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明亮压缩态光场的操控及量子层析

李庆回 姚文秀 李番 田龙 王雅君 郑耀辉

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明亮压缩态光场的操控及量子层析

李庆回, 姚文秀, 李番, 田龙, 王雅君, 郑耀辉

Manipulations and quantum tomography of bright squeezed states

Li Qing-Hui, Yao Wen-Xiu, Li Fan, Tian Long, Wang Ya-Jun, Zheng Yao-Hui
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  • 连续变量量子态的制备与操控是进行量子通信、量子密钥分发以及量子网络构建的重要基础. 本文基于二阶非线性过程, 利用周期极化磷酸氧钛钾晶体构成的简并光学参量放大腔, 在实验上实现了1064 nm波段明亮压缩态光场的制备, 所制备的明亮压缩态光场在泵浦光功率为310 mW、分析频率为3 MHz处的压缩度为–11.6 dB. 当注入50 mW泵浦光时, 实现了压缩度为–6 dB, 纯度为98.5%的压缩态光场; 在此基础上, 利用光电调制器进行明亮压缩态光场的线性光学操控, 并基于平衡零拍探测系统的直流信号准确判断压缩态光场时域信号对应的相位, 之后结合极大似然估计算法实现压缩态的量子层析, 得到量子态的密度矩阵及相空间的Wigner函数, 从而获得量子态的光子数分布等全部信息.
    Generation and manipulation of continuous variable quantum states are the building blocks of quantum communication, quantum key distribution and quantum networks. According to the second-order nonlinear process of the periodically-poled potassium titanyl phosphate (PPKTP) crystal, we design a semi-monolithic optical parametric amplifier (OPA) cavity to generate the bright squeezed light at a wavelength of 1064 nm. With the injection of a seed beam, the squeezed state generated by the OPA has a coherent amplitude, so called bright squeezed state. The squeezing level is directly observed to be –11.6 dB when the pump power is 310 mW at an analysis frequency of 3 MHz. However, with the increase of the pump power, the purity of the squeezed state gets lower and lower due to the increased influence of the anti-squeezing quadrature component on the squeezed quadrature component in the detection process. To obtain a higher purity of the squeezed state for achieving linear optical manipulation and quantum tomography, we choose the pump power of 50 mW, the squeezing level decreases to –6 dB, and the purity of the squeezed state is 98.5% in this case. An electro-optic modulator is adopted to realize the liner manipulation of the squeezed light in the phase space. During the measurement of the bright squeezed state, all the data are taken on condition that the length of the OPA cavity and relative phase between the seed beam and the pump beam are locked by a locking loop. The direct current (DC) signal of the balanced homodyne detection (BHD) is used to accurately determine the phase corresponding to the time domain signal of the squeezed state, while the alternate current (AC) signal of the BHD is mixed with the signal generated by the function generator, after passing through a low-pass filter and a high-pass filter, the signal is then amplified by using a low-noise amplifier. A high-performance oscilloscope is finally used to simultaneously collect the signals, thus obtaining the quantum noise signal of the bright squeezed light after linear manipulation. Together with the maximum likelihood estimation algorithm, the quantum tomography, the density matrix and the Wigner function of the bright squeezed light are obtained, that is, all the information such as the photon number distribution of the quantum state is determined. Multiple iterations are taken in the maximum likelihood estimation algorithm process to eliminate the influence of the low quantum efficiency on the detection system, so that the density matrix is fitted well with the theoretical results.
      通信作者: 田龙, tianlong@sxu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 62027821, 11654002, 11874250, 11804207, 11804206, 62035015)、国家重点研发计划(批准号: 2020YFC2200402)、山西省重点研发计划(批准号: 201903D111001)、陕西省自然科学基础研究计划(批准号: 2019JQ-943)、山西省三晋学者特聘教授项目、山西省“1331”重点建设学科和山西省高等学校中青年拔尖创新人才计划资助的课题
      Corresponding author: Tian Long, tianlong@sxu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grants Nos. 62027821, 11654002, 11874250, 11804207, 11804206, 62035015), the National Key R&D Program of China (Grant No. 2020YFC2200402), the Key R&D Program of Shanxi Province, China (Grant No. 201903D111001), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2019JQ-943), the Program for Sanjin Scholar of Shanxi Province, China, the Fund for Shanxi 1331 Project Key Subjects Construction, China, and the Program for the Top Young and Middle-aged Innovative Talents of Higher Learning Institutions of Shanxi Province, China
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  • 图 1  实验装置图(SHG, 倍频腔; OPA, 光学参量放大腔; EOM, 光电调制器; MC, 模式清洁器; DBS, 双色镜; FI, 隔离器; PZT, 压电驱动器; PD, 光电探测器; BHD, 平衡零拍探测器; SA, 频谱分析仪; LPF, 低通滤波器; HPF, 高通滤波器)

    Fig. 1.  Experimental setup. SHG, second harmonic generation; OPA, optical parameter amplifier; EOM, electric-optic modular; MC, mode cleaner; DBS, dichroic beam splitter; FI, Faraday isolator; PZT, piezoe-lectric transducer; PD, photodetector; BHD, balance homodyne detector; SA, spectrum analyzer; LPF, low-pass filter; HPF, high-pass filter.

    图 2  压缩和反压缩随泵浦功率的变化趋势图, 分析频率为3 MHz, 分辨率带宽(RBW)为300 kHz, 视频带宽(VBW) 200 Hz. 所有的数据点均包括探测器的电子学噪声的影响, 为直接测量结果

    Fig. 2.  Pump power dependence of anti-squeezed and squeezed quadrature variances. These measurements are recorded at a Fourier frequency of 3 MHz, with a resolution bandwidth (RBW) of 300 kHz and a video bandwidth (VBW) of 200 Hz. The data still include electronic noise, and represent direct observations.

    图 3  (a), (b)未进行线性操控的明亮压缩态噪声时域测量结果及量子层析后对应的密度矩阵; (c), (d)进行线性操控后的明亮压缩态噪声时域测量结果及量子层析后对应的密度矩阵

    Fig. 3.  (a), (b) Time domain signal and corresponding density matrix of bright squeezed state before linearly manipulating, respectively; (c), (d) time domain signal and corresponding density matrix of linearly manipulated bright squeezed state, respectively.

    图 4  明亮压缩态光场在3 MHz分析边带的光子数分布概率 (a)线性操控光学前; (b)线性操控光学后

    Fig. 4.  Photon number distribution of the bright squeezed state at 3 MHz: (a) Before linearly manipulating optics; (b) after linearly manipulating optics.

    图 5  (a), (c)从极大似然估计重构得到的无调制时的明亮压缩态Wigner函数和等高线图; (b), (d)从极大似然估计重构得到的光电相位调制器操控后的明亮压缩态Wigner 函数和等高线图; (e), (f)利用均匀相位分配法重构得到的无操控时以及操控后的明亮压缩态Wigner函数的等高线图

    Fig. 5.  (a), (c) Wigner function and the contour plot of the bright squeezed state obtained by maximum likelihood estimation without linearly manipulating optics, respectively; (b), (d) Wigner function and the contour plot of the squeezed state obtained by maximum likelihood estimation with linearly manipulating optics, respectively; (e), (f) Wigner functions of the bright squeezed state obtained by the method of artificially homogeneous phase distribution without or with linearly manipulating optics, respectively.

  • [1]

    Schrödinger E 1926 Sci. Nat. 14 664Google Scholar

    [2]

    Kennard E H 1927 J. Z. Phys. 44 326Google Scholar

    [3]

    Darwin C G 1927 Proc. R. Soc. London, Ser. A 117 258Google Scholar

    [4]

    Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valley J F 1985 Phys. Rev. Lett. 55 2409Google Scholar

    [5]

    Walls D F 1983 Nature 306 141Google Scholar

    [6]

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

    [7]

    Acernese F, et al. (Virgo Collaboration). 2019 Phys. Rev. Lett. 123 231108Google Scholar

    [8]

    Acernese F, et al. (Virgo Collaboration). 2020 Phys. Rev. Lett. 125 131101Google Scholar

    [9]

    Eberle T, Händchen V, Schnabel R 2013 Opt. Express 21 11546Google Scholar

    [10]

    Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706Google Scholar

    [11]

    Asavanant W, Nakashima K, Shiozawa Y, Yoshikawa J I, Furusawa A 2017 Opt. Express 25 32227Google Scholar

    [12]

    Polzik E S, Carri J, Kimble H J 1992 Phys. Rev. Lett. 68 3020Google Scholar

    [13]

    Yang W, Shi S, Wang Y, Ma W, Zheng Y, Peng K 2017 Opt. Lett. 42 4553Google Scholar

    [14]

    Madsen L S, Usenko V C, Lassen M, Filip R, Andersen U L 2012 Nat. Commun. 3 1083Google Scholar

    [15]

    Shi S, Tian L, Wang Y, Zheng Y, Xie C, Peng K 2020 Phys. Rev. Lett. 125 070502Google Scholar

    [16]

    Li Y Q, Guzun D, Xiao M 1999 Phys. Rev. Lett. 82 5225Google Scholar

    [17]

    Xu C, Zhang L, Huang S, Ma T, Liu F, Yonezawa H, Zhang Y, Xiao M 2019 Photonics Res. 7 A14Google Scholar

    [18]

    Schönbeck A, Thies F, Schnabel R 2018 Opt. Lett. 43 110Google Scholar

    [19]

    Sun X, Wang Y, Tian L, Zheng Y, Peng K 2019 Chin. Opt. Lett. 17 072701Google Scholar

    [20]

    Zhao J, Liu K, Jeng H, Gu M, Thompson J, Lam P K, Assad S M 2020 Nat. Photonics 14 306Google Scholar

    [21]

    仲银银, 潘晓州, 荆杰泰 2020 物理学报 69 130301Google Scholar

    Zhong Y Y, Pan X Z, Jing J T 2020 Acta Phys. Sin. 69 130301Google Scholar

    [22]

    Wang W, Zhang K, Jing J T 2020 Phys. Rev. Lett. 125 140501Google Scholar

    [23]

    Shi S, Wang Y, Yang W, Zheng Y, Peng K 2018 Opt. Lett 43 5411Google Scholar

    [24]

    Vahlbruch H, Mehmet M, Danzmann K, Schnabel R 2016 Phys. Rev. Lett. 117 110801Google Scholar

    [25]

    Sun X C, Wang Y J, Tian L, Shi S P, Zheng Y H, Peng K C 2019 Opt. Lett. 44 1789Google Scholar

    [26]

    Chelkowski S, Vahlbruch H, Danzmann K, Schnabel R 2007 Phys. Rev. A 75 043814Google Scholar

    [27]

    Vogel K, Risken H 1989 Phys. Rev. A 40 2847Google Scholar

    [28]

    Schiller S, Breitenbach G, Pereira S F, Müller T, Mlynek J 1996 Phys. Rev. Lett. 77 2933Google Scholar

    [29]

    Beck M, Smithey D T, Raymer M G 1993 Phys. Rev. A 48 R890Google Scholar

    [30]

    Smithey D T, Beck M, Cooper J, Raymer M G 1993 Phys. Rev. A 48 3159Google Scholar

    [31]

    Lvovsky A I, Raymer M G 2009 Rev. Mod. Phys. 81 299Google Scholar

    [32]

    Lvovsky A I 2004 J. Opt. B: Quantum Semiclassical Opt. 6 S556Google Scholar

    [33]

    李淑静, 张娜娜, 闫红梅, 徐忠孝, 王海 2018 物理学报 67 094204Google Scholar

    Li S J, Zhang N N, Yan H M, Xu Z X, Wang H 2018 Acta Phys. Sin. 67 094204Google Scholar

    [34]

    叶晨光, 张靖 2008 物理学报 57 6962Google Scholar

    Ye C G, Zhang J 2008 Acta Phys. Sin. 57 6962Google Scholar

    [35]

    Breitenbach G, Schiller S, Mlynek J 1997 Nature 387 471Google Scholar

    [36]

    Smithey D T, Beck M, Cooper J, Raymer M G, Faridani A 1993 Phys. Scr. 1993 35Google Scholar

    [37]

    Neergaard-Nielsen J S, Nielsen B M, Takahashi H, Vistnes A I, Polzik E S 2007 Opt. Express 15 7940Google Scholar

    [38]

    Zavatta A, Parigi V, Bellini M 2007 Phys. Rev. A 75 052106Google Scholar

    [39]

    Ourjoumtsev A, Tualle-Brouri R, Laurat J, Grangier P J S 2006 Science 312 83Google Scholar

    [40]

    Yao W, Wang Q, Tian L, Li R, Shi S, Wang J, Wang Y, Zheng Y 2020 Laser Phys. Lett. 18 015001Google Scholar

    [41]

    Yang W, Wang Y, Zheng Y, Lu H 2015 Opt. Express 23 19624Google Scholar

    [42]

    Wang J R, Wang Q W, Tian L, Su J, Zheng Y H 2020 Chin. Phys. B 29 034205Google Scholar

    [43]

    Wang J R, Zhang H Y, Zhao Z L, Zheng Y H 2020 Chin. Phys. B 29 124207Google Scholar

    [44]

    Li Z, Tian Y, Wang Y, Ma W, Zheng Y 2019 Opt. Express 27 7064Google Scholar

    [45]

    张宏宇, 王锦荣, 李庆回, 吉宇杰, 贺子洋, 杨荣草, 田龙 2019 量子光学学报 25 456Google Scholar

    Zhang H Y, Wang J R, Li Q H, Ji Y J, He Z Y, Yang R C, Tian L 2019 Acta Sin. Quantum Opt. 25 456Google Scholar

    [46]

    Schneider K, Bruckmeier R, Hansen H, Schiller S, Mlynek J 1996 Opt. Lett. 21 1396Google Scholar

    [47]

    Morgan P H 2011 Ph. D. Dissertation (Canberra: Australian National University)

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    [19] 孟祥国, 王继锁, 梁宝龙. 增光子奇偶相干态的Wigner函数. 物理学报, 2007, 56(4): 2160-2167. doi: 10.7498/aps.56.2160
    [20] 杨庆怡, 孙敬文, 韦联福, 丁良恩. 增、减光子奇偶相干态的Wigner函数. 物理学报, 2005, 54(6): 2704-2709. doi: 10.7498/aps.54.2704
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出版历程
  • 收稿日期:  2021-02-11
  • 修回日期:  2021-03-04
  • 上网日期:  2021-06-07
  • 刊出日期:  2021-08-05

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