Experimental generation of multimode quantum correlations between a conical probe and a conical conjugate based on a four-wave mixing process

Cao Lei-Ming; Du Jin-Jian; Zhang Kai; Liu Sheng-Shuai; Jing Jie-Tai

doi:10.7498/aps.71.20220081

Abstract

Multimode quantum correlations and entanglements has drawn much attention recently due to its importance for both fundamental science and the future development of quantum information processing and quantum communication. Here, by using a four-wave mixing process with a conical pump beam and a conical probe beam, we experimentally generate the multimode quantum correlations between a conical probe beam and a conical conjugate beam, and we also observe about –2.6-dB intensity-difference squeezing between these two conical beams. In addition, we find the optimal value of each parameter in this scheme for further applications. Besides, the multi-spatial-mode nature of the generated quantum correlated beams is shown by comparing the variation tendencies of the intensity-difference noise of the probe and conjugate beams under global attenuation and local cutting attenuation. Our scheme may find potential applications in quantum information processing and quantum communication.

Keywords:

Authors and contacts

1.
Physics and Electronic Information College, Luoyang Normal College, Luoyang 471022, China
2.
State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
3.
CAS Center for Excellence in Ultra-intense Laser Science, Chinese Academy of Sciences, Shanghai 201800, China
4.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Corresponding author: Jing Jie-Tai, jtjing@phy.ecnu.edu.cn

Funds: Project supported by the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 2021-01-07-00-08-E00100), the National Natural Science Foundation of China (Grant Nos. 11874155, 11804141, 91436211, 11374140), the Natural Science Foundation of Shanghai, China (Grant No. 17ZR1442900), the Basic Research Project of Shanghai Science and Technology Commission, China (Grant No. 20JC1416100), the Program of Scientific and Technological Innovation of Shanghai, China (Grant No. 17JC1400401), the Shanghai Municipal Science and Technology Major Project, China (Grant No. 2019SHZDZX01), the Shanghai Sailing Program, China (Grant No. 21YF1410800), the Minhang Leading Talents, China (Grant No. 201971), and the 111 Project, China (Grant No. B12024).

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References

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[7]	Yonezawa H, Aoki T, Furasawa A 2004 Nature 431 430 Google Scholar
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[25]	Cao L M, Wang W, Lou Y B, Du J J, Jing J T 2018 Appl. Phys. Lett. 112 251102 Google Scholar
[26]	Wang H L, Zheng Z, Wang Y X, Jing J T 2016 Opt. Express 24 23459 Google Scholar
[27]	Lv S C, Jing J T 2017 Phys. Rev. A 96 043873 Google Scholar
[28]	Chen Y X, Liu S S, Lou Y B, Jing J T 2021 Phys. Rev. Lett. 127 093601 Google Scholar
[29]	Liu S S, Lou Y B, Chen Y X, Jing J T 2021 Phys. Rev. Lett. 126 060503 Google Scholar
[30]	Liu S S, Lou Y B, Jing J T 2020 Nat. Commun. 11 3875 Google Scholar
[31]	Lou Y B, Liu S S, Jing J T 2021 Phys. Rev. Lett. 126 210507 Google Scholar
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[37]	Cao L M, Du J J, Feng J L, Qin Z Z, Marino A M, Kolobov M I, Jing J T 2017 Opt. Lett. 42 1201 Google Scholar
[38]	Marino A M, Boyer V, Pooser R C, Lett P D, Lemons K, Jones K M 2008 Phys. Rev. Lett. 101 093602 Google Scholar

Cited By

图 1 利用锥形泵浦光和锥形探针光产生和测量多模量子关联的实验系统　(a) 基于铷⁸⁵ 原子D₁线的双“Λ”能级跃迁示意图. Probe是探针光; Conjugate是共轭光; Pump是泵浦光; ∆是单光子失谐; δ是双光子失谐. (b) 实验装置图. M₁—M₃是高反射率的平面反镜; L₁—L₅是透镜; Axicon是锥形棱镜; GL是格兰-激光偏振棱镜; GT是格兰-托马斯棱镜; SA是频谱分析仪; SMF是单模光纤; PBS是偏振光分束器. (c) 锥形泵浦光和锥形探针光通过四波混频反应产生锥形共轭光的示意图. (d) 经四波混频反应后的探针光、共轭光和经过滤后泵浦光在光斑分析仪上呈现的二维和三维图像

Figure 1. Scheme for generating and detecting multimode quantum correlation: (a) Double-Λ energy level diagram of the ⁸⁵Rb D₁ line. (b) Experimental layout. M₁–M₃, high reflectivity mirrors; L₁–L₅, lenses; Axicon, metal axicon mirror; GL, Glan-Laser polarizer; GT, Glan-Thompson polarizer; SA, spectrum analyzer. (c) Schematic of the conical-pump-based FWM. (d) Two-dimensional and three-dimensional beam pattern captured by a laser beam profiler.

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图 2 量子关联的实验测量结果　(a) 经四波混频反应后, 归一化的散粒噪声极限SNL (曲线A)、探针光和共轭光的强度差噪声功率(曲线B)、经四波混频放大后的探针光噪声功率(曲线C)、四波混频产生的共轭光的噪声功率(曲线D); (b) 频谱分析仪设置在2 MHz时, 实验测量到的强度差噪声(直线B)和相应的SNL(直线A)随总光功率的变化关系

Figure 2. Experimental results of quantum correlations: (a) Normalized noise powers of the corresponding SNLs (trace A), intensity-difference noise power between the probe and the conjugate beams (trace B), probe beam (trace C) and conjugate beam (trace D); (b) intensity-difference noise power versus total optical power at 2 MHz. Red line: SNL (trace A), Green line: intensity-difference noise power between the probe and the conjugate (trace B).

DownLoad: Full-Size Img PowerPoint

图 3 实验测量强度差噪声和四波混频的增益随单光子失谐∆、双光子失谐δ、泵浦光功率PP以及铷原子池温度T等实验参数的变化关系

Figure 3. Dependence of the intensity-difference noise and the power gain on (a) one-photon detuning, (b) two-photon detuning, (c) pump power and (d) temperature in vapor cell. The traces for the intensity-difference noise are plotted in red and the traces for the power gain are plotted in green.

DownLoad: Full-Size Img PowerPoint

图 4 实验测量锥形探针光和锥形共轭光之间量子关联的多模特性　(a) 通过“整体衰减法”和“局部切割法”进行多模特性测量的实验方案示意图. (b) 实验测量的以不同的衰减方式减小功率时, 强度差压缩噪声随透射率的变化关系. 曲线A表示对两束光用半波片和PBS进行整体衰减时, 强度差噪声随透射率的变化关系; 曲线B/C/D分别表示对两束光用薄刀片进行同向、反向和垂直方向的局部切割时, 强度差噪声随透射率的变化关系. (c) 锥形探针光和锥形共轭光之间量子关联的同侧对应关系示意图

Figure 4. Experimental measurement of multimode quantum correlations between the conical probe and the conical conjugate: (a) The schematic of global attenuation and local attenuation for experimentally measuring multimode quantum correlation. (b) The intensity-difference noise power as a function of the transmittance as the two beams are attenuated equally; Trace A, the two beams are globally attenuated with a variable beam splitter; Trace B/C/D, the two beams are locally attenuated with razor blades cutting from same direction, opposite direction and the perpendicular direction. (c) The schematic of multimode quantum correlations with correspondence on the same side.

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[1]	Weedbrook C, Pirandola S, Patrón R G, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Rev. Mod. Phys. 84 621 Google Scholar
[2]	DiVincenzo D P 1995 Science 270 255 Google Scholar
[3]	Lloyd S, Braunstein S L 1999 Phys. Rev. Lett. 82 1784 Google Scholar
[4]	Braunstein S L, van Loock P 2005 Rev. Mod. Phys. 77 513 Google Scholar
[5]	Weedbrook C, Pirandola S, García-Patrón R, Cerf N J, Ralph T C, Shapiro J H, Lloyd S 2012 Reviews of Modern Physics 84 621
[6]	Jing J T, Zhang J, Yan Y, Zhao F G, Xie C D, Peng K C 2003 Phys. Rev. Lett. 90 167903 Google Scholar
[7]	Yonezawa H, Aoki T, Furasawa A 2004 Nature 431 430 Google Scholar
[8]	van Loock P, Braunstein S L 2000 Phys. Rev. Lett. 84 3482 Google Scholar
[9]	Coelho A S, Barbosa F A S, Cassemiro K N, Villar A S, Martinelli M, Nussenzveig P 2009 Science 326 823 Google Scholar
[10]	Armstrong S, Wang M, Teh R Y, Gong Q, He Q, Janousek J, Bachor H A, Reid M D, Lam P K 2015 Nat. Phys. 11 167 Google Scholar
[11]	Cassemiro K N, Villar A S 2008 Phys. Rev. A 77 022311 Google Scholar
[12]	Su X L, Hao S H, Deng X W, Ma L Y, Wang M H, Jia X J, Xie C D, Peng K C 2013 Nat. Commun. 4 2828 Google Scholar
[13]	Wang X L, Chen L K, Li W, Huang H L, Liu C, Chen C, Luo Y H, Su Z E, Wu D, Li Z D, Lu H, Hu Y, Jiang X, Peng C Z, Li L, Liu N L, Chen Y A, Lu C Y, Pan J W 2016 Phys. Rev. Lett. 117 210502 Google Scholar
[14]	Armstrong S, Wang M, Teh R Y, Gong Q, He Q, Janousek J, Bachor H A, Reid M D, Lam P K 2015 Nature Physics 11 167
[15]	Cassemiro K N, Villar A S 2008 Physical Review A 77 022311
[16]	Yokoyama S, Ukai R, Armstrong S C, Sornphiphatphong C, Kaji T, Suzuki S, Yoshikawa J I, Yonezawa H, Menicucci N C, Furusawa A 2013 Nat. Photonics 7 982 Google Scholar
[17]	Roslund J, De Araújo R M, Jiang S F, Fabre C, Treps N 2014 Nat. Photonics 8 109 Google Scholar
[18]	McCormick C F, Boyer V, Arimondo E, Lett P D 2007 Opt. Lett. 32 178 Google Scholar
[19]	Boyer V, Marino A M, Pooser R C, Lett P D 2008 Science 321 544 Google Scholar
[20]	Marino A M, Pooser R C, Boyer V, Lett P D 2009 Nature 457 859 Google Scholar
[21]	Embrey C S, Turnbull M T, Petrov P G, Boyer V 2015 Phys. Rev. X 5 031004
[22]	Qin Z Z, Cao L M, Wang H L, Marino A M, Zhang W P, Jing J T 2014 Phys. Rev. Lett. 113 023602 Google Scholar
[23]	Cao L M, Qi J, Du J J, Jing J T 2017 Phys. Rev. A 95 023803 Google Scholar
[24]	Liu S S, Wang H L, Jing J T 2018 Phys. Rev. A 97 043846 Google Scholar
[25]	Cao L M, Wang W, Lou Y B, Du J J, Jing J T 2018 Appl. Phys. Lett. 112 251102 Google Scholar
[26]	Wang H L, Zheng Z, Wang Y X, Jing J T 2016 Opt. Express 24 23459 Google Scholar
[27]	Lv S C, Jing J T 2017 Phys. Rev. A 96 043873 Google Scholar
[28]	Chen Y X, Liu S S, Lou Y B, Jing J T 2021 Phys. Rev. Lett. 127 093601 Google Scholar
[29]	Liu S S, Lou Y B, Chen Y X, Jing J T 2021 Phys. Rev. Lett. 126 060503 Google Scholar
[30]	Liu S S, Lou Y B, Jing J T 2020 Nat. Commun. 11 3875 Google Scholar
[31]	Lou Y B, Liu S S, Jing J T 2021 Phys. Rev. Lett. 126 210507 Google Scholar
[32]	Daems D, Bernard F, Cerf N J, Kolobov M I 2010 J. Opt. Soc. Am. B 27 447 Google Scholar
[33]	Daems D, Cerf N J 2010 Phys. Rev. A 82 032303 Google Scholar
[34]	Zhang K, Wang W, Liu S S, Pan X Z, Du J J, Lou Y B, Yu S, Lv S C, Treps N, Fabre C, Jing J T 2020 Phys. Rev. Lett. 124 090501 Google Scholar
[35]	Wang H L, Fabre C, Jing J T 2017 Phys. Rev. A 95 051802 Google Scholar
[36]	Liu S S, Wang H L, Jing J T 2018 Physical Review A 97 043846
[37]	Cao L M, Du J J, Feng J L, Qin Z Z, Marino A M, Kolobov M I, Jing J T 2017 Opt. Lett. 42 1201 Google Scholar
[38]	Marino A M, Boyer V, Pooser R C, Lett P D, Lemons K, Jones K M 2008 Phys. Rev. Lett. 101 093602 Google Scholar

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