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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.
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Keywords:
- N00N state /
- wigner function /
- phase space /
- quantum interference
[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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[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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