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Comparative study of squeezed vacuum states prepared by using 1064-nm solid-state and fiber-laser as pump source

Yang Wen-Hai Diao Wen-Ting Cai Chun-Xiao Song Xue-Rui Feng Fu-Pan Zheng Yao-Hui Duan Chong-Di

Comparative study of squeezed vacuum states prepared by using 1064-nm solid-state and fiber-laser as pump source

Yang Wen-Hai, Diao Wen-Ting, Cai Chun-Xiao, Song Xue-Rui, Feng Fu-Pan, Zheng Yao-Hui, Duan Chong-Di
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  • Squeezed states, which have fewer fluctuations in one quadrature than vacuum noise at the expense of increasing fluctuations in the other quadrature, can be used to enhance measurement accuracy, increase detection sensitivity, and improve fault tolerance performance for quantum information and quantum computation. In this paper, the influences of relative intensity noise (RIN) of all-solid-state single-frequency laser and single-frequency fiber laser on the squeezing factor of squeezed vacuum states are experimentally and theoretically studied. Here, an all-solid-state single-frequency laser and a single-frequency fiber laser each are used as a light source of the system generating squeezed vacuum states. The homodyne detection is used to compare the RIN of all-solid-state single-frequency laser and that of single-frequency fiber laser at the analysis frequency of 1 MHz. The results show that the RIN of the all-solid-state single-frequency laser and single-frequency fiber laser are higher than those of the shot noise limitation 2.3 dB and 30 dB at the analysis frequency of 1 MHz, respectively. The RIN of all-solid-state single-frequency laser is far less than that of the single-frequency fiber laser. As a result, squeezed vacuum state with maximum quantum noise reduction of (13.2 ± 0.2) dB and (10 ± 0.2) dB are directly detected. Theoretical calculation shows that the influence of the RIN on the measurement accuracy is the major factor of degrading the squeezing factor with the fiber laser as the pump source. The measurement error of squeezed vacuum state caused by the RIN of single-frequency fiber laser is about 2.6 dB. The discrepancy of the pump power between the two lasers is another factor of affecting the squeezing factor, corresponding to 0.6 dB quantum noise difference. The theoretical calculations are consistent with the experimental results, which provides some guidance for developing the practical squeezed states with highly squeezing level.
      Corresponding author: Zheng Yao-Hui, yhzheng@sxu.edu.cn
    [1]

    Yin J, Cao Y, Li Y H 2017 Science 356 1140

    [2]

    霍美如, 秦际良, 孙颍榕, 成家霖, 闫智辉, 贾晓军 2018 量子光学学报 24 134

    Huo M R, Qin J L, Sun Y R, Cheng J L, Yan Z H, Jia X J 2018 Acta Sin. Quantum Opt. 24 134

    [3]

    Bai S, Wang J Y, Qiang J, Zhang L, Wang J J 2014 Opt. Express 22 26462

    [4]

    张逸伦, 蓝天, 高明光, 赵涛, 沈振民 2015 物理学报 64 164201

    Zhang Y L, Lan T, Gao M G, Zhao T, Shen Z M 2015 Acta Phys. Sin. 64 164201

    [5]

    Liu J J, Chang Q, Bao M M, Yuan B, Yang K, Ma Y Q 2018 Chin. Phys. B 26 098102

    [6]

    姜海峰 2018 物理学报 67 160602

    Jiang H F 2018 Acta Phys. Sin. 67 160602

    [7]

    彭世杰, 刘颖, 马文超, 石发展, 杜江峰 2018 物理学报 67 167601

    Peng S J, Liu Y, Ma W C, Shi F Z, Du J F 2018 Acta Phys. Sin. 67 167601

    [8]

    Lu H D, Su J, Zheng Y H, Peng K C 2014 Opt. Lett. 39 1117

    [9]

    杨文海, 王雅君, 李志秀, 郑耀辉 2014 中国激光 41 0502002

    Yang W H, Wang Y J, Li Z X, Zheng Y H 2014 Chin. J. Laser 41 0502002

    [10]

    严雄伟, 王振国, 蒋新颖, 郑建刚, 李敏, 荆玉峰 2018 物理学报 67 184201

    Yan X W, Wang Z G, Jiang X Y, Zheng J G, Li M, Jing Y F 2018 Acta Phys. Sin. 67 184201

    [11]

    Xu S H, Yang Z M, Zhang W N, Wei X M, Qian Q, Chen D D, Zhang Q Y, Shen S X, Peng M Y, Qiu J R 2011 Opt. Lett. 36 3708

    [12]

    冯晋霞, 杜京师, 靳小丽, 李渊冀, 张宽收 2018 物理学报 67 174203

    Feng J X, Du J S, Jin X L, Li Y J, Zhang K S 2018 Acta Phys. Sin. 67 174203

    [13]

    Wang Y J, Yang W H, Zheng Y H, Peng K C 2015 Chin. Phys. B 24 070303

    [14]

    马亚云, 冯晋霞, 万振菊, 高英豪, 张宽收 2017 物理学报 66 244205

    Ma Y Y, Feng J X, Wan Z J, Gao Y H, Zhang K S 2017 Acta Phys. Sin. 66 244205

    [15]

    Chen C Y, Li Z X, Jin X L, Zheng Y H 2016 Rev. Sci. Instrum. 87 103114

    [16]

    Li Z X, Ma W G, Yang W H, Wang Y J, Zheng Y H, Peng K C 2016 Opt. Lett. 41 3331

    [17]

    Yang W H, Shi S P, Wang Y J, Ma W G, Zheng Y H, Peng K C 2017 Opt. Lett. 42 4553

    [18]

    Gardiner C W, Collett M J 1985 Phys. Rev. A 30 3761

    [19]

    Yang W H, Jin X L, Yu X D, Zheng Y H, Peng K C 2017 Opt. Express 25 24262

    [20]

    Jin X L, Su J, Zheng Y H, Chen C Y, Wang W Z, Peng K C 2015 Opt. Express 23 23859

  • 图 1  本底光RIN测量装置和压缩态光场产生实验系统(SHG, 倍频; EOM, 电光调制器; PZT, 锆钛酸铅压电陶瓷; BHD, 平衡零拍探测器; DBS, 分束镜; OPA, 光参量放大器; LO beam, 本底光; SA, 频谱仪)

    Figure 1.  Schematic of the experimental setup for measuring the local oscillator intensity noise and generating the squeezed state (SHG, second-harmonic generation; EOM, electro-optic modulator; PZT, piezoelectric ceramic transducer; BHD, balanced homodyne detector; DBS, dichroic beam splitter; OPA, optical parametric amplifier; LO, local oscillator; SA, spectrum analyzer).

    图 2  单频光纤激光器经MC滤除一部分RIN和相位噪声后对应的本底光RIN

    Figure 2.  RIN of local oscillator with single-frequency Yb3+-doped phosphate fiber laser after MC.

    图 3  单频固体激光器经MC滤除一部分RIN和相位噪声后对应的本底光RIN

    Figure 3.  RIN of local oscillator with single-frequency Nd:YVO4 laser after MC.

    图 4  单频固体激光器制备的压缩真空态光场的噪声谱, 分析频率1 MHz (分辨带宽RBW = 300 kHz, 视频带宽VBW = 200 Hz)

    Figure 4.  Balance homodyne measurements of the quadrature noise variances at a Fourier frequency of 1 MHz, with a resolution bandwidth RBW of 300 kHz and a video bandwidth VBW of 200 Hz.

    图 5  单频光纤激光器制备的真空压缩态光场的噪声谱, 分析频率1 MHz (RBW = 300 kHz, VBW = 200 Hz)

    Figure 5.  Balance homodyne measurements of the quadrature noise variances at a Fourier frequency of 1 MHz, with a RBW of 300 kHz and a NBW of 200 Hz.

  • [1]

    Yin J, Cao Y, Li Y H 2017 Science 356 1140

    [2]

    霍美如, 秦际良, 孙颍榕, 成家霖, 闫智辉, 贾晓军 2018 量子光学学报 24 134

    Huo M R, Qin J L, Sun Y R, Cheng J L, Yan Z H, Jia X J 2018 Acta Sin. Quantum Opt. 24 134

    [3]

    Bai S, Wang J Y, Qiang J, Zhang L, Wang J J 2014 Opt. Express 22 26462

    [4]

    张逸伦, 蓝天, 高明光, 赵涛, 沈振民 2015 物理学报 64 164201

    Zhang Y L, Lan T, Gao M G, Zhao T, Shen Z M 2015 Acta Phys. Sin. 64 164201

    [5]

    Liu J J, Chang Q, Bao M M, Yuan B, Yang K, Ma Y Q 2018 Chin. Phys. B 26 098102

    [6]

    姜海峰 2018 物理学报 67 160602

    Jiang H F 2018 Acta Phys. Sin. 67 160602

    [7]

    彭世杰, 刘颖, 马文超, 石发展, 杜江峰 2018 物理学报 67 167601

    Peng S J, Liu Y, Ma W C, Shi F Z, Du J F 2018 Acta Phys. Sin. 67 167601

    [8]

    Lu H D, Su J, Zheng Y H, Peng K C 2014 Opt. Lett. 39 1117

    [9]

    杨文海, 王雅君, 李志秀, 郑耀辉 2014 中国激光 41 0502002

    Yang W H, Wang Y J, Li Z X, Zheng Y H 2014 Chin. J. Laser 41 0502002

    [10]

    严雄伟, 王振国, 蒋新颖, 郑建刚, 李敏, 荆玉峰 2018 物理学报 67 184201

    Yan X W, Wang Z G, Jiang X Y, Zheng J G, Li M, Jing Y F 2018 Acta Phys. Sin. 67 184201

    [11]

    Xu S H, Yang Z M, Zhang W N, Wei X M, Qian Q, Chen D D, Zhang Q Y, Shen S X, Peng M Y, Qiu J R 2011 Opt. Lett. 36 3708

    [12]

    冯晋霞, 杜京师, 靳小丽, 李渊冀, 张宽收 2018 物理学报 67 174203

    Feng J X, Du J S, Jin X L, Li Y J, Zhang K S 2018 Acta Phys. Sin. 67 174203

    [13]

    Wang Y J, Yang W H, Zheng Y H, Peng K C 2015 Chin. Phys. B 24 070303

    [14]

    马亚云, 冯晋霞, 万振菊, 高英豪, 张宽收 2017 物理学报 66 244205

    Ma Y Y, Feng J X, Wan Z J, Gao Y H, Zhang K S 2017 Acta Phys. Sin. 66 244205

    [15]

    Chen C Y, Li Z X, Jin X L, Zheng Y H 2016 Rev. Sci. Instrum. 87 103114

    [16]

    Li Z X, Ma W G, Yang W H, Wang Y J, Zheng Y H, Peng K C 2016 Opt. Lett. 41 3331

    [17]

    Yang W H, Shi S P, Wang Y J, Ma W G, Zheng Y H, Peng K C 2017 Opt. Lett. 42 4553

    [18]

    Gardiner C W, Collett M J 1985 Phys. Rev. A 30 3761

    [19]

    Yang W H, Jin X L, Yu X D, Zheng Y H, Peng K C 2017 Opt. Express 25 24262

    [20]

    Jin X L, Su J, Zheng Y H, Chen C Y, Wang W Z, Peng K C 2015 Opt. Express 23 23859

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  • Received Date:  29 December 2018
  • Accepted Date:  18 April 2019
  • Available Online:  16 August 2019
  • Published Online:  01 June 2019

Comparative study of squeezed vacuum states prepared by using 1064-nm solid-state and fiber-laser as pump source

    Corresponding author: Zheng Yao-Hui, yhzheng@sxu.edu.cn
  • 1. China Academy of Space Technology (Xi’an), Xi’an 710100, China
  • 2. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
  • 3. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Abstract: Squeezed states, which have fewer fluctuations in one quadrature than vacuum noise at the expense of increasing fluctuations in the other quadrature, can be used to enhance measurement accuracy, increase detection sensitivity, and improve fault tolerance performance for quantum information and quantum computation. In this paper, the influences of relative intensity noise (RIN) of all-solid-state single-frequency laser and single-frequency fiber laser on the squeezing factor of squeezed vacuum states are experimentally and theoretically studied. Here, an all-solid-state single-frequency laser and a single-frequency fiber laser each are used as a light source of the system generating squeezed vacuum states. The homodyne detection is used to compare the RIN of all-solid-state single-frequency laser and that of single-frequency fiber laser at the analysis frequency of 1 MHz. The results show that the RIN of the all-solid-state single-frequency laser and single-frequency fiber laser are higher than those of the shot noise limitation 2.3 dB and 30 dB at the analysis frequency of 1 MHz, respectively. The RIN of all-solid-state single-frequency laser is far less than that of the single-frequency fiber laser. As a result, squeezed vacuum state with maximum quantum noise reduction of (13.2 ± 0.2) dB and (10 ± 0.2) dB are directly detected. Theoretical calculation shows that the influence of the RIN on the measurement accuracy is the major factor of degrading the squeezing factor with the fiber laser as the pump source. The measurement error of squeezed vacuum state caused by the RIN of single-frequency fiber laser is about 2.6 dB. The discrepancy of the pump power between the two lasers is another factor of affecting the squeezing factor, corresponding to 0.6 dB quantum noise difference. The theoretical calculations are consistent with the experimental results, which provides some guidance for developing the practical squeezed states with highly squeezing level.

    • 量子精密测量是继激光精密测量之后兴起的一项颠覆性技术, 传统的激光精密测量技术利用激光的相干性实现目标相位信息的高精度采集, 实现对目标信息的高精度重构; 该技术具有非接触性和高灵敏度的特性, 已经在科学研究、生物医学、工业生产、空间技术和国防技术中得到了广泛应用[17]. 随着科技的进步和发展, 基于相干态光场的经典测量已不能满足人们对测量精度的要求. 为了突破散粒噪声基准(shot noise limit, SNL)进一步提升测量精度, 量子技术成为人们研究的焦点. 而压缩态光场作为一种潜在应用十分广泛的非经典光场, 可用于量子信息、量子成像和精密测量等诸多领域, 所以性能优良的压缩态光场是提升量子态保真度和测量灵敏度的必要条件. 而制备性能优良的压缩态光场的一个基本前提就是需要一款性能优良的激光光源.

      近年随着技术和工艺不断进步, 半导体激光二极管(laser diode, LD)抽运的全固态激光系统体积更小、功率更高, 可长期稳定运转且相对强度噪声(relative intensity noise, RIN)可在1.5 MHz之后达到SNL[810]. 这期间LD抽运的单频光纤激光器同样也发展的更加成熟和稳定[11]. 激光光源的不断完善解决了基于激光器的各种光学系统的实用化问题, 如激光雷达、激光通信以及用于探测引力波的激光干涉仪等. 随着量子技术的发展, 激光器作为制备非经典光场的光源, 成为制备高品质非经典光场的关键, 其强度噪声特性与非经典光场的噪声水平直接相关[1214]. 如在压缩真空态光场的测量中, 激光器的RIN会通过本底光耦合到平衡零拍探测过程进而影响测量精度.

      本文从全固态单频固体激光器和单频光纤激光器的强度噪声特性出发, 对比研究了这两种单频激光器作为非经典光场实验产生系统的光源, 在制备得到压缩真空态光场后使用平衡零拍探测系统测量压缩真空态光场噪声水平时, 本底光的RIN对压缩度测量精度的影响, 进而为研制高压缩度压缩真空态光源和优化平衡零拍探测系统的性能提供了新的思路.

    2.   实验分析
    • 图1所示为制备压缩态光场的实验系统. 本实验系统的光源部分由一台1064 nm单频激光器构成. 分别采用山西大学研制的单频Nd:YVO4固体激光器和华南理工大学研制的掺Yb磷酸盐单频光纤激光器作为光源进行对比研究[4]. 本实验系统采用外腔倍频的方式获得532 nm激光, 用于抽运光学参量振荡器产生压缩真空态光场. 故该实验系统的核心部分为倍频腔和光学参量振荡腔. 然后是实验系统的探测部分由测量压缩真空态光场压缩度的平衡零拍探测装置和测量本底光RIN的自零拍探测装置组成, 用于探测压缩真空态光场的噪声水平和本底光的RIN. 此外还在实验系统各部分光路中插入了多个模式清洁器(mode clear, MC), 用于优化系统各处光束的空间模式分布和滤除激光携带的经典技术噪声. MC的详细参数如下: 腔长为430 mm, 两个平面镜45°入射透射率均为1%@1064 nm/532 nm, 凹面镜0°入射反射率为99.95%@1064 nm/532 nm, 曲率半径为1000 mm. 为了保证实验系统的稳定运转, 改进了光学谐振腔和移相器的机械结构以及电光相位调制器和探测器的电学性能[15, 16], 而且还根据锁定环路的传递函数针对性地优化了边带锁频环路的各项参数, 保证了谐振腔腔长和光场相对相位的稳定, 为获得高压缩度的压缩态光场奠定了基础.

      Figure 1.  Schematic of the experimental setup for measuring the local oscillator intensity noise and generating the squeezed state (SHG, second-harmonic generation; EOM, electro-optic modulator; PZT, piezoelectric ceramic transducer; BHD, balanced homodyne detector; DBS, dichroic beam splitter; OPA, optical parametric amplifier; LO, local oscillator; SA, spectrum analyzer).

      为了分析激光器的RIN对实验测量压缩真空态光场压缩度的影响, 需要测量单频固体激光器和单频光纤激光器作为实验系统光源时本底光的RIN(测量光功率1 mW), 图2图3所示为对本底光RIN的测量结果. 图2为采用光纤激光器为实验系统光源时, 对应的本底光的RIN在分析频率1 MHz处高出SNL约30 dB, 此处恰好对应单频光纤激光器的弛豫振荡峰. 图3为采用单频固体激光器为实验系统光源时, 对应的本底光的RIN在分析频率1 MHz处高出SNL约2.3 dB. 以上测量所用仪器为罗德斯瓦茨FSW公司的Signal & Spectrum Analyzer·2 Hz to 13 GHz频谱仪. 对比以上两种本底光的RIN数据, 发现单频固体激光器输出的激光经MC滤除一部分噪声后本底光的RIN在分析频率1 MHz处远低于单频光纤激光器输出的激光经MC滤除噪声后本底光的RIN.

      Figure 2.  RIN of local oscillator with single-frequency Yb3+-doped phosphate fiber laser after MC.

      Figure 3.  RIN of local oscillator with single-frequency Nd:YVO4 laser after MC.

      图4是采用山西大学研制的单频Nd:YVO4固体激光器作为实验系统的光源时, 直接测量到的压缩真空态光场的最大压缩度, 图5是采用华南理工大学研制的掺Yb磷酸盐单频光纤激光器作为实验系统的光源时, 直接测量到的压缩真空态光场的最大压缩度.

      Figure 4.  Balance homodyne measurements of the quadrature noise variances at a Fourier frequency of 1 MHz, with a resolution bandwidth RBW of 300 kHz and a video bandwidth VBW of 200 Hz.

      Figure 5.  Balance homodyne measurements of the quadrature noise variances at a Fourier frequency of 1 MHz, with a RBW of 300 kHz and a NBW of 200 Hz.

      采用山西大学研制的单频Nd:YVO4固体激光器作为实验系统的光源, 在抽运功率为180 mW时(实测参量振荡器的阈值为200 mW), 直接探测到的压缩真空态光场的压缩度最大为(13.2 ± 0.2) dB, 反压缩为(24.7 ± 0.2) dB; 采用华南理工大学研制的掺Yb磷酸盐单频光纤激光器作为实验系统的光源, 在抽运功率为140 mW时(实测参量振荡器的阈值为200 mW), 直接探测到的压缩真空态光场的压缩度最大为(10 ± 0.2) dB, 反压缩为(19 ± 0.2) dB. 以上测量所用仪器为罗德斯瓦茨公司的Signal & Spectrum Analyzer·2 Hz to 13 GHz频谱仪. 由于单频光纤激光器的相位噪声较大, 继续增加抽运光功率会使相位噪声耦合到压缩分量中从而导致压缩度降低, 所以两种激光器作为系统光源时在不同的抽运光功率时压缩度达到最大值, 使得所测反压缩度相差5.7 dB. 此外图5中反压缩曲线顶端比较平缓即为相位噪声大所致. 根据参考文献[17]参量振荡器产生压缩真空态的理论公式和参量振荡器参数可知, 在抽运光功率为140 mW时, 理论上可直接探测到的压缩度为(12.6 ± 0.2) dB, 实际却只探测到了(10 ± 0.2) dB. 推测产生以上实验结果的原因是单频固体激光器和单频光纤激光器的RIN值相差悬殊, 致使平衡零拍探测系统在测量压缩真空态光场的噪声水平时产生了较大的测量误差. 下面对以上实验结果进行理论分析和验证.

    3.   理论分析
    • 在以LD作为抽运源的全固态单频激光器系统中, 抽运光的强度噪声、激光上能级自发辐射噪声、偶极起伏噪声、腔内损耗和输出耦合镜等均会将经典技术噪声和真空起伏噪声引入激光器中, 导致激光器输出的激光的RIN在低频段远大于SNL, 一般在几兆赫兹处才能达到SNL. 20世纪80年代发展的传递函数理论, 通过解量子朗之万方程求出了各种噪声源对激光器RIN的影响[18]. 此外, 抽运功率不稳定、环境温度变化和机械振动均会引起输出激光功率的随机波动产生强度噪声. 由于固体激光器和光纤激光器的谐振腔结构以及增益介质工作机制不同, 导致其RIN会有较大差异.

      图2图3证实了本文实验使用的单频光纤激光器的RIN远大于单频固体激光器的RIN. 根据参考文献[12]可知, 影响平衡零拍探测系统测量误差的两个主要因素是激光的RIN和平衡零拍探测器的共模抑制比(common mode rejection ratio, CMRR). 由于本实验采用成型的商用平衡零拍探测器, 其CMRR已经确定, 所以本文主要研究激光器的RIN对平衡零拍探测系统测量精度的影响.

      在平衡零拍探测系统测量压缩真空态光场的压缩度时, 本底光的RIN引入的测量误差可以由下式表示[19]:

      式中$V\left({{{\hat X}_{\rm{a}}}\left(\theta \right)} \right)$为压缩真空态光场的噪声方差; $V\left({{{\hat X}_{\rm{b}}}} \right)$为本底光RIN方差; $G$与平衡零拍探测器的CMRR的关系如下式[19]:

      当本底光的RIN高于SNL时, 压缩度的测量值与实际值之间就会产生偏差. 这个偏差值$E$的大小由平衡零拍探测器的CMRR和本底光的RIN共同决定.

      本文探测压缩真空态光场使用的是山西大学光电研究所研制的带有差分微调电路和可调偏压的高共模抑制比平衡零拍探测器, 其共模抑制比在分析频率1 MHz附近最高可达75.2 dB[20], 本实验所用的平衡零拍探测器为同款商用产品, 电子元件和电路参数没有经过严格筛选和反复优化, 其CMRR约为37.5 dB. 根据上述数据可以计算出采用华南理工大学研制的掺Yb磷酸盐单频光纤激光器作为实验系统的光源时, 直接探测到的压缩真空态光场的压缩度的测量误差约2.6 dB, 采用山西大学研制的单频Nd:YVO4固体激光器作为实验系统的光源时, 直接探测到的压缩真空态光场的压缩度的测量误差约0.006 dB. 从计算结果可知, 本底光的RIN较大时对平衡零拍探测系统的测量精度影响很大.

    4.   结 论
    • 单频固体激光器的RIN在分析频率1 MHz之后均低于单频光纤激光器, 且从1.5 MHz之后就下降到了SNL, 这是由于山西大学研制的单频Nd:YVO4固体激光器的光学谐振腔的机械结构是由一整块高强度的航空铝在数控机床上一次加工而成, 然后经过热处理技术进行时效硬化并释放机械应力, 使得单频固体激光器的光学谐振腔的机械稳定性明显优于单频光纤激光器由光纤和光栅构成的光学谐振腔的机械稳定性. 这就使得环境温度变化和周围各种振动噪声对单频固体激光器光学谐振腔的影响远小于对单频光纤激光器光学谐振腔的影响; 此外单频固体激光器谐振腔内只有激光晶体和光学单向器引入的光学损耗, 而单频光纤激光器谐振腔内的增益光纤和光栅以及后续的放大过程均会引入光学损耗, 导致在1 MHz附近的中频段具有较强的弛豫振荡峰, 所以单频固体激光器的RIN明显低于单频光纤激光器.

      实验测得单频光纤激光器和单频固体激光器的RIN在分析频率1 MHz处分别高于SNL约30 dB和2.3 dB, 导致两种激光器作为实验系统的光源时, 探测到的压缩真空态光场的最大压缩度分别为(13.2 ± 0.2) dB和(10 ± 0.2) dB. 此外由于单频光纤激光器的相位噪声较大在制备压缩真空态光场时所用抽运光功率比单频固体激光器低了40 mW, 因此产生的压缩度也会低0.6 dB. 根据上述理论计算结果可知单频光纤激光器的RIN导致的压缩度测量误差约2.6 dB; 单频固体激光器的RIN导致的压缩度测量误差约0.006 dB可忽略不计. 综上所述, 实验结果与理论计算结果基本吻合, 证实了单频光纤激光器较大的RIN是影响本实验平衡零拍探测系统测量精度的主要因素. 所以降低单频光纤激光器的RIN是其应用于非经典光场制备之前要解决的关键问题之一.

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