Manipulations and quantum tomography of bright squeezed states

Li Qing-Hui; Yao Wen-Xiu; Li Fan; Tian Long; Wang Ya-Jun; Zheng Yao-Hui

doi:10.7498/aps.70.20210318

Abstract

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.

Keywords:

Authors and contacts

1.
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
2.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

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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References

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Cited By

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)

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

[1]	Schrödinger E 1926 Sci. Nat. 14 664 Google Scholar
[2]	Kennard E H 1927 J. Z. Phys. 44 326 Google Scholar
[3]	Darwin C G 1927 Proc. R. Soc. London, Ser. A 117 258 Google Scholar
[4]	Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valley J F 1985 Phys. Rev. Lett. 55 2409 Google Scholar
[5]	Walls D F 1983 Nature 306 141 Google Scholar
[6]	Caves C M 1981 Phys. Rev. D 23 1693 Google Scholar
[7]	Acernese F, et al. (Virgo Collaboration). 2019 Phys. Rev. Lett. 123 231108 Google Scholar
[8]	Acernese F, et al. (Virgo Collaboration). 2020 Phys. Rev. Lett. 125 131101 Google Scholar
[9]	Eberle T, Händchen V, Schnabel R 2013 Opt. Express 21 11546 Google Scholar
[10]	Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706 Google Scholar
[11]	Asavanant W, Nakashima K, Shiozawa Y, Yoshikawa J I, Furusawa A 2017 Opt. Express 25 32227 Google Scholar
[12]	Polzik E S, Carri J, Kimble H J 1992 Phys. Rev. Lett. 68 3020 Google Scholar
[13]	Yang W, Shi S, Wang Y, Ma W, Zheng Y, Peng K 2017 Opt. Lett. 42 4553 Google Scholar
[14]	Madsen L S, Usenko V C, Lassen M, Filip R, Andersen U L 2012 Nat. Commun. 3 1083 Google Scholar
[15]	Shi S, Tian L, Wang Y, Zheng Y, Xie C, Peng K 2020 Phys. Rev. Lett. 125 070502 Google Scholar
[16]	Li Y Q, Guzun D, Xiao M 1999 Phys. Rev. Lett. 82 5225 Google Scholar
[17]	Xu C, Zhang L, Huang S, Ma T, Liu F, Yonezawa H, Zhang Y, Xiao M 2019 Photonics Res. 7 A14 Google Scholar
[18]	Schönbeck A, Thies F, Schnabel R 2018 Opt. Lett. 43 110 Google Scholar
[19]	Sun X, Wang Y, Tian L, Zheng Y, Peng K 2019 Chin. Opt. Lett. 17 072701 Google Scholar
[20]	Zhao J, Liu K, Jeng H, Gu M, Thompson J, Lam P K, Assad S M 2020 Nat. Photonics 14 306 Google Scholar
[21]	仲银银, 潘晓州, 荆杰泰 2020 物理学报 69 130301 Google Scholar Zhong Y Y, Pan X Z, Jing J T 2020 Acta Phys. Sin. 69 130301 Google Scholar
[22]	Wang W, Zhang K, Jing J T 2020 Phys. Rev. Lett. 125 140501 Google Scholar
[23]	Shi S, Wang Y, Yang W, Zheng Y, Peng K 2018 Opt. Lett 43 5411 Google Scholar
[24]	Vahlbruch H, Mehmet M, Danzmann K, Schnabel R 2016 Phys. Rev. Lett. 117 110801 Google Scholar
[25]	Sun X C, Wang Y J, Tian L, Shi S P, Zheng Y H, Peng K C 2019 Opt. Lett. 44 1789 Google Scholar
[26]	Chelkowski S, Vahlbruch H, Danzmann K, Schnabel R 2007 Phys. Rev. A 75 043814 Google Scholar
[27]	Vogel K, Risken H 1989 Phys. Rev. A 40 2847 Google Scholar
[28]	Schiller S, Breitenbach G, Pereira S F, Müller T, Mlynek J 1996 Phys. Rev. Lett. 77 2933 Google Scholar
[29]	Beck M, Smithey D T, Raymer M G 1993 Phys. Rev. A 48 R890 Google Scholar
[30]	Smithey D T, Beck M, Cooper J, Raymer M G 1993 Phys. Rev. A 48 3159 Google Scholar
[31]	Lvovsky A I, Raymer M G 2009 Rev. Mod. Phys. 81 299 Google Scholar
[32]	Lvovsky A I 2004 J. Opt. B: Quantum Semiclassical Opt. 6 S556 Google Scholar
[33]	李淑静, 张娜娜, 闫红梅, 徐忠孝, 王海 2018 物理学报 67 094204 Google Scholar Li S J, Zhang N N, Yan H M, Xu Z X, Wang H 2018 Acta Phys. Sin. 67 094204 Google Scholar
[34]	叶晨光, 张靖 2008 物理学报 57 6962 Google Scholar Ye C G, Zhang J 2008 Acta Phys. Sin. 57 6962 Google Scholar
[35]	Breitenbach G, Schiller S, Mlynek J 1997 Nature 387 471 Google Scholar
[36]	Smithey D T, Beck M, Cooper J, Raymer M G, Faridani A 1993 Phys. Scr. 1993 35 Google Scholar
[37]	Neergaard-Nielsen J S, Nielsen B M, Takahashi H, Vistnes A I, Polzik E S 2007 Opt. Express 15 7940 Google Scholar
[38]	Zavatta A, Parigi V, Bellini M 2007 Phys. Rev. A 75 052106 Google Scholar
[39]	Ourjoumtsev A, Tualle-Brouri R, Laurat J, Grangier P J S 2006 Science 312 83 Google Scholar
[40]	Yao W, Wang Q, Tian L, Li R, Shi S, Wang J, Wang Y, Zheng Y 2020 Laser Phys. Lett. 18 015001 Google Scholar
[41]	Yang W, Wang Y, Zheng Y, Lu H 2015 Opt. Express 23 19624 Google Scholar
[42]	Wang J R, Wang Q W, Tian L, Su J, Zheng Y H 2020 Chin. Phys. B 29 034205 Google Scholar
[43]	Wang J R, Zhang H Y, Zhao Z L, Zheng Y H 2020 Chin. Phys. B 29 124207 Google Scholar
[44]	Li Z, Tian Y, Wang Y, Ma W, Zheng Y 2019 Opt. Express 27 7064 Google 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 25 456 Google 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. 25 456 Google Scholar
[46]	Schneider K, Bruckmeier R, Hansen H, Schiller S, Mlynek J 1996 Opt. Lett. 21 1396 Google Scholar
[47]	Morgan P H 2011 Ph. D. Dissertation (Canberra: Australian National University)

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