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基于SSA-BP网络模型的Hong-Ou-Mandel干涉时延测量研究及其在量子陀螺仪中的应用

翟艺伟 李旺

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基于SSA-BP网络模型的Hong-Ou-Mandel干涉时延测量研究及其在量子陀螺仪中的应用

翟艺伟, 李旺

SSA-BP network model based Hong-Ou-Mandel interference delay measurement and its application in quantum gyroscope

Zhai Yi-Wei, Li Wang
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  • 作为航空航天导航系统的重要器件, 高灵敏度的光学陀螺仪一直是国内外科研工作者的研究重点. 经典光学陀螺仪因真空零点波动使其灵敏度受到散粒噪声极限的制约, 无法满足日益发展的量子导航需求. 本文提出了基于频率纠缠源及Hong-Ou-Mandel (HOM)干涉的量子陀螺仪方案, 利用SSA-BP神经网络模型模拟不同的泵浦光和非线性晶体参数, 以预测HOM干涉图谱的特性参量干涉可见度及干涉宽度. 结合量子Fisher信息理论, 获得时延差的最大量子Fisher信息可达1.999, 计算得出时延差的不确定度与散粒噪声极限的最小比值为0.707, 并依据量子陀螺仪时延差与旋转角速度的关系, 验证出旋转角速度的测量灵敏度较经典光学陀螺仪提高了2个数量级. 证明上述方案可以实现超越散粒噪声极限的测量灵敏度, 能为后续量子陀螺仪的实验验证提供理论支持.
    High sensitivity optical gyroscopes, as an important component of aerospace navigation system, have become a research hotspot. The sensitivity of the classical optical gyroscope is restricted by the shot-noise-limit owing to the vacuum zero energy fluctuation. Therefore, the classical optical gyroscope cannot meet the growing demand of navigation, sensing and communication. In this work, a measurement scheme of quantum gyroscope based on frequency entangled source and Hong-Ou-Mandel (HOM) interference is proposed. In order to realize high-precision delay measurement, the interference visibility and width of HOM interferogram are regulated by changing the bandwidth of pump laser and the length of nonlinear crystal. However, traditional experimental regulation method is inefficient and time consuming. On the basis of the above scheme, a delay measurement scheme of HOM interference based on SSA-BP network is established. The SSA-BP network is used to simulate different bandwidths of pump laser and the lengths of nonlinear crystal to predict the interference visibility and width of HOM interferogram. The verification results show that the mean square error (MSE), the mean absolute error (MAE) and the mean absolute percentage error (MAPE) predicted by SSA-BP network are smallest. Based on the above SSA-BP network model, the interference visibility and width of HOM interferogram are $\alpha = 1$ and $\sigma = 5.9\;{\text{ ps}}$ respectively. Combined with quantum Fisher information, the maximum value of F is obtained to be 1.999. Meanwhile, according to the Cramer-Rao bound theory, the minimum ratio of the uncertainty of the delay to the shot-noise-limit can reach 0.707, indicating that the precision of delay measurement is increased by 2 orders of magnitude. According to the relationship between delay and rotational angular velocity, the measurement sensitivity of the rotational angular velocity is improved by 2 orders of magnitude compared with that of the classical optical gyroscope. These results prove that the above quantum gyroscope scheme can realize the measurement sensitivity of rotational angular velocity beyond the shot-noise-limit. Therefore, the SSA-BP network model can provide theoretical support for the subsequent experimental verification of quantum gyroscopes based on HOM interference delay measurement, and is the technical basis for the development of quantum navigation, quantum sensing and quantum communication.
      通信作者: 翟艺伟, zhaiyiwei@sust.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 12205178)资助的课题.
      Corresponding author: Zhai Yi-Wei, zhaiyiwei@sust.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12205178).
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    Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photonics 5 222Google Scholar

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    Kolkiran A, Agarwal G S 2007 Opt. Express 15 6798Google Scholar

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    陈坤, 陈树新, 吴德伟, 杨春燕, 吴昊 2016 物理学报 65 054203Google Scholar

    Chen K, Chen S X, Wu D W, Yang C Y, Wu H 2016 Acta Phys. Sin. 65 054203Google Scholar

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    Fink M, Steinlechner F, Handsteiner J, Dowling J P, Scheidl T, Ursin R 2019 New J. Phys. 21 053010Google Scholar

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    Bertocchi G, Alibart O, Ostrowsky D B, Tanzilli S, Baldi P 2006 J. Phys. B 39 1011Google Scholar

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    Yang Y, Xu L, Giovannetti V 2019 Sci. Rep. 9 10821Google Scholar

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    Napolitano M, Koschorreck M, Dubost B, Behbood N, Sewell R J, Mitchell M W 2011 Nature 471 486Google Scholar

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    Flammia S T, Caves C M, Geremia J M, Boixo S 2007 Phys. Rev. Lett. 98 90401Google Scholar

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    Barnett S M, Fabre C, Maıtre A 2003 Eur. Phys. J. D 22 513Google Scholar

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    Dowling J P 2008 Contemp. Phys. 49 125Google Scholar

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    Jiang L, Lukin M D, Rey A M 2007 Phys. Rev. A 76 53617Google Scholar

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    Lee C, Huang J, Deng H, et al. 2012 Front. Phys. 7 109Google Scholar

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    Giovannetti V, Lloyd S, Maccone L 2001 Nature 412 417Google Scholar

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    张瑶, 张云波, 陈立 2021 物理学报 70 168701Google Scholar

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    郎利影, 陆佳磊, 于娜娜, 席思星, 王雪光, 张雷, 焦小雪 2020 物理学报 69 244204Google Scholar

    Lang L Y, Lu J L, Yu N N, Xi S X, Wang X G, Zhang L, Jiao X X 2020 Acta Phys.Sin. 69 244204Google Scholar

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    Xue J, Shen B 2020 Syst. Sci. Control Eng. 8 22Google Scholar

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    孟彩霞, 吴迪, 雷雨 2022 大地测量与地球动力学 42 125

    Meng C X, Wu D, Lei Y 2022 J. Geodesy and Geodynamics 42 125

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    Maccone L, Shapiro J H, Wong F N C, Giovannetti V 2002 Phys. Rev. A 66 43813Google Scholar

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    Maccone L, Shapiro J H, Wong F N C, Giovannetti V 2002 Phys. Rev. Lett. 88 183602Google Scholar

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    翟艺伟, 董瑞芳, 权润爱, 项晓, 刘涛, 张首刚 2021 物理学报 70 120302Google Scholar

    Zhai Y W, Dong R F, Quan R A, Xiang X, Liu T, Zhang S G 2021 Acta Phys. Sin. 70 120302Google Scholar

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    Royfriened B 1998 Physics from Fisher Information (Cambridge: Cambridge University Press) pp22–62

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    任志红, 李岩, 李艳娜, 李卫东 2019 物理学报 68 040601Google Scholar

    Ren Z H, Li Y, Li Y N, Li W D 2019 Acta Phys. Sin. 68 040601Google Scholar

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    牛明丽, 王月明, 李志坚 2022 物理学报 71 090601Google Scholar

    Niu M L, Wang Y M, Li Z J 2022 Acta Phys. Sin. 71 090601Google Scholar

    [27]

    Lyons A, Knee G C, Bolduc E, Roger T, Leach J, Gauger E M, Faccio D 2018 Sci. Adv. 4 9416Google Scholar

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    Fisher R A 1925 Proc. Camb. Phil. Soc. 22 700Google Scholar

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    Holevo A S 2001 Statistical Structure of Quantum Theory (Berlin, Heidelberg: Springer) pp45–70

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    Paris M G A 2009 arxiv: 0804.2981v3 [quant-ph]

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    Pérez-Delgado C A, Kok P, Zwierz M 2010 Phys. Rev. Lett. 105 180402Google Scholar

    [32]

    袁春华, 张可烨, 张卫平 2014 中国科学: 信息科学 44 345

    Yuan C H, Zhang K Y, Zhang W P 2014 Sci. Sin. Informat. 44 345

    [33]

    Lloyd S, Maccone L, Giovannetti V 2006 Phys. Rev. Lett. 96 10401Google Scholar

    [34]

    Efremov M A, Kazakov, A E, Chan K W, Law C K, Eberly J H, Fedorov M V 2004 Phys. Rev. A 69 52117Google Scholar

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    Volkov P A, Fedorov M V, Mikhailova Y M 2008 Phys. Rev. A 78 62327Google Scholar

    [36]

    Fedorov M V, Efremov M A, Volkov P A, Eberly J H 2006 J. Phys. B 39 S467Google Scholar

  • 图 1  基于频率纠缠光源与HOM干涉的量子陀螺仪原理框图

    Fig. 1.  Principle block diagram of quantum gyroscope based on frequency entangled light source and HOM interference.

    图 2  HOM干涉图谱

    Fig. 2.  HOM interferogram.

    图 3  SSA-BP神经网络拓扑结构

    Fig. 3.  SSA-BP neural network topology.

    图 4  不同BP网络预测数据集性能对比图 (a) $\alpha $值; (b) $\sigma $

    Fig. 4.  Performance comparison chart of different BP network prediction data sets: (a) $\alpha $ values; (b) $\sigma $values.

    图 5  (a) 在不同的W值下, $\alpha $L的变化图; (b) 在不同的L值下, $\sigma $W的变化图

    Fig. 5.  (a) $\alpha $ as a function of L at different W; (b) $\sigma $ as a function of W at different L.

    图 6  (a)$\sigma = 4~{\text{ps}}$, F$\tau $的变化图; (b)$\alpha = 1$, F$\tau $的变化图

    Fig. 6.  (a) F as a function of delay$\tau $at $\sigma = 4{\text{ ps}}$; (b) F as a function of delay$\tau $at $\alpha = 1$

    图 7  (a) 参数$ \xi $$ \tau $值的变化; (b) $ \xi $最小值的变化图像

    Fig. 7.  (a) Parameter $ \xi $ as a function of delay $ \tau $; (b) minimum value change image of $ \xi $.

    表 1  不同BP网络预测$\sigma $$\alpha $的性能表

    Table 1.  Performance table of different BP networks for predicting $\sigma $ and $\alpha$

    神经网络类型T/S预测$\sigma $/ps预测$\alpha $
    MSE/10–6MAE/10–3MAPE/10–4MSE/10–5MAE/10–3MAPE/10–2
    BP1.333.65209.071.3
    GA-BP38.99.2238.17.561.2
    PSO-BP158.121.74107.06.11.18
    SSA-BP60.45.0127.253.551.0
    下载: 导出CSV
  • [1]

    Scully M O, Zubairy M S 1997 Quantum Optics (Cambridge: Cambridge University Press) pp271–281, 442–454

    [2]

    Giovannetti V, Lloyd S, Maccone L 2011 Nat. Photonics 5 222Google Scholar

    [3]

    Kolkiran A, Agarwal G S 2007 Opt. Express 15 6798Google Scholar

    [4]

    陈坤, 陈树新, 吴德伟, 杨春燕, 吴昊 2016 物理学报 65 054203Google Scholar

    Chen K, Chen S X, Wu D W, Yang C Y, Wu H 2016 Acta Phys. Sin. 65 054203Google Scholar

    [5]

    Fink M, Steinlechner F, Handsteiner J, Dowling J P, Scheidl T, Ursin R 2019 New J. Phys. 21 053010Google Scholar

    [6]

    Bertocchi G, Alibart O, Ostrowsky D B, Tanzilli S, Baldi P 2006 J. Phys. B 39 1011Google Scholar

    [7]

    Yang Y, Xu L, Giovannetti V 2019 Sci. Rep. 9 10821Google Scholar

    [8]

    Napolitano M, Koschorreck M, Dubost B, Behbood N, Sewell R J, Mitchell M W 2011 Nature 471 486Google Scholar

    [9]

    Flammia S T, Caves C M, Geremia J M, Boixo S 2007 Phys. Rev. Lett. 98 90401Google Scholar

    [10]

    Caves C M 1981 Phys. Rev. D 23 1693Google Scholar

    [11]

    Barnett S M, Fabre C, Maıtre A 2003 Eur. Phys. J. D 22 513Google Scholar

    [12]

    Dowling J P 2008 Contemp. Phys. 49 125Google Scholar

    [13]

    Jiang L, Lukin M D, Rey A M 2007 Phys. Rev. A 76 53617Google Scholar

    [14]

    Lee C, Huang J, Deng H, et al. 2012 Front. Phys. 7 109Google Scholar

    [15]

    Giovannetti V, Lloyd S, Maccone L 2001 Nature 412 417Google Scholar

    [16]

    张瑶, 张云波, 陈立 2021 物理学报 70 168701Google Scholar

    Zhang Y, Zhang Y B, Chen L 2021 Acta Phys. Sin. 70 168701Google Scholar

    [17]

    郎利影, 陆佳磊, 于娜娜, 席思星, 王雪光, 张雷, 焦小雪 2020 物理学报 69 244204Google Scholar

    Lang L Y, Lu J L, Yu N N, Xi S X, Wang X G, Zhang L, Jiao X X 2020 Acta Phys.Sin. 69 244204Google Scholar

    [18]

    Xue J, Shen B 2020 Syst. Sci. Control Eng. 8 22Google Scholar

    [19]

    孟彩霞, 吴迪, 雷雨 2022 大地测量与地球动力学 42 125

    Meng C X, Wu D, Lei Y 2022 J. Geodesy and Geodynamics 42 125

    [20]

    Maccone L, Shapiro J H, Wong F N C, Giovannetti V 2002 Phys. Rev. A 66 43813Google Scholar

    [21]

    Maccone L, Shapiro J H, Wong F N C, Giovannetti V 2002 Phys. Rev. Lett. 88 183602Google Scholar

    [22]

    翟艺伟, 董瑞芳, 权润爱, 项晓, 刘涛, 张首刚 2021 物理学报 70 120302Google Scholar

    Zhai Y W, Dong R F, Quan R A, Xiang X, Liu T, Zhang S G 2021 Acta Phys. Sin. 70 120302Google Scholar

    [23]

    Zheng Y, Yao A, Wang R 2004 Phys. Rev. Lett. 93 143901Google Scholar

    [24]

    Royfriened B 1998 Physics from Fisher Information (Cambridge: Cambridge University Press) pp22–62

    [25]

    任志红, 李岩, 李艳娜, 李卫东 2019 物理学报 68 040601Google Scholar

    Ren Z H, Li Y, Li Y N, Li W D 2019 Acta Phys. Sin. 68 040601Google Scholar

    [26]

    牛明丽, 王月明, 李志坚 2022 物理学报 71 090601Google Scholar

    Niu M L, Wang Y M, Li Z J 2022 Acta Phys. Sin. 71 090601Google Scholar

    [27]

    Lyons A, Knee G C, Bolduc E, Roger T, Leach J, Gauger E M, Faccio D 2018 Sci. Adv. 4 9416Google Scholar

    [28]

    Fisher R A 1925 Proc. Camb. Phil. Soc. 22 700Google Scholar

    [29]

    Holevo A S 2001 Statistical Structure of Quantum Theory (Berlin, Heidelberg: Springer) pp45–70

    [30]

    Paris M G A 2009 arxiv: 0804.2981v3 [quant-ph]

    [31]

    Pérez-Delgado C A, Kok P, Zwierz M 2010 Phys. Rev. Lett. 105 180402Google Scholar

    [32]

    袁春华, 张可烨, 张卫平 2014 中国科学: 信息科学 44 345

    Yuan C H, Zhang K Y, Zhang W P 2014 Sci. Sin. Informat. 44 345

    [33]

    Lloyd S, Maccone L, Giovannetti V 2006 Phys. Rev. Lett. 96 10401Google Scholar

    [34]

    Efremov M A, Kazakov, A E, Chan K W, Law C K, Eberly J H, Fedorov M V 2004 Phys. Rev. A 69 52117Google Scholar

    [35]

    Volkov P A, Fedorov M V, Mikhailova Y M 2008 Phys. Rev. A 78 62327Google Scholar

    [36]

    Fedorov M V, Efremov M A, Volkov P A, Eberly J H 2006 J. Phys. B 39 S467Google Scholar

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出版历程
  • 收稿日期:  2023-02-27
  • 修回日期:  2023-04-19
  • 上网日期:  2023-05-08
  • 刊出日期:  2023-07-05

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