N00N态的Wigner函数及N00N态作为输入的量子干涉

徐学翔; 张英孔; 张浩亮; 陈媛媛

doi:10.7498/aps.62.114204

摘要

根据量子力学相干态表象下的Wigner函数公式, 推导了N00N态在相空间的Wigner分布函数的解析表达式. 基于相空间方法, 研究N00N态作为输入的量子干涉. 推导了与输入光场参数和干涉仪参数相关的输出端探测光子概率的解析表达式, 并进行了数值分析. 从分析结果发现, 当相移参数φ取0和π时, 输出量子态仍为N00N态. 当输入2002态时, 输出结果总是2002态, 与相移参数无关. 随着N的增加, 条件概率随相位的分布峰数一般只有一个, 两个, 三个或四个, 且峰变得更窄. 这些结果可以为实验提供理论指导.

关键词:

N00N态 /
Wigner函数 /
相空间 /
量子干涉

Abstract

Using the formula of Wigner function in coherent representation, we have obtained the analytical expression for Wigner function of N00N state. Based on phase space method, we study the quantum interference with N00N state as input. We derive the analytical expression of conditional probability related with the input parameter N and phase parameter φ and analyze it numerically. It is shown that, when φ is 0 or π, the output is just N00N state. It is also shown that, for 2002 state as input, the output must be 2002 state, which is independent of phase parameters. Moreover, as the number of input photon N increases, the phase probability distributions remain to have one, two, three and four peaks and get narrower. All these results can offer theoretical reference for experiments.

Keywords:

作者及机构信息

1.
江西师范大学物理与通信电子学院, 南昌 330022;

2.
广州杰赛科技股份有限公司, 广州 510310

基金项目: 国家自然科学基金 (批准号: 11175113, 11264018, 11247301), 江西省自然科学基金 (批准号: 2011BAB202004)和江西省教育厅科技项目 (批准号: GJJ12171)资助的课题.

Authors and contacts

1.
College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China;

2.
Guangzhou GCI Science & Technology Corporation Limited, Guangzhou 510310, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11175113, 11264018, 11247301), the Natural Science Foundation of Jiangxi Province, China (Grant No. 2011BAB202004), and the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ12171).

参考文献

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[2]	Taylor G I 1909 Proceedings of the Cambridge Philosophical Society 15 14
[3]	Paul H 1986 Rev. Mod. Phys. 58 209
[4]	Dirac P A M 1930 The Principles of Quantum Mechanics (Clarendon: Oxford University Press)
[5]	Hong C K, Ou Z Y, Mandel L 1987 Phys. Rev. Lett. 59 204
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[7]	Glauber R J 1995 Am. J. Phys. 63 12
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[9]	Bahder T B, Lopata P A 2006 Phase Sensitivity of a Mach-Zehnder Quantum Sensor (Conference proceedings of QCMC)
[10]	Escher B M, de Matos Filho R L, Davidovich L 2011 Nature Phys. 7 406
[11]	Giovannetti V, Lloyd S, Maccone L 2011 Nature Photon. 5 222
[12]	Grangier P, Slusher R E, Yurke B, LaPorta A 1986 Phys. Rev. Lett. 59 2153
[13]	O'Brien J L 2007 Science 318 1393
[14]	Dorner U, Dobrzanski R D, Smith B J, Lundeen J S, Wasilewski W, Banaszek K, Walmsley I A 2009 Phys. Rev. Lett. 102 040403
[15]	Gerry C C, Mimih J 2010 Contemp. Phys. 51 497
[16]	Giovannetti V, Lloyd S, Maccone L 2004 Science 306 1330
[17]	Bouwmeester D, Ekert A, Zeilinger A 2000 The Physics of Quantum Information (Berlin: Springer-Verlag)
[18]	Dowling J P 2008 Contemp. Phys. 49 125
[19]	Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033
[20]	Ekert A K, knight P L 1991 Phys. Rev. A 43 3934
[21]	Windhager A, Suda M, Pache C, Peev M, Poppe A 2011 Opt. Commu. 284 1907
[22]	Xu X X, Jia F, Hu L Y, Duan Z L, Guo Q, Ma S J 2012 J. Mod. Opt. 59 1624
[23]	Schleich W P 2001 Quantum Optics in Phase space (Berlin: Verlag)
[24]	Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661
[25]	Zhang H L, Jia Fang, Xu X X, Guo Q, Tao X Y, Hu L Y 2013 Acta Phys. Sin. 62 014208
[26]	Hu L Y, Xu X X, Fan H Y 2010 J. Opt. Soc. Am. B 27 286
[27]	Glauber R 1963 Phys. Rev. 131 2766
[28]	Puri R R 2001 Mathematical Methods of Quantum Optics (Berlin: Springer-Verlag) Appendix A
[29]	Hu L Y, Fan H Y 2009 Chin Phys. B 18 4657
[30]	Leonhardt U 1997 Measuring the quantum state of light (Cambridge: Cambridge University Press)
[31]	Wang K, Zhu S 2003 Euro Phys. Lett. 64 22
[32]	Wang K, Yang G 2004 Chin. Phys. Lett. 21 302

施引文献

[1]	Hariharan P 2003 Optical interferometry, (2nd Edn) (Elsevier)
[2]	Taylor G I 1909 Proceedings of the Cambridge Philosophical Society 15 14
[3]	Paul H 1986 Rev. Mod. Phys. 58 209
[4]	Dirac P A M 1930 The Principles of Quantum Mechanics (Clarendon: Oxford University Press)
[5]	Hong C K, Ou Z Y, Mandel L 1987 Phys. Rev. Lett. 59 204
[6]	Mandel L 1999 Rev. Mod. Phys. 71 S274
[7]	Glauber R J 1995 Am. J. Phys. 63 12
[8]	Long G L, Deng F G, Zeng J Y 2011 Recent Progress in Quantum Mechanics, fifth volume (Beijing: Tsinghua University Press) [龙桂鲁, 邓富国, 曾谨言 2011 量子力学新进展第五辑 (北京: 清华大学出版社)]
[9]	Bahder T B, Lopata P A 2006 Phase Sensitivity of a Mach-Zehnder Quantum Sensor (Conference proceedings of QCMC)
[10]	Escher B M, de Matos Filho R L, Davidovich L 2011 Nature Phys. 7 406
[11]	Giovannetti V, Lloyd S, Maccone L 2011 Nature Photon. 5 222
[12]	Grangier P, Slusher R E, Yurke B, LaPorta A 1986 Phys. Rev. Lett. 59 2153
[13]	O'Brien J L 2007 Science 318 1393
[14]	Dorner U, Dobrzanski R D, Smith B J, Lundeen J S, Wasilewski W, Banaszek K, Walmsley I A 2009 Phys. Rev. Lett. 102 040403
[15]	Gerry C C, Mimih J 2010 Contemp. Phys. 51 497
[16]	Giovannetti V, Lloyd S, Maccone L 2004 Science 306 1330
[17]	Bouwmeester D, Ekert A, Zeilinger A 2000 The Physics of Quantum Information (Berlin: Springer-Verlag)
[18]	Dowling J P 2008 Contemp. Phys. 49 125
[19]	Yurke B, McCall S L, Klauder J R 1986 Phys. Rev. A 33 4033
[20]	Ekert A K, knight P L 1991 Phys. Rev. A 43 3934
[21]	Windhager A, Suda M, Pache C, Peev M, Poppe A 2011 Opt. Commu. 284 1907
[22]	Xu X X, Jia F, Hu L Y, Duan Z L, Guo Q, Ma S J 2012 J. Mod. Opt. 59 1624
[23]	Schleich W P 2001 Quantum Optics in Phase space (Berlin: Verlag)
[24]	Xu X X, Yuan H C, Hu L Y 2010 Acta Phys. Sin. 59 4661
[25]	Zhang H L, Jia Fang, Xu X X, Guo Q, Tao X Y, Hu L Y 2013 Acta Phys. Sin. 62 014208
[26]	Hu L Y, Xu X X, Fan H Y 2010 J. Opt. Soc. Am. B 27 286
[27]	Glauber R 1963 Phys. Rev. 131 2766
[28]	Puri R R 2001 Mathematical Methods of Quantum Optics (Berlin: Springer-Verlag) Appendix A
[29]	Hu L Y, Fan H Y 2009 Chin Phys. B 18 4657
[30]	Leonhardt U 1997 Measuring the quantum state of light (Cambridge: Cambridge University Press)
[31]	Wang K, Zhu S 2003 Euro Phys. Lett. 64 22
[32]	Wang K, Yang G 2004 Chin. Phys. Lett. 21 302

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