu J 2008 Phys. Rev. A 78 063621
[31]	Ishkhanyan A, Sokhoyan R, Joulakian B, Suominen K A 2009 Optics Communications 282 218
[32]	Xu X Q, Lu L H, Li Y Q 2008 Phys. Rev. A 78 043609
[33]	Torosov B T, Vitanov N V 2007 Phys. Rev. A 76 053404
[34]	Lu L H, Xu X Q, Li Y Q 2011 J. Phys. B: At. Opt. Phys. 44 145301
[35]	Klich I, Lannert C, Refael G 2007 Phys. Rev. Lett 99 205303
[36]	Franco D, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys 71 463
[37]	Anthony L 2001 Rev. Mod. Phys 73 307
[38]	Steel M J, Collett M J 1998 Phys. Rev. A 57 2920
[39]	Cirac J I, Lewenstein M, Momer K, Zoller P 1998 Phys. Rev. A 57 1208

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