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As is well known, quantum optics has developed significantly in recent years and advanced several hot research topics, such as quantum communications, quantum sensing, quantum calculations, etc. Among these researches, it is important to understand the quantum information transmitting in optical fiber. For realizing longer transmission distance and better transmission quality, great effort has devoted to the researches of encoding and decoding at the transmitter and the receiver end. However, less attention was paid to the fading of signal in the transmission channel. In this work, we mainly focus on the transmission model of optical quantum transmission and the influences of loss, dispersion and nonlinear effect on fiber transmission of optical quantum information are also discussed.Quantum information transmission can be influenced by loss, dispersion and nonlinear effect in optical fiber, leading to transmission state evolution and energy transfer. Based on the transmission equation of single mode fiber and quantum theory of electromagnetic field, the fundamental mode field of single mode fiber is quantized. A quantum transmission equation is deduced from the classical optical transmission equation through quantizing the amplitude of electromagnetic field. Compared with classic wave theory, the photon transmission equation quantizing the slowly-varying amplitude in the coupled nonlinear Schrdinger equation is obtained. In the classic wave equation, light is interpreted as energy which propagates as waves. The photon transmission equation is obtained by quantizing the slowly-varying amplitude of light, that is, the particle nature of light. The energy propagates through alternative interaction between creation and annihilation operator on photons. The transmission equations show that photons will interact with the transmission medium during propagation and be influenced by dispersion, nonlinear effect, loss, etc. By giving a trail solution and introducing a perturbation term, the transmission equation is solved for the complicated case where the dispersion, loss and nonlinear effect are all involved. A dispersion equation that should be satisfied for nontrivial solution is then obtained. From this dispersion equation, the relation between photon power and perturbation frequency is calculated and analyzed. The change of photon power in generalized field with perturbation frequency is discussed, and the influences of fiber dispersion and nonlinearity on the solution are analyzed.Some conclusions are obtained by perturbed solution and analyses of single photon transmission equation in optical fiber. It is found that photon power decreases with the increase of perturbation frequency and reaches its maximum value for zero perturbation frequency. At the same time, the optical power is affected by the dispersion of the optical fiber. Photon power decreases with the GVD coefficient far from the zero dispersion point. It is also found that photon power decreases with the increase of nonlinear coefficient. This work may contribute to the research of the properties of quantum fiber transmission system.
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Keywords:
- single mode optical fiber /
- optical quantum /
- transmission equation /
- dispersion
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[18] Pan J W, Bouwmeester D, Weinfurter H, Zeilinger A 1998 Phys. Rev. Lett. 80 3891
[19] Inagaki T, Matsuda N, Tadanaga O, Asobe M, Takesue H 2013 Opt. Express 21 23241
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[22] Zhou N R, Zeng B Y, Wang L J, Gong L H 2010 Acta Phys. Sin. 59 2193 (in Chinese) [周南润, 曾宾阳, 王立军, 龚黎华 2010 物理学报 59 2193]
[23] Ma X S, Herbst T, Scheidl T, Wang D Q, Kropatschek S, Naylor W, Wittmann B, Mech A, Kofler J, Anisimona E, Makarov V, Jennewein T, Ursin R, Zeilinger A 2012 Nature 489 7415
[24] Inagaki T, Matsuda N, Tadanaga O, Takesue H 2013 Opt. Expess 21 23241
[25] Tang Y L, Yin H L, Chen S J, Liu Y, Zhang W J, Jiang X, Zhang L, Wang J, You L X, Guan J Y, Yang D X, Wang Z, Liang H, Zhang Z, Zhou N, Ma X F, Chen T Y, Zhang Q, Pan J W 2014 Phys. Rev. Lett. 113 190501
[26] Filippo C, Francesco M, Hammam Q, Ebrahim K, Sergei S, Domenico P, Corrado L, Fabio S, Enrico S, Robert W B, Lorenzo M 2015 Sci. Adv. 1 1500087
[27] Martin P, Tomas T, Tomas C 2015 Natue Photonics 9 529
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[1] Vance R W C 2007 J. Opt. Soc. Am. B 24 000928
[2] Vance R W C 2007 J. Opt. Soc. Am. B 24 000942
[3] Andres R P, Bein T, Dorogi T, Feng S, Henderson J I 1996 Science 272 1323
[4] Datta S, Tian W 1997 Phys. Rev. B 55 R1914
[5] Taylor J, Guo H, Wang J 2001 Phys. Rev. B 63 245407
[6] Wang L G, Chen L, Yu D W, Li Y 2007 Acta Phys. Sin. 56 6526 (in Chinese) [王利光, 陈蕾, 郁鼎文, 李勇 2007 物理学报 56 6526]
[7] Wang C, Huo X X, Zhang X M, Wang L G 2010 Acta Phys. Sin. 59 4955 (in Chinese) [王畅, 霍新霞, 张秀梅, 王利光 2010 物理学报 59 4955]
[8] Pirandola S, Braunstein S L, Mancini S, Lloyd S 2008 Eur. Phys. Lett. 84 20013
[9] Meslouhi A, Hassouni Y 2013 Quantum Inf. Process. 12 2603
[10] Wang C, Deng F G, Long G L 2005 Opt. Commun. 253 15
[11] Shi J, Gong Y X, Xu P, Zhu Y B 2011 Commun. Theor. Phys. 56 83
[12] Banerjee A, Patha A 2012 Phys. Lett. A 376 2944
[13] Li X H, Zeng Z, Wang C 2014 J. Opt. Soc. Am. B 31 002334
[14] Wang T J, Song S Y, Long G L 2012 Phys. Rev. A 85 062311
[15] Rebentrost P, Mohseni M, Kassal I, Lloyd S 2009 New J. Phys. 11 033003
[16] Chin A, Datta A, Caruso F, Huelga S 2010 New J. Phys. 12 065002
[17] Bartlett S D, Munro W J 2003 Phys. Rev. Lett. 90 117901
[18] Pan J W, Bouwmeester D, Weinfurter H, Zeilinger A 1998 Phys. Rev. Lett. 80 3891
[19] Inagaki T, Matsuda N, Tadanaga O, Asobe M, Takesue H 2013 Opt. Express 21 23241
[20] Bouwmeester D, Pan J W, Mattle K, Weinfurtor H, Zeiling A 1997 Nature 390 575
[21] Liu J, Wang Q, Kuang L M, Zeng H S 2010 Chin. Phys. B 19 030313
[22] Zhou N R, Zeng B Y, Wang L J, Gong L H 2010 Acta Phys. Sin. 59 2193 (in Chinese) [周南润, 曾宾阳, 王立军, 龚黎华 2010 物理学报 59 2193]
[23] Ma X S, Herbst T, Scheidl T, Wang D Q, Kropatschek S, Naylor W, Wittmann B, Mech A, Kofler J, Anisimona E, Makarov V, Jennewein T, Ursin R, Zeilinger A 2012 Nature 489 7415
[24] Inagaki T, Matsuda N, Tadanaga O, Takesue H 2013 Opt. Expess 21 23241
[25] Tang Y L, Yin H L, Chen S J, Liu Y, Zhang W J, Jiang X, Zhang L, Wang J, You L X, Guan J Y, Yang D X, Wang Z, Liang H, Zhang Z, Zhou N, Ma X F, Chen T Y, Zhang Q, Pan J W 2014 Phys. Rev. Lett. 113 190501
[26] Filippo C, Francesco M, Hammam Q, Ebrahim K, Sergei S, Domenico P, Corrado L, Fabio S, Enrico S, Robert W B, Lorenzo M 2015 Sci. Adv. 1 1500087
[27] Martin P, Tomas T, Tomas C 2015 Natue Photonics 9 529
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