搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

光纤中单光子传输方程的求解及分析

陶在红 秦媛媛 孙斌 孙小菡

引用本文:
Citation:

光纤中单光子传输方程的求解及分析

陶在红, 秦媛媛, 孙斌, 孙小菡

Perturbed solution and analyses for single photon transmission equation in optical fiber

Tao Zai-Hong, Qin Yuan-Yuan, Sun Bing, Sun Xiaohan
PDF
导出引用
  • 量子信息在光纤中传输时, 会受到光纤损耗、色散、非线性效应等多因素的影响, 将产生传输态的演化与能量转移. 本文以单模光纤传输方程以及电磁场量子化理论为基础, 对单模光纤中基模模场进行量子化处理, 推导并建立了考虑损耗、色散、非线性效应后的单光子传输方程. 基于微扰法对单光子非线性传输方程进行了求解, 给出了稳定解存在的必要条件及其所满足的色散方程. 深入讨论了广域光功率随微扰频率的变化关系, 并且分析了光纤色散、非线性效应对解的影响. 为量子光纤传输系统性能的深入研究奠定了理论基础.
    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.
      通信作者: 孙小菡, xhsun@seu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 60271206)资助的课题.
      Corresponding author: Sun Xiaohan, xhsun@seu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60271206).
    [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

  • [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

  • [1] 周康, 黎华, 万文坚, 李子平, 曹俊诚. 太赫兹量子级联激光器频率梳的色散. 物理学报, 2019, 68(10): 109501. doi: 10.7498/aps.68.20190217
    [2] 吕志国, 杨直, 李峰, 李强龙, 王屹山, 杨小君. 基于光纤中超短脉冲非线性传输机理与特定光谱选择技术的多波长飞秒激光的产生. 物理学报, 2018, 67(18): 184205. doi: 10.7498/aps.67.20181026
    [3] 张羚翔, 魏薇, 张志明, 廖文英, 杨振国, 范万德, 李乙钢. 环形光子晶体光纤中涡旋光的传输特性研究. 物理学报, 2017, 66(1): 014205. doi: 10.7498/aps.66.014205
    [4] 王鑫, 娄淑琴, 廉正刚. 空芯光子带隙光纤色散特性的实验研究. 物理学报, 2016, 65(19): 194212. doi: 10.7498/aps.65.194212
    [5] 李政颖, 孙文丰, 李子墨, 王洪海. 基于色散补偿光纤的高速光纤光栅解调方法. 物理学报, 2015, 64(23): 234207. doi: 10.7498/aps.64.234207
    [6] 陈翔, 张心贲, 祝贤, 程兰, 彭景刚, 戴能利, 李海清, 李进延. 色散补偿光子晶体光纤结构参数对其色散的影响. 物理学报, 2013, 62(4): 044222. doi: 10.7498/aps.62.044222
    [7] 王伟, 杨博, 宋鸿儒, 范岳. 八边形高双折射双零色散点光子晶体光纤特性分析. 物理学报, 2012, 61(14): 144601. doi: 10.7498/aps.61.144601
    [8] 王伟, 杨博. 菱形纤芯光子晶体光纤色散与双折射特性分析. 物理学报, 2012, 61(6): 064601. doi: 10.7498/aps.61.064601
    [9] 闫海峰, 俞重远, 田宏达, 刘玉敏, 韩利红. 八角光子晶体光纤传输特性与非线性特性研究. 物理学报, 2010, 59(5): 3273-3277. doi: 10.7498/aps.59.3273
    [10] 赵岩, 施伟华, 姜跃进. 中心外缺陷对带隙型光子晶体光纤色散特性的影响. 物理学报, 2010, 59(9): 6279-6283. doi: 10.7498/aps.59.6279
    [11] 黄小东, 张小民, 王建军, 许党朋, 张锐, 林宏焕, 邓颖, 耿远超, 余晓秋. 色散对高能激光光纤前端FM-AM效应的影响. 物理学报, 2010, 59(3): 1857-1862. doi: 10.7498/aps.59.1857
    [12] 李林栗, 冯国英, 杨浩, 周国瑞, 周昊, 朱启华, 王建军, 周寿桓. 纳米光纤的色散特性及其超连续谱产生. 物理学报, 2009, 58(10): 7005-7011. doi: 10.7498/aps.58.7005
    [13] 王士鹤, 任立勇, 刘宇. 光纤中基于双宽带抽运的受激布里渊散射增益谱展宽及慢光传输中脉冲失真减小的理论研究. 物理学报, 2009, 58(6): 3943-3948. doi: 10.7498/aps.58.3943
    [14] 赵兴涛, 侯蓝田, 刘兆伦, 王 伟, 魏红彦, 马景瑞. 改进的全矢量有效折射率方法分析光子晶体光纤的色散特性. 物理学报, 2007, 56(4): 2275-2280. doi: 10.7498/aps.56.2275
    [15] 张德生, 董孝义, 张伟刚, 王 志. 用阶跃有效折射率模型研究光子晶体光纤色散特性. 物理学报, 2005, 54(3): 1235-1240. doi: 10.7498/aps.54.1235
    [16] 李曙光, 周桂耀, 邢光龙, 侯蓝田, 王清月, 栗岩锋, 胡明列. 微结构光纤中超短激光脉冲传输的数值模拟. 物理学报, 2005, 54(4): 1599-1606. doi: 10.7498/aps.54.1599
    [17] 宋 峰, 苏瑞渊, 傅 强, 覃 斌, 田建国, 张光寅. 高浓度镱铒共掺磷酸盐光纤放大器增益特性. 物理学报, 2005, 54(11): 5228-5232. doi: 10.7498/aps.54.5228
    [18] 李曙光, 刘晓东, 侯蓝田. 一种晶体光纤基模色散特性的矢量法分析. 物理学报, 2004, 53(6): 1873-1879. doi: 10.7498/aps.53.1873
    [19] 任国斌, 王 智, 娄淑琴, 简水生. 高折射率芯Bragg光纤的色散特性研究. 物理学报, 2004, 53(6): 1862-1867. doi: 10.7498/aps.53.1862
    [20] 李曙光, 刘晓东, 侯蓝田. 光子晶体光纤色散补偿特性的数值研究. 物理学报, 2004, 53(6): 1880-1886. doi: 10.7498/aps.53.1880
计量
  • 文章访问数:  3287
  • PDF下载量:  567
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-03-05
  • 修回日期:  2016-04-03
  • 刊出日期:  2016-07-05

光纤中单光子传输方程的求解及分析

  • 1. 东南大学光传感/通信综合网络国家研究中心, 南京 210096;
  • 2. 南京信息工程大学电子信息与工程学院, 南京 210044
  • 通信作者: 孙小菡, xhsun@seu.edu.cn
    基金项目: 国家自然科学基金(批准号: 60271206)资助的课题.

摘要: 量子信息在光纤中传输时, 会受到光纤损耗、色散、非线性效应等多因素的影响, 将产生传输态的演化与能量转移. 本文以单模光纤传输方程以及电磁场量子化理论为基础, 对单模光纤中基模模场进行量子化处理, 推导并建立了考虑损耗、色散、非线性效应后的单光子传输方程. 基于微扰法对单光子非线性传输方程进行了求解, 给出了稳定解存在的必要条件及其所满足的色散方程. 深入讨论了广域光功率随微扰频率的变化关系, 并且分析了光纤色散、非线性效应对解的影响. 为量子光纤传输系统性能的深入研究奠定了理论基础.

English Abstract

参考文献 (27)

目录

    /

    返回文章
    返回