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Generation of bright polarization squeezed light at cesium D2 line based on optical parameter amplifier

Zuo Guan-Hua Yang Chen Zhao Jun-Xiang Tian Zhuang-Zhuang Zhu Shi-Yao Zhang Yu-Chi Zhang Tian-Cai

Generation of bright polarization squeezed light at cesium D2 line based on optical parameter amplifier

Zuo Guan-Hua, Yang Chen, Zhao Jun-Xiang, Tian Zhuang-Zhuang, Zhu Shi-Yao, Zhang Yu-Chi, Zhang Tian-Cai
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  • Quantum light field is very important source in quantum optics and quantum precision measurement, and the generation of quantum state of light is significant in quantum storage, quantum metrology and studying the interaction between nonclassical light and matter. The polarization squeezed light near the atomic transition has great potential applications in the precise measurement of magnetic field as its Stokes parameter’s noise is less than the standard quantum limit (SQL). Therefore, it is very important to generate the polarization squeezed light at atomic transition. We report in this paper the experiment on generating the bright polarization squeezed light at cesium D2 line based on an optical parametric amplifier (OPA). The experimental system includes the following three parts: 1) a second harmonic generator (SHG), 2) an OPA, and 3) a detection system. The OPA has a similar structure to the SHG system with four-mirror ring cavity in which only the fundamental wave is resonant. A nonlinear type-I periodically-poled KTiOPO4 (PPKTP) crystal with a size of 1 mm × 2 mm × 20 mm is placed in the center of the cavity waist and its temperature is precisely controlled. The OPA is pumped by the 426 nm blue light which is generated by SHG and this OPA is operating below the threshold. The squeezed light at cesium D2 line is produced when the crystal temperature is at its optimum phase-matching temperature and the OPA cavity is stabilized based on resonance. The generated squeezed light is combined with the coherent light on a polarizing beam splitter (PBS) to obtain the polarized squeezed light for either ${\hat S_2} $ or ${\hat S_3} $ of the Stokes parameter by controlling the type of squeezed light (parametric amplification or de-amplification) and the relative phase (0 or π/2) of two beams. And for ${\hat S_1} $, the amplitude-squeezed light (corresponding to parametric de-amplification) is the ${\hat S_1} $ squeezed light. The maximum squeezing of 4.3 dB (actually 5.2 dB) is observed in a bandwidth range of 2-10 MHz. At present, the squeezing is mainly limited by the escape efficiency of OPA and the detection efficiency, and the OPA escape efficiency is mainly limited by the blue-light-induced loss of PPKTP crystal and the thermal effect of crystal. In the optical atomic magnetometer, increasing the signal-to-noise ratio (SNR) of the system can effectively improve the sensitivity of the magnetic field measurement. This bright polarization squeezed light is expected to be used in the optical cesium atomic magnetometer to improve the sensitivity of the magnetometer.
      Corresponding author: Zhang Yu-Chi, yczhang@sxu.edu.cn ; Zhang Tian-Cai, tczhang@sxu.edu.cn
    [1]

    Appel J, Figueroa E, Korystov D, Lobino M, Lvovsky A I 2008 Phys. Rev. Lett. 100 093602

    [2]

    Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nat. Phys. 4 472

    [3]

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

    [4]

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

    [5]

    Seshadreesan K P, Anisimov P M, Lee H, Dowling J P 2011 New J. Phys. 13 083026

    [6]

    Hou L L, Sui Y X, Wang S, Xu X F 2019 Chin. Phys. B 28 044203

    [7]

    Kr4420 1990 Phys. Rev. A 42 4177

    [8]

    Gao J R, Cui F Y, Xue C Y, Xie C D, Peng K C 1998 Opt. Lett. 23 870

    [9]

    Hong C K, Mandel L 1985 Phys. Rev. A 32 974

    [10]

    Bowen W P, Schnabel R, Bachor H A, Lam P K 2002 Phys. Rev. Lett. 88 093601

    [11]

    Zhang T C, Hou Z J, Wang J M, Xie C D, Peng K C 1996 Chin. Phys. Lett. 13 734

    [12]

    Andersen U L, Gehring T, Marquardt C, Leuchs G 2016 Phys. Scr. 91 053001

    [13]

    Wolfgramm F, Cerè A, Beduini F A, Predojević A, Koschorreck M, Mitchell M W 2010 Phys. Rev. Lett. 105 053601

    [14]

    Grangier P, Slusher R E, Yurke B, LaPorta A 1987 Phys. Rev. Lett. 59 2153

    [15]

    Chirkin A S, Orlov A A, Parashchuk D Y 1993 Quantum Electron. 23 870

    [16]

    Hald J, Sørensen J L, Schori C, Polzik E S 1999 Phys. Rev. Lett. 83 1319

    [17]

    Wu L, Yan Z H, Liu Y H, Deng R J, Jia X J, Xie C D, Peng K C 2016 Appl. Phys. Lett. 108 161102

    [18]

    Yan Z H, Wu L, Jia X J, Liu Y H, Deng R J, Li S J, Wang H, Xie C D, Peng K C 2017 Nat. Commun. 8 718

    [19]

    Wen X, Han Y S, Liu J Y, He J, Wang J M 2017 Opt. Express 25 020737

    [20]

    Heersink J, Gaber T, Lorenz S, Glöckl O, Korolkova N, Leuchs G 2003 Phys. Rev. A 68 013815

    [21]

    Barreiro S, Valente P, Failache H, Lezama A 2011 Phys. Rev. A 84 033851

    [22]

    Bowen W P, Treps N, Buchler B C et al. 2003 Phys. Rev. A 67 032302

    [23]

    Agha I H, Messin G, Grangier P 2010 Opt. Express 18 4198

    [24]

    Matsko A B, Novikova I, Welch G R, Budker D, Kimball D F, Rochester S M 2002 Phys. Rev. A 66 043815

    [25]

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

    [26]

    Korolkova N, Leuchs G, Loudon R, Ralph T C, Silberhorn C 2002 Phys. Rev. A 65 052306

    [27]

    Schnabel R, Bowen W P, Treps N, Ralph T C, Bachor H-A, Lam P K 2003 Phys. Rev. A 67 012316

    [28]

    田剑锋 2018 博士学位论文(太原: 山西大学)

    Tian J F 2018 Ph. D. Dissertation (Taiyuan: Shanxi University) (in Chinese)

    [29]

    Tian J F, Zuo G H, Zhang Y C, Li G, Zhang P F, Zhang T C 2017 Chin. Phys. B 26 124206

    [30]

    Tian J F, Yang C, Xue J, Zhang Y C, Li G, Zhang T C 2016 J. Opt. 18 055506

    [31]

    Boyd G D, Kleinman D A 1968 J. Appl. Phys. 39 3597

    [32]

    Black E D 2001 Am. J. Phys. 69 79

    [33]

    Zhang T C, Goh K W, Chou C W, Lodahl P, Kimble H J 2003 Phys. Rev. A 67 033802

    [34]

    Hansson G, Karlsson H, Wang S, Laurell F 2000 Appl. Opt. 39 5058

  • 图 1  量子化的庞加莱球和斯托克斯参量图示

    Figure 1.  Diagrammatic illustration of the quantum Poincaré sphere and Stokes parameters.

    图 2  四个斯托克斯参量的测量装置. PBS, 偏振分束棱镜; $\lambda /2$$\lambda /4$分别是半波片和四分之波片; 加号和减号分别代表电流信号相加减; SA, 频谱分析仪

    Figure 2.  Apparatus required to measure four Stokes parameters. PBS, polarizing beam splitter; $\lambda /2$ and $\lambda /4$, half-and quarter-wave plates, respectively; the plus and minus signs imply that an electrical sum or difference has been taken; SA, Spectrum analyzer.

    图 3  明亮偏振压缩光合成装置

    Figure 3.  Apparatus used to produce the bright polarizationsqueezed beam.

    图 4  实验装置图

    Figure 4.  Schematic of experimental setup.

    图 5  参量增益随泵浦光功率的变化, 其中绿(红)色实点是参量放大(缩小)的实验结果. 实线是理论拟合结果

    Figure 5.  Parametric gain versus pump power, where green (red) solid dots denote the experimental results of amplified (deamplified) gain. The solid lines represent the theoretical results.

    图 6  扫描本地光相位时得到的噪声. 谱仪中心频率为2 MHz, 分辨率带宽(RBW)为100 kHz, 视频带宽(VBW)为500 Hz

    Figure 6.  Noise power when scanning the local beam phase. The spectrum analyzer’s center frequency is 2 MHz with RBW = 100 kHz and VBW = 500 Hz.

    图 7  不同斯托克斯参量的噪声测量结果. 其中左图是测量的斯托克斯参量的噪声谱, 已归一化到标准量子噪声基准. 右图是与之对应的噪声分布球及投影噪声分布, 其中蓝色椭球体代表噪声球, 椭圆表示噪声球投影到各个面上的噪声分布. 红色虚线表示相干光对应的噪声, 蓝色实线表示偏振压缩光 (a) ${\hat S_2}$压缩; (b) ${\hat S_3}$压缩; (c) ${\hat S_1}$压缩

    Figure 7.  Measured noise results for different Stokes parameters. The results on the left are the measured variance spectra of Stokes parameters normalized to quantum noise limit. The results on the right are the corresponding diagrammatic illustration of the Stokes parameters’ variance ellipsoid, and the blue ellipsoid is the noise ball, and these ellipses are the noise projections at each plane. The red dashed circles represent the noise of the coherent state and the blue solid circles show the squeezing. (a) Squeezing for Stokes parameter ${\hat S_2}$; (b) Squeezing for Stokes parameter ${\hat S_3}$; (c) Squeezing for Stokes parameter ${\hat S_1}$.

    表 1  影响OPA产生压缩和探测过程的实验参数

    Table 1.  Factors of effecting squeezing from the OPA and the detection system.

    参数
    传输效率0.99
    量子效率0.95
    干涉效率0.986
    逃逸率0.73
    归一化泵浦因子0.71
    归一化测量频率0.18
    DownLoad: CSV
  • [1]

    Appel J, Figueroa E, Korystov D, Lobino M, Lvovsky A I 2008 Phys. Rev. Lett. 100 093602

    [2]

    Goda K, Miyakawa O, Mikhailov E E, Saraf S, Adhikari R, McKenzie K, Ward R, Vass S, Weinstein A J, Mavalvala N 2008 Nat. Phys. 4 472

    [3]

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

    [4]

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

    [5]

    Seshadreesan K P, Anisimov P M, Lee H, Dowling J P 2011 New J. Phys. 13 083026

    [6]

    Hou L L, Sui Y X, Wang S, Xu X F 2019 Chin. Phys. B 28 044203

    [7]

    Kr4420 1990 Phys. Rev. A 42 4177

    [8]

    Gao J R, Cui F Y, Xue C Y, Xie C D, Peng K C 1998 Opt. Lett. 23 870

    [9]

    Hong C K, Mandel L 1985 Phys. Rev. A 32 974

    [10]

    Bowen W P, Schnabel R, Bachor H A, Lam P K 2002 Phys. Rev. Lett. 88 093601

    [11]

    Zhang T C, Hou Z J, Wang J M, Xie C D, Peng K C 1996 Chin. Phys. Lett. 13 734

    [12]

    Andersen U L, Gehring T, Marquardt C, Leuchs G 2016 Phys. Scr. 91 053001

    [13]

    Wolfgramm F, Cerè A, Beduini F A, Predojević A, Koschorreck M, Mitchell M W 2010 Phys. Rev. Lett. 105 053601

    [14]

    Grangier P, Slusher R E, Yurke B, LaPorta A 1987 Phys. Rev. Lett. 59 2153

    [15]

    Chirkin A S, Orlov A A, Parashchuk D Y 1993 Quantum Electron. 23 870

    [16]

    Hald J, Sørensen J L, Schori C, Polzik E S 1999 Phys. Rev. Lett. 83 1319

    [17]

    Wu L, Yan Z H, Liu Y H, Deng R J, Jia X J, Xie C D, Peng K C 2016 Appl. Phys. Lett. 108 161102

    [18]

    Yan Z H, Wu L, Jia X J, Liu Y H, Deng R J, Li S J, Wang H, Xie C D, Peng K C 2017 Nat. Commun. 8 718

    [19]

    Wen X, Han Y S, Liu J Y, He J, Wang J M 2017 Opt. Express 25 020737

    [20]

    Heersink J, Gaber T, Lorenz S, Glöckl O, Korolkova N, Leuchs G 2003 Phys. Rev. A 68 013815

    [21]

    Barreiro S, Valente P, Failache H, Lezama A 2011 Phys. Rev. A 84 033851

    [22]

    Bowen W P, Treps N, Buchler B C et al. 2003 Phys. Rev. A 67 032302

    [23]

    Agha I H, Messin G, Grangier P 2010 Opt. Express 18 4198

    [24]

    Matsko A B, Novikova I, Welch G R, Budker D, Kimball D F, Rochester S M 2002 Phys. Rev. A 66 043815

    [25]

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

    [26]

    Korolkova N, Leuchs G, Loudon R, Ralph T C, Silberhorn C 2002 Phys. Rev. A 65 052306

    [27]

    Schnabel R, Bowen W P, Treps N, Ralph T C, Bachor H-A, Lam P K 2003 Phys. Rev. A 67 012316

    [28]

    田剑锋 2018 博士学位论文(太原: 山西大学)

    Tian J F 2018 Ph. D. Dissertation (Taiyuan: Shanxi University) (in Chinese)

    [29]

    Tian J F, Zuo G H, Zhang Y C, Li G, Zhang P F, Zhang T C 2017 Chin. Phys. B 26 124206

    [30]

    Tian J F, Yang C, Xue J, Zhang Y C, Li G, Zhang T C 2016 J. Opt. 18 055506

    [31]

    Boyd G D, Kleinman D A 1968 J. Appl. Phys. 39 3597

    [32]

    Black E D 2001 Am. J. Phys. 69 79

    [33]

    Zhang T C, Goh K W, Chou C W, Lodahl P, Kimble H J 2003 Phys. Rev. A 67 033802

    [34]

    Hansson G, Karlsson H, Wang S, Laurell F 2000 Appl. Opt. 39 5058

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  • Received Date:  02 July 2019
  • Accepted Date:  07 September 2019
  • Available Online:  05 December 2019
  • Published Online:  01 January 2020

Generation of bright polarization squeezed light at cesium D2 line based on optical parameter amplifier

    Corresponding author: Zhang Yu-Chi, yczhang@sxu.edu.cn
    Corresponding author: Zhang Tian-Cai, tczhang@sxu.edu.cn
  • 1. Collaborative Innovation Center of Extreme Optics, State Key Laboratory of Quantum Qptics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
  • 2. College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China
  • 3. Department of Physics, Zhejiang University, Hangzhou 310027, China

Abstract: Quantum light field is very important source in quantum optics and quantum precision measurement, and the generation of quantum state of light is significant in quantum storage, quantum metrology and studying the interaction between nonclassical light and matter. The polarization squeezed light near the atomic transition has great potential applications in the precise measurement of magnetic field as its Stokes parameter’s noise is less than the standard quantum limit (SQL). Therefore, it is very important to generate the polarization squeezed light at atomic transition. We report in this paper the experiment on generating the bright polarization squeezed light at cesium D2 line based on an optical parametric amplifier (OPA). The experimental system includes the following three parts: 1) a second harmonic generator (SHG), 2) an OPA, and 3) a detection system. The OPA has a similar structure to the SHG system with four-mirror ring cavity in which only the fundamental wave is resonant. A nonlinear type-I periodically-poled KTiOPO4 (PPKTP) crystal with a size of 1 mm × 2 mm × 20 mm is placed in the center of the cavity waist and its temperature is precisely controlled. The OPA is pumped by the 426 nm blue light which is generated by SHG and this OPA is operating below the threshold. The squeezed light at cesium D2 line is produced when the crystal temperature is at its optimum phase-matching temperature and the OPA cavity is stabilized based on resonance. The generated squeezed light is combined with the coherent light on a polarizing beam splitter (PBS) to obtain the polarized squeezed light for either ${\hat S_2} $ or ${\hat S_3} $ of the Stokes parameter by controlling the type of squeezed light (parametric amplification or de-amplification) and the relative phase (0 or π/2) of two beams. And for ${\hat S_1} $, the amplitude-squeezed light (corresponding to parametric de-amplification) is the ${\hat S_1} $ squeezed light. The maximum squeezing of 4.3 dB (actually 5.2 dB) is observed in a bandwidth range of 2-10 MHz. At present, the squeezing is mainly limited by the escape efficiency of OPA and the detection efficiency, and the OPA escape efficiency is mainly limited by the blue-light-induced loss of PPKTP crystal and the thermal effect of crystal. In the optical atomic magnetometer, increasing the signal-to-noise ratio (SNR) of the system can effectively improve the sensitivity of the magnetic field measurement. This bright polarization squeezed light is expected to be used in the optical cesium atomic magnetometer to improve the sensitivity of the magnetometer.

    • 量子光源是量子光学和量子精密测量中非常重要的资源, 它在实现量子存储[1]、量子计量[2]和研究非经典光与物质的相互作用[3]等方面具有重要意义. 压缩光场是一种典型的量子光源. 自从1985年Slusher等[4]在实验上产生压缩光以来, 人们对压缩态光场的制备和量子特性作了广泛深入的研究. 高质量压缩光源在精密测量方面已经得到应用, 例如利用压缩光注入到干涉仪中可以实现超越标准量子极限的测量等[5,6]. 随着研究的深入, 不同特性的压缩光被产生出来, 包括粒子数压缩、强度差压缩、高阶模压缩和偏振压缩等[7-11]. 这些不同种类的量子光源具有各自不同的特点和应用[12]. 其中与特定原子线共振的量子光源因其在量子存储和精密测量方面的应用, 一直得到人们的关注.

      原子线附近的偏振压缩光源因其斯托克斯参量噪声低于标准量子噪声基准, 在弱磁以及高精度惯性测量方面具有应用价值[13]. 因此, 产生特定原子线的偏振压缩光源对推进量子光源的实际应用具有重要意义. 1987年, Grangier等[14]在实验上产生了偏振压缩光并将其应用于偏振测量中, 使测量信噪比高于标准量子噪声基准2 dB. 1993年, Chirkin等[15]提出了连续变量偏振压缩光的概念. 1999年, Polzik研究组[16]利用偏振压缩光与铯原子系综相互作用, 在实验上观测到了大量原子组成的原子系综产生的自旋压缩. 2010年, Wolfgramm等[13]利用光学参量振荡器产生的正交压缩光与一束正交偏振的强相干光在一个偏振分束器上耦合, 获得了3.6 dB的对应铷原子吸收线的偏振压缩光, 并将其注入铷原子磁力仪中, 得到了低于标准量子噪声基准3.2 dB的测量灵敏度. 2017年贾晓军研究组[17]利用光学参量放大器(optical parameter amplifier, 简记为OPA)产生的与铷原子D1线共振的偏振压缩态光场制备了三组份偏振纠缠态光场, 并实现了在三个铷原子系综内的量子存储和原子系综间的量子纠缠[18]. 同年, 王军民研究组[19]利用OPA过程产生了频率低至2.6 kHz的与铷原子线D1共振的斯托克斯参量${\hat S_2}$压缩的偏振压缩光. 国际上有多个研究组开展了偏振压缩光的实验研究. 目前实验上制备偏振压缩光主要有三种方法: 第一种是基于光纤的克尔效应[20]; 第二种是基于原子系综的PSR(polarization-self rotation, 简记为PSR)效应[21]; 第三种是利用光学参量过程[22]. 基于原子系综的PSR效应的实验装置简单且产生的偏振压缩光直接与原子线共振, 但是由于原子系综对光场较高的吸收损耗和原子本身带来的自发辐射噪声等原因, 使其获得的压缩度较低, 限制了其在精密测量等领域的应用[23,24]. 而利用参量过程产生的压缩主要受到晶体损耗的影响, 具有很大的潜力[25]. 而且非线性晶体的透光范围很大, 产生的压缩光波长调谐范围很宽, 因此利用参量过程的方案来产生偏振压缩光源有其优势.

      本文报道了在实验上首次采用基于PPKTP (periodically-poled KTiOPO4, 简记为PPKTP)晶体二阶非线性效应的光学参量放大器, 产生了与铯原子D2线共振的明亮偏振压缩光. 在频率范围2—10 MHz, 我们分别观察到了斯托克斯参量${\hat S_1}$${\hat S_2}$${\hat S_3}$的偏振压缩光, 其压缩度最大约为4.3 dB. 该量子光源有望应用到铯原子磁力仪中, 提高磁场测量灵敏度.

    2.   偏振压缩及其产生
    • 光场的偏振态可以用庞加莱球上的斯托克斯参量来描述[26]. 斯托克斯参量${\hat S_0}$代表光场的强度, ${\hat S_1}$, ${\hat S_2}$${\hat S_3}$分别代表光场的水平偏振、45°线偏振和右旋圆偏振. 量子化的庞加莱球和斯托克斯参量如图1所示, 其中斯托克斯参量末端的球代表其在该方向上的量子噪声大小.

      Figure 1.  Diagrammatic illustration of the quantum Poincaré sphere and Stokes parameters.

      量子化的斯托克斯参量可由水平偏振模式H和垂直偏振模式V的产生算符$\hat a_{\rm{H}}^ + $, $\hat a_{\rm{V}}^+$和湮灭算符${\hat a_{\rm{H}}}$, ${\hat a_{\rm{V}}}$来表示[27]:

      其中$\theta $表示两个偏振模式的相位差.

      根据算符的不确定性关系可以得到各斯托克算符的对易关系为

      这4个斯托克斯参量及其噪声可以用图2装置来测量.

      Figure 2.  Apparatus required to measure four Stokes parameters. PBS, polarizing beam splitter; $\lambda /2$ and $\lambda /4$, half-and quarter-wave plates, respectively; the plus and minus signs imply that an electrical sum or difference has been taken; SA, Spectrum analyzer.

      当光场比较强时, 光场的噪声起伏将远小于其相干振幅, 此时可以得到斯托克斯参量的均值为

      其中$\hat n$为光子数算符.

      斯托克斯参量的噪声为

      其中${\alpha _{{\rm{H}}\left( {\rm{V}} \right)}}$$\hat X_{{\rm{H}}\left( {\rm{V}} \right)}^ \pm $分别代表光场水平(垂直)偏振模式的相干振幅和两个正交分量算符.

      由(4)式可知参量${\hat S_0}$${\hat S_1}$的噪声是一样的. 将上述参量的噪声都归一化到相干分量上, 即定义相干光场的斯托克斯参量的噪声为标准量子噪声基准或量子噪声极限(quantum noise limit, 简记为QNL). 如果光场的某个斯托克斯参量的噪声小于QNL, 那么该斯托克斯参量是压缩的. 反之, 则为反压缩的. 在实验上我们采用光学参量放大过程产生一束功率很低的垂直偏振的压缩光(即${\alpha _{\rm{H}}} \gg {\alpha _{\rm{V}}}$), 将其与一束功率较高的水平偏振的相干光在偏振分束棱镜上合成, 即可产生偏振压缩光. 通过控制两束光的相对相位($\theta {\rm{ = 0}}$${{\text{π}}}/{{\rm{2}}}$)以及压缩光的压缩类型(振幅压缩或者位相压缩), 可以分别获得斯托克斯参量${\hat S_2}$${\hat S_3}$的偏振压缩. 对于参量${\hat S_1}$, 如果产生的压缩光是振幅压缩, 那么根据上面的分析其参量${\hat S_1}$是压缩的, ${\hat S_2}$, ${\hat S_3}$为标准量子噪声基准. 合成装置如图3所示.

      Figure 3.  Apparatus used to produce the bright polarizationsqueezed beam.

    3.   实验系统及结果
    • 实验上采用光学参量放大过程产生偏振压缩光. 实验装置如图4所示, 系统主要包括以下三个部分: 二次谐波产生器(second harmonic generator, 简记为SHG)[28]、参量放大器(OPA)、偏振压缩合成和探测部分. 实验上所用的激光器是Msquare公司的可调谐钛宝石激光器. 激光器产生的激光频率首先被锁定在铯原子D2线上. 晶体为以色列Raicol公司的Ⅰ类PPKTP晶体, 尺寸为1 mm × 2 mm × 20 mm, 极化周期为4.15 μm, 晶体放置在谐振腔的腰斑中心, 并精确控制温度为最佳相位匹配温度46.6 ± 0.1 ℃[29]. 倍频腔和OPA腔腔型结构相同, 均为四镜环形腔. 为了减少各种机械振动对腔体带来的干扰, 以获得稳定的压缩光输出, 我们将所有腔镜固定在一块低膨胀系数的殷钢体上, 并且使用顶部调节镜架(NEWPORT 9814), 使腔镜之间结构更加紧凑, 而且腔内光路的折叠角减小到3°, 有效地减小了像散, 最后将整个腔体放置在隔热隔振的屏蔽罩中. 腔镜包括两个平镜和两个曲率半径为100 mm的凹面镜, 两凹面镜的距离为118 mm, 总腔长为638 mm. 通过适当选择腰斑大小可以减小晶体热效应, 提高倍频效率[30]. 我们选择了弱聚焦方案, 腰斑为39.4 μm, 比Boyd和Kleinman[31]理论计算的最佳腰斑大1.7倍. 倍频输入镜和OPA腔输出镜透射率均为10.76%. 钛宝石激光器的大部分输出进入倍频腔, 倍频产生大约150 mW的波长在426 nm的蓝光, 倍频效率约为60%. 倍频蓝光用于泵浦OPA, 其匹配效率约为87%, 倍频光单次穿过晶体. OPA腔和倍频腔均采用PDH(pound-drever-hall, 简记为PDH)技术予以锁定[32]. 腔长锁定后的OPA腔产生的压缩光与本地相干光在偏振分束器(PBS)上合成, 产生偏振压缩光. 由于OPA产生的明亮压缩光功率很低, 而且要尽量减小压缩光的传输损耗, 所以实验上得到的压缩光和本地相干光的干涉信号很弱, 这导致相位锁定效果较差. 为了解决这一困难, 我们在本地光光路上加入一个40 kHz左右的相位调制, 通过调制解调技术大幅度提高了相位锁定鉴频信号的信噪比. 最后利用自制的平衡零拍探测器进行噪声测量和分析.

      Figure 4.  Schematic of experimental setup.

      我们在实验上首先研究了OPA腔的参量放大的特性. 将OPA腔腔长锁定, 通过扫描探测光的相位获得参量放大和参量缩小. 通过测量光强的变化来获得增益因子G. 实验结果如图5所示, 其中点为测量数据, 线为根据实验参数拟合的曲线[33].

      Figure 5.  Parametric gain versus pump power, where green (red) solid dots denote the experimental results of amplified (deamplified) gain. The solid lines represent the theoretical results.

      其中P2为泵浦功率, Pth为OPA腔阈值功率. 根据拟合得到OPA腔的阈值功率约为208 mW.

      在分析频率为2 MHz处, 通过扫描本地光相位, 得到了归一化噪声, 结果如图6所示. 此时倍频功率约为105 mW, 增益因子为12, 本地光功率为2 mW, 谱仪参数为RBW = 100 kHz, VBW = 500 Hz, 扫描时间49.5 ms, 数据平均为30次. 我们在该频率处得到最大4.3 dB压缩和10 dB反压缩.

      Figure 6.  Noise power when scanning the local beam phase. The spectrum analyzer’s center frequency is 2 MHz with RBW = 100 kHz and VBW = 500 Hz.

      对于低于阈值的OPA, 其输出光场的起伏为[29]

      其中${V_+}$表示归一化反压缩起伏, ${V_ - }$表示归一化压缩起伏. ${\eta _{\det }} = {\eta _{{\rm{tr}}}} \times {\eta ^2}_{{\rm{vis}}} \times {\eta _{{\rm{qu}}}}$为探测效率, 其中${\eta _{{\rm{tr}}}}$为传输效率, ${\eta _{{\rm{vis}}}}$为平衡零拍干涉效率, ${\eta _{{\rm{qu}}}}$为探测器的量子效率; ${\eta _{{\rm{esc}}}} = T/\left( {T + l} \right)$为OPA腔的逃逸率, 其中T为OPA腔镜输出透射率, l为OPA腔内额外损耗. $x = \sqrt {{P_2}/{P_{{\rm{th}}}}} $为归一化泵浦因子. $\Omega = 2{\text{π}}f/\kappa $为归一化测量频率, 其中f为测量频率; $\kappa = c\left( {T + l} \right)/L$为OPA腔的衰减率, 其中c为光速, L为腔长. 系统的实验参数如表1所列.

      参数
      传输效率0.99
      量子效率0.95
      干涉效率0.986
      逃逸率0.73
      归一化泵浦因子0.71
      归一化测量频率0.18

      Table 1.  Factors of effecting squeezing from the OPA and the detection system.

      根据实验参数, 在2 MHz处理论上应该得到4.5 dB的压缩和12 dB的反压缩. 理论结果与实验得到的结果基本上是吻合的. 通过对影响压缩的因素进行分析, 在目前的实验参数下, 获得4.3 dB的压缩是合理的. 限制压缩的主要因素是探测效率和OPA的逃逸效率. 为了获得更高的压缩度, 需要在后续的实验中在本地光光路中加入模式清洁器提高干涉效率, 同时进一步提高传输效率和采用量子效率更高的探测器. 提高泵浦光的模式匹配效率来降低晶体的热效应, 同时采用更优质的腔镜和晶体降低OPA的内腔损耗, 这样可以提高逃逸率.

      利用两束光的干涉获得它们之间的相位信息并利用反馈系统控制相位为0或${\text{π}}/2$. 当压缩光为振幅压缩, 与本地相干光相位差锁定为0时(或压缩光为位相压缩, 相位锁定为${\text{π}}/2$时)可以得到${\hat S_2}$压缩、${\hat S_3}$反压缩, ${\hat S_1}$为标准量子噪声基准. 相应的实验结果如图7(a)所示. 同理, 当压缩光为位相压缩, 相位差锁定为0时(或压缩光为振幅压缩, 相位差锁定为${\text{π}}/2$)时得到${\hat S_3}$压缩、${\hat S_2}$反压缩, ${\hat S_1}$为标准量子噪声基准. 相应的实验结果如图7(b)所示. 其中实验参数为: 本地光功率为1 mW, 振幅压缩光功率约为4 μW, 倍频蓝光功率约为110 mW, 谱仪参数RBW = 100 kHz, VBW = 500 Hz, 数据平均为30次. 这两个实验结果中参量${\hat S_1}$噪声在较低频率处略高于标准量子噪声基准. 这是由于激光在较低频率范围内的额外强度噪声所引起的. 如果产生的压缩光是振幅压缩, 那么参量${\hat S_1}$是压缩的, ${\hat S_2}$${\hat S_3}$为标准量子噪声基准. 实验上测量了一束功率为10 μW的振幅压缩光的斯托克斯参量噪声谱. 相应的实验结果如图7(c)所示. 其中实验参数为: 倍频蓝光功率为85 mW, 谱仪参数RBW = 100 kHz, VBW = 500 Hz, 数据平均为30次. 因为倍频蓝光功率比较低, 相应的压缩度偏低. 从实验结果可以看出, 单束振幅压缩光实际上就是对应斯托克斯参量${\hat S_1}$的偏振压缩光.

      Figure 7.  Measured noise results for different Stokes parameters. The results on the left are the measured variance spectra of Stokes parameters normalized to quantum noise limit. The results on the right are the corresponding diagrammatic illustration of the Stokes parameters’ variance ellipsoid, and the blue ellipsoid is the noise ball, and these ellipses are the noise projections at each plane. The red dashed circles represent the noise of the coherent state and the blue solid circles show the squeezing. (a) Squeezing for Stokes parameter ${\hat S_2}$; (b) Squeezing for Stokes parameter ${\hat S_3}$; (c) Squeezing for Stokes parameter ${\hat S_1}$.

    4.   总 结
    • 我们在实验上利用倍频器产生的426 nm的蓝光, 泵浦工作在低于阈值的环形OPA腔, 产生了与铯原子D2线共振的振幅压缩光, 实现了在2—10 MHz带宽范围内斯托克斯参量${\hat S_1}$最大达3 dB的偏振压缩光的制备, 并且利用OPA腔产生的正交压缩光与明亮的相干光在偏振分束棱镜上合成, 实现了在2—10 MHz带宽范围内斯托克斯参量${\hat S_2}$, ${\hat S_3}$分别最大达4.3 dB的偏振压缩光的制备. 考虑到传输和测量效率, 实际输出压缩达5.2 dB, 即噪声只有真空起伏的30%左右. 目前压缩度主要限制于OPA腔的内腔损耗和探测效率, 而OPA的内腔损耗主要受限PPKTP晶体质量和晶体的热效应[30]、对短波长强烈的吸收效应和蓝光诱导红外吸收效应[34]. 在全光学原子磁力仪中, 提高系统的信噪比可以有效地提高磁场测量的灵敏度, 由于偏振压缩光的斯托克斯参量的量子噪声低于标准量子噪声基准的特性, 该明亮的量子光源有望应用到铯原子磁力仪中, 代替系统原有的相干探测光, 提高磁场测量灵敏度.

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