单双模连续压缩真空态及其量子统计性质

袁洪春; 徐学翔

doi:10.7498/aps.61.064205

摘要

利用有序算符内的积分技术研究了通过双模压缩算符作用于两个单模压缩态上得到的单双模连续压缩态. 导出了单双模连续压缩算符的正规乘积形式, 并在此基础上研究了单双模连续压缩真空态的量子统计性质. 特别是利用Weyl编序算符在相似变换下的不变性, 简洁地导出了单双模连续压缩真空态的Wigner函数. 最后, 还简单地提出了单双模连续压缩真空态的实验产生方案.

关键词:

One- and two-mode successively squeezed state, obtained through re-squeezing two single mode squeezed states by the two-mode squeezing operator, is studied in terms of the technique of integration within an ordered product (IWOP) of operators. We first derive the normally ordered form of this one- and two-mode successively squeezing operator, and then investigate the quantum statistical properties of the corresponding squeezed state. Particularly, we use the Weyl ordering invariance under a similar transformation to derive the analytical expression of its Wigner function, which seems very easy and concise. Finally, the experimental generation of one- and two-mode successively squeezed state is also proposed simply.

Keywords:

one- and two-mode successively squeezing operator /
squeezing effect /
Wigner function /
the IWOP technique

作者及机构信息

袁洪春¹,
徐学翔²

1.
常州工学院光电工程学院, 常州, 213002;

2.
江西师范大学物理与通信电子学院, 南昌, 330022

通信作者: 袁洪春, yuanhch@126.com

基金项目: 国家自然科学基金(批准号: 11174114)、常州工学院自然科学研究计划 (批准号: YN1106) 和江西省教育厅科学技术研究计划(批准号: GJJ12171, GJJ11390)资助的课题.

Authors and contacts

Yuan Hong-Chun¹,
Xu Xue-Xiang²

1.
College of Optoelectronic Engineering, Changzhou Institute of Technology, Changzhou 213002, China;

2.
College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China

Corresponding author: Yuan Hong-Chun, yuanhch@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11174114), the Research Foundation of Changzhou Institute of Technology, China (Grant No. YN1106) and the Research Foundation of Education Department of Jiangxi Province, China (Grant Nos. GJJ12171, GJJ11390).

参考文献

[1]	Dodonov V V 2002 J. Opt. B: Quantum Semiclass. Opt. 4 R1
[2]	Loudon R, Knight P L 1987 J. Mod. Opt. 34 709
[3]	Walls D F 1983 Nature 306 141
[4]	Collet M J, Walls D F 1985 Phys. Rev. A 32 2887
[5]	Lakshmi P A, Agarwal G S 1984 Phys. Rev. A 29 2260
[6]	Milburn G J, Braunstein S L 1999 Phys. Rev. A 60 937
[7]	Zhang J, Peng K C 2000 Phys. Rev. A 62 064302
[8]	Song T Q 2004 Acta Phys. Sin. 53 3358 (in Chinese) [宋同强 2004 物理学报 53 3358]
[9]	Ban M 1999 J. Opt. B: Quantum Semiclass. Opt. 1 L9
[10]	He G Q, Yi Z, Zhu J, Zeng G H 2007 Acta Phys. Sin. 56 6427 (in Chinese) [何广强, 易智, 朱俊, 曾贵华 2007 物理学报 56 6427]
[11]	Yi Z, He G Q, Zeng G H 2007 Acta Phys. Sin. 58 3166 (in Chinese) [易智, 何广强, 曾贵华 2009 物理学报 58 3166]
[12]	Hu L Y, Fan H Y 2008 J. Opt. Soc. Am. B 25 1955
[13]	Sun Z H, Fan H Y 2000 Acta Phys. Sin. 49 74 (in Chinese) [孙治湖, 范洪义 2000 物理学报 49 74]
[14]	Fan H Y 1990 Phys. Rev. A 41 1526
[15]	Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 物理学报 59 4661]
[16]	Jiang N Q, Zheng Y Z 2006 Phys. Rev. A 74 012306
[17]	Jiang N Q, Jing N Q, Zhang Y, Cai G C 2008 Europhys. Lett. 84 14002
[18]	Jiang N Q, Fan H Y 2008 Commun. Theor. Phys. 49 225
[19]	Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
[20]	Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
[21]	Fan H Y, VanderLinde J 1989 Phys. Rev. A 39 1552
[22]	Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[23]	Lai W K, Buek V, Knight P L 1991 Phys. Rev. A 44 6043
[24]	Meng X G, Wang J S 2007 Acta Phys. Sin. 56 4578 (in Chinese) [孟祥国, 王继锁 2007 物理学报 56 4578]
[25]	Lee C T 1990 Phys. Rev. A 41 1569
[26]	Buek V, Barranco A, Knight P L 1992 Phys. Rev. A 45 6570
[27]	Zhao J Q, Lu H X 2010 Acta Phys. Sin. 59 7875 (in Chinese) [赵加强, 逯怀新 2010 物理学报 59 7875]
[28]	Lee C T 1990 Phys. Rev. A 42 1608
[29]	Schleich P W 2001 Quantum Optics in Phase Space (Berlin: Wiley-Vch)
[30]	Zhang Z M 2004 Acta Phys. Sin. 53 70 (in Chinese) [ 2004 53 70]
[31]	Meng X G, Wang J S, Liang B L 2007 Acta Phys. Sin. 56 2160 (in Chinese) [张智明 2004 物理学报 53 70]
[32]	Hu L Y, Fan H Y 2009 Chin. Phys. B 18 4657
[33]	Xu X X, Yuan H C, Fan H Y 2011 Chin. Phys. B 20 024203
[34]	Fan H Y 2008 Ann. Phys. 323 500
[35]	Bachor H A, Ralph T C 2003 A Guide to Experiments in Quantum Optics (Berlin: Wiley-Vch)
[36]	Yang Y, Li F L 2009 Phys. Rev. A 80 022315 064205-7

施引文献

[1]	Dodonov V V 2002 J. Opt. B: Quantum Semiclass. Opt. 4 R1
[2]	Loudon R, Knight P L 1987 J. Mod. Opt. 34 709
[3]	Walls D F 1983 Nature 306 141
[4]	Collet M J, Walls D F 1985 Phys. Rev. A 32 2887
[5]	Lakshmi P A, Agarwal G S 1984 Phys. Rev. A 29 2260
[6]	Milburn G J, Braunstein S L 1999 Phys. Rev. A 60 937
[7]	Zhang J, Peng K C 2000 Phys. Rev. A 62 064302
[8]	Song T Q 2004 Acta Phys. Sin. 53 3358 (in Chinese) [宋同强 2004 物理学报 53 3358]
[9]	Ban M 1999 J. Opt. B: Quantum Semiclass. Opt. 1 L9
[10]	He G Q, Yi Z, Zhu J, Zeng G H 2007 Acta Phys. Sin. 56 6427 (in Chinese) [何广强, 易智, 朱俊, 曾贵华 2007 物理学报 56 6427]
[11]	Yi Z, He G Q, Zeng G H 2007 Acta Phys. Sin. 58 3166 (in Chinese) [易智, 何广强, 曾贵华 2009 物理学报 58 3166]
[12]	Hu L Y, Fan H Y 2008 J. Opt. Soc. Am. B 25 1955
[13]	Sun Z H, Fan H Y 2000 Acta Phys. Sin. 49 74 (in Chinese) [孙治湖, 范洪义 2000 物理学报 49 74]
[14]	Fan H Y 1990 Phys. Rev. A 41 1526
[15]	Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661 (in Chinese) [徐学翔, 袁洪春, 胡利云 2010 物理学报 59 4661]
[16]	Jiang N Q, Zheng Y Z 2006 Phys. Rev. A 74 012306
[17]	Jiang N Q, Jing N Q, Zhang Y, Cai G C 2008 Europhys. Lett. 84 14002
[18]	Jiang N Q, Fan H Y 2008 Commun. Theor. Phys. 49 225
[19]	Fan H Y 2003 J. Opt. B: Quantum Semiclass. Opt. 5 R147
[20]	Fan H Y, Lu H L, Fan Y 2006 Ann. Phys. 321 480
[21]	Fan H Y, VanderLinde J 1989 Phys. Rev. A 39 1552
[22]	Fan H Y, Zaidi H R, Klauder J R 1987 Phys. Rev. D 35 1831
[23]	Lai W K, Buek V, Knight P L 1991 Phys. Rev. A 44 6043
[24]	Meng X G, Wang J S 2007 Acta Phys. Sin. 56 4578 (in Chinese) [孟祥国, 王继锁 2007 物理学报 56 4578]
[25]	Lee C T 1990 Phys. Rev. A 41 1569
[26]	Buek V, Barranco A, Knight P L 1992 Phys. Rev. A 45 6570
[27]	Zhao J Q, Lu H X 2010 Acta Phys. Sin. 59 7875 (in Chinese) [赵加强, 逯怀新 2010 物理学报 59 7875]
[28]	Lee C T 1990 Phys. Rev. A 42 1608
[29]	Schleich P W 2001 Quantum Optics in Phase Space (Berlin: Wiley-Vch)
[30]	Zhang Z M 2004 Acta Phys. Sin. 53 70 (in Chinese) [ 2004 53 70]
[31]	Meng X G, Wang J S, Liang B L 2007 Acta Phys. Sin. 56 2160 (in Chinese) [张智明 2004 物理学报 53 70]
[32]	Hu L Y, Fan H Y 2009 Chin. Phys. B 18 4657
[33]	Xu X X, Yuan H C, Fan H Y 2011 Chin. Phys. B 20 024203
[34]	Fan H Y 2008 Ann. Phys. 323 500
[35]	Bachor H A, Ralph T C 2003 A Guide to Experiments in Quantum Optics (Berlin: Wiley-Vch)
[36]	Yang Y, Li F L 2009 Phys. Rev. A 80 022315 064205-7

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