Deterministic quantum entanglement among multiple quantum nodes

Liu Yan-Hong; Wu Liang; Yan Zhi-Hui; Jia Xiao-Jun; Peng Kun-Chi

doi:10.7498/aps.68.20181614

Abstract

Quantum entanglement is a significant quantum resource, which plays a central role in quantum communication. For realizing quantum information network, it is important to establish deterministic quantum entanglement among multiple spatial-separated quantum memories, and then the stored entanglement is transferred into the quantum channels for distributing and transmitting the quantum information at the user-control time. Firstly, we introduce the scheme of deterministic generation polarization squeezed state at 795 nm. A pair of quadrature amplitude squeezed optical fields are prepared by two degenerate optical parameter amplifiers pumped by a laser at 398 nm, and then the polarization squeezed state of light appears by combining the generated two quadrature amplitude squeezed optical beams on a polarizing beam splitter. Secondly, we present the experimental demonstration of tripartite polarization entanglement described by Stokes operators of optical field. The quadrature tripartite entangled states of light corresponding to the resonance with D1 line of rubidium atoms are transformed into the continuous-variable polarization entanglement via polarization beam splitter with three bright local optical beams. Finally, we propose the generation, storage and transfer of deterministic quantum entanglement among three spatially separated atomic ensembles. By the method of electromagnetically induced transparency light-matter interaction, the optical multiple entangled state is mapped into three distant atomic ensembles to build the entanglement among three atomic spin waves. Then, the quantum noise of entanglement stored in the atomic ensembles is transferred to the three space-seperated quadrature entangled light fields through three quantum channels. The existence of entanglement among the three released beams verifies that the system has the ability to maintain the multipartite entanglement. This protocol realizes the entanglement among three distant quantum nodes, and it can be extended to quantum network with more quantum nodes. All of these lay the foundation for realizing the large-scale quantum network communication in the future.

Keywords:

deterministic quantum entanglement /
electromagnetically induced transparency /
multipartite entanglement /
quantum nodes

Authors and contacts

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

Corresponding author: Jia Xiao-Jun, jiaxj@sxu.edu.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2016YFA0301402), the National Natural Science Foundation of China (Grant Nos. 61775127, 11474190, 11654002), the Program for Sanjin Scholars of Shanxi Province, China, the Shanxi Scholarship Council of China, and the Fund for Shanxi “1331 Project” Key Subjects Construction, China.

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References

[1]	Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Żukowski M 2012 Rev. Mod. Phys. 84 777 Google Scholar
[2]	Braunstein S L, van Loock P 2005 Rev. Mod. Phys. 77 513 Google Scholar
[3]	Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575 Google Scholar
[4]	Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706 Google Scholar
[5]	Huo M R, Qin J L, Cheng J L, Yan Z H, Qin Z Z, Su X L, Jia X J, Xie C D, Peng K C 2018 Sci. Adv. 4 eaas9401 Google Scholar
[6]	Pan J W, Bouwmeester D, Weinfurter H, Zeilinger A 1998 Phys. Rev. Lett. 80 3891 Google Scholar
[7]	Jia X J, Su X L, Pan Q, Gao J R, Xie C D, Peng K C 2004 Phys. Rev. Lett. 93 250503 Google Scholar
[8]	Takeda S, Fuwa M, van Loock P, Furusawa A 2015 Phys. Rev. Lett. 114 100501 Google Scholar
[9]	Chen Y A, Zhang A N, Zhao Z, Zhou X Q, Lu C Y, Peng C Z, Yang T, Pan J W 2005 Phys. Rev. Lett. 95 200502 Google Scholar
[10]	Lance A M, Symul T, Bowen W P, Sanders B C, Lam P K 2004 Phys. Rev. Lett. 92 177903 Google Scholar
[11]	Zhou Y Y, Yu J, Yan Z H, Jia X J, Zhang J, Xie C D, Peng K C 2018 Phys. Rev. Lett. 121 150502 Google Scholar
[12]	Cai X D, Wu D, Su Z S, Chen M C, Wang X L, Li L, Liu N L, Lu C Y, Pan J W 2015 Phys. Rev. Lett. 114 110504 Google Scholar
[13]	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
[14]	Kimble H J 2008 Nature 453 1023 Google Scholar
[15]	Glöckl O, Heersink J, Korolkova N, Leuchs G, Lorenz S 2003 J. Opt. B: Quantum Semiclass. Opt. 5 S492 Google Scholar
[16]	Iskhakov T Sh, Agafonov I N, Chekhova M V, Leuchs G 2012 Phys. Rev. Lett. 109 150502 Google Scholar
[17]	Hosseini M, Sparkes B M, Campbell G, Lam P K, Buchler B C 2011 Nat. Commun. 2 174 Google Scholar
[18]	Parigi V, Ambrosio V, Arnold C, Marrucci L, Sciarrino F, Laurat J 2015 Nat. Commun. 6 7706 Google Scholar
[19]	Yan Z H, Jia X J 2017 Quantum Sci. Technol. 2 024003 Google Scholar
[20]	Pu Y F, Jiang N, Chang W, Yang H X, Li C, Duan L M 2017 Nat. Commun. 8 15359 Google Scholar
[21]	Colangelo G, Ciurana F M, Bianchet L C, Sewell R J, Mitchell M W 2017 Nature 543 525 Google Scholar
[22]	Specht H P, Nolleke C, Reiserer A, Uphoff M, Figueroa E, Ritter S, Rempe G 2011 Nature 473 190 Google Scholar
[23]	Facon A, Dietsche E K, Grosso D, Haroche S, Raimond J M, Brune M, Gleyzes S 2016 Nature 535 262 Google Scholar
[24]	Stute A, Casabone B, Schindler P, Monz T, Schmidt P O, Brandstätter B, Northup T E, Blatt R 2012 Nature 485 482 Google Scholar
[25]	Hucul D, Inlek I V, Vittorini G, Crocker C, Debnath S, Clark S M, Monroe C 2014 Nat. Phys. 11 37 Google Scholar
[26]	Fiore V, Yang Y, Kuzyk M C, Barbour R, Tian L, Wang H 2011 Phys. Rev. Lett. 107 133601 Google Scholar
[27]	Lee H, Suh M G, Chen T, Li J, Diddams S A, Vahala K J 2013 Nat. Commun. 4 2468 Google Scholar
[28]	Riedinger R, Hong S, Norte R A, Slater J A, Shang J, Krause A G, Anant V, Aspelmeyer M, Gröblacher S 2016 Nature 530 313 Google Scholar
[29]	Kiesewetter S, Teh R Y, Drummond P D, Reid M D 2017 Phys. Rev. Lett. 119 023601 Google Scholar
[30]	Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys. Rev. Lett. 114 090503 Google Scholar
[31]	Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussieres F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512 Google Scholar
[32]	Zhong M, Hedges M P, Ahlefeldt R L, Bartholomew J G, Beavan S E, Wittig S E, Longdell J J, Sellars M J 2015 Nature 517 177 Google Scholar
[33]	Gao W B, Fallahi P, Togan E, Miguel-Sanchez J, Imamoglu A 2012 Nature 491 426 Google Scholar
[34]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413 Google Scholar
[35]	Chou C W, de Riedmatten H, Felinto D, Polyakov S V, van Enk S J, Kimble H J 2005 Nature 438 828 Google Scholar
[36]	Yuan Z S, Chen Y A, Zhao B, Chen S, Schmiedmayer J, Pan J W 2008 Nature 454 1098 Google Scholar
[37]	Choi K S, Deng H, Laurat J, Kimble H J 2008 Nature 452 67 Google Scholar
[38]	Zhang W, Ding D S, Dong M X, Shi S, Wang K, Liu S L, Li Y, Zhou Z Y, Shi B S, Guo G C 2016 Nat. Commun. 7 13514 Google Scholar
[39]	Choi K S, Goban A, Papp S B, van Enk S J, Kimble H J 2010 Nature 468 412 Google Scholar
[40]	Julsgaard B, Kozhekin A E, Polzik E S 2001 Nature 413 400 Google Scholar
[41]	Krauter H, Muschik C A, Jensen K, Wasilewski W, Petersen J M, Cirac J I, Polzik E S 2011 Phys. Rev. Lett. 107 080503 Google Scholar
[42]	Ou Z Y 2008 Phys. Rev. A 78 023819 Google Scholar
[43]	Yang X H, Zhou Y Y, Xiao M 2013 Sci. Rep. 3 3479 Google Scholar
[44]	Liu Y H, Yan Z H, Jia X J, Xie C D 2016 Sci. Rep. 6 25715 Google Scholar
[45]	Yadsanappleby H, Serafini A 2011 Phys. Lett. A 375 1864 Google Scholar
[46]	Tikhonov K S, Golubeva T Y, Golubev Y M 2015 Opt. Spectrosc. 118 773 Google Scholar
[47]	Honda K, Akamatsu D, Arikawa M, Yokoi Y, Akiba K, Nagatsuka S, Tanimura T, Furusawa A, Kozuma M 2008 Phys. Rev. Lett. 100 093601 Google Scholar
[48]	Appel J, Figueroa E, Korystov D, Lobino M, Lvovsky A I 2008 Phys. Rev. Lett. 100 093602 Google Scholar
[49]	Jensen K, Wasilewski W, Krauter H, Fernholz T, Nielsen B M, Owari M, Plenio M B, Serafini A, Wolf M M, Polzik E S 2011 Nat. Phys. 7 13 Google Scholar
[50]	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 Google Scholar
[51]	Grangien P, Slusheg R E, Yurke B, LaPorta A 1987 Phys. Rev. Lett. 59 2153 Google Scholar
[52]	Polzik E S, Carri J, Kimble H J 1992 Phys. Rev. Lett. 68 3020 Google Scholar
[53]	孙恒信, 刘奎, 张俊香, 郜江瑞 2015 64 234210 Google Scholar Sun H X, Liu K, Zhang J X, Gao J R 2015 Acta Phys. Sin. 64 234210 Google Scholar
[54]	左小杰, 孙颍榕, 闫智辉, 贾晓军 2018 67 134202 Google Scholar Zuo X J, Sun Y R, Yan Z H, Jia X J 2018 Acta Phys. Sin. 67 134202 Google Scholar
[55]	Vahlbruch H, Chelkowski S, Hage B 2006 Phys. Rev. Lett. 97 011101 Google Scholar
[56]	万振菊, 冯晋霞, 孙志妮, 要立婷, 张宽收 2014 量子光学学报 20 271 Google Scholar Wan Z J, Feng J X, Sun Z N, Yao L T, Zhang K S 2014 Acta Sin. Quantum Opt. 20 271 Google Scholar
[57]	Korolkova N, Leuchs G, Loudon R, Ralph T C, Silberhorn C 2002 Phys. Rev. A 65 052306 Google Scholar
[58]	Peuntinger C, Heim B, Müller C R, Gabriel C, Marquardt C, Leuchs G 2014 Phys. Rev. Lett. 113 060502 Google Scholar
[59]	Josse V, Dantan A, Vernac L, Bramati A, Pinard M, Giacobino E 2003 Phys. Rev. Lett. 91 103601 Google Scholar
[60]	Bowen W P, Schnabel R, Bachor H A, Lam P K 2002 Phys. Rev. Lett. 88 093601 Google Scholar
[61]	Wu L, Liu Y H, Deng R J, Yan Z H, Jia X J, Peng K C 2016 J. Opt. Soc. Am. B 33 2296 Google Scholar
[62]	Josse V, Dantan A, Vernac L, Bramati A, Pinard M, Giacobino E 2004 Phys. Rev. Lett. 92 123601 Google Scholar
[63]	闫智辉, 贾晓军, 谢常德, 彭堃墀 2012 61 014206 Google Scholar Yan Z H, Jia X J, Xie C D, Peng K C 2012 Acta Phys. Sin. 61 014206 Google Scholar
[64]	Jia X J, Yan Z H, Duan Z Y, Su X L, Wang H, Xie C D, Peng K C 2012 Phys. Rev. Lett. 109 253604 Google Scholar
[65]	Su X L, Zhao Y P, Hao S H, Jia X J, Xie C D, Peng K C 2012 Opt. Lett. 37 5178 Google Scholar
[66]	Yan Z H, Jia X J 2015 J. Opt. Soc. Am. B 32 2139 Google Scholar
[67]	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 Google Scholar
[68]	Teh R Y, Reid M D 2014 Phys. Rev. A 90 062337 Google Scholar
[69]	Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev. Lett. 84 2722 Google Scholar
[70]	Bowen W P, Treps N, Schnabel R, Lam P K 2002 Phys. Rev. Lett. 89 253601 Google Scholar
[71]	van Loock P, Furusawa A 2003 Phys. Rev. A 67 052315 Google Scholar
[72]	Hofmann H F, Takeuchi S 2003 Phys. Rev. A 68 032103 Google Scholar
[73]	Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633 Google Scholar
[74]	Lvovsky A I, Sander B C, Tittel W 2009 Nat. Photon. 3 706 Google Scholar
[75]	Duan L M, Monroe C 2010 Rev. Mod. Phys. 82 1209 Google Scholar
[76]	Hammerer K, Sørensen A S, Polzik E S 2010 Rev. Mod. Phys. 82 1041 Google Scholar
[77]	Sangouard N, Simon C, de Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33 Google Scholar
[78]	Wootton J R 2012 J. Mod. Opt. 59 1717 Google Scholar
[79]	Bussières F, Sangouard N, Afzelius M, de Riedmatten H, Simon C, Tittel W 2013 J. Mod. Opt. 60 1519 Google Scholar
[80]	Northup T E, Blatt R 2014 Nat. Photon. 8 356 Google Scholar
[81]	Phillips D F, Fleischhauer A, Mair A, Walsworth R L 2001 Phys. Rev. Lett. 86 783 Google Scholar
[82]	Fleischhayer M, Lukin M 2002 Phys. Rev. A 65 022314 Google Scholar
[83]	邓瑞婕, 闫智辉, 贾晓军 2017 66 074201 Google Scholar Deng R J, Yan Z H, Jia X J 2017 Acta Phys. Sin. 66 074201 Google Scholar
[84]	Julsgaard B, Sherson J, Cirac J I, Fiurasek J, Polzik E S 2004 Nature 432 482 Google Scholar
[85]	Hétet G, Longdell J J, Sellars M J, Lam P K, Buchler B C 2008 Phys. Rev. Lett. 101 203601 Google Scholar
[86]	Moiseev S, Kröll S 2001 Phys. Rev. Lett. 87 173601 Google Scholar
[87]	Fleischhauer M, Lukin M D 2000 Phys. Rev. Lett. 84 5094 Google Scholar
[88]	杨胜军 2014 博士学位论文 (合肥: 中国科学技术大学) Yang S J 2014 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[89]	Alexander A L, Longdell J J, Sellars M J, Manson N B 2006 Phys. Rev. Lett. 96 043602 Google Scholar
[90]	Ding D S, Zhang W, Zhou Z Y, Shi S, Xiang G Y, Wang X S, Jiang Y K, Shi B S, Guo G C 2015 Phys. Rev. Lett. 114 050502 Google Scholar
[91]	Simon R 2000 Phys. Rev. Lett. 84 2726 Google Scholar
[92]	温馨, 韩亚帅, 刘金玉, 白乐乐, 何军, 王军民 2018 67 024207 Google Scholar Wen X, Han Y S, Liu J Y, Bai L L, He J, Wang J M 2018 Acta Phys. Sin. 67 024207 Google Scholar
[93]	吴量, 刘艳红, 邓瑞婕, 闫智辉, 贾晓军 2017 光学学报 37 0527001 Google Scholar Wu L, Liu Y H, Deng R J, Yan Z H, Jia X J 2017 Acta Opt. Sin. 37 0527001 Google Scholar
[94]	Yokoyama S, Ukai R, Armstrong S C, Sornphiphatphong C, Kaji T, Suzuki S, Yoshikawa J, Yonezawa H, Menicucci N C, Furusawa A 2013 Nat. Photon. 7 982 Google Scholar
[95]	Roslund J, Medeiros R, Jiang S, Fabre C, Treps N 2014 Nat. Photon. 8 109 Google Scholar
[96]	Phillips N B, Gorshkov A V, Novikova I 2011 Phys. Rev. A 83 063823 Google Scholar
[97]	Lobino M, Kupchak C, Figueroa E, Lvovsky A I 2009 Phys. Rev. Lett. 102 203601 Google Scholar
[98]	Lauk N, O’Brien C, Fleischhauer M 2013 Phys. Rev. A 88 013823 Google Scholar
[99]	Barrett S D 2010 New J. Phys. 12 093032 Google Scholar
[100]	Datta A, Zhang L J, Nunn J, Langford N K, Feito A, Plenio M B, Walmsley I A 2012 Phys. Rev. Lett. 108 060502 Google Scholar
[101]	Bao X H, Reingruber A, Dietrich P, Rui J, Dück A, Strassel T, Li L, Liu N L, Zhao B, Pan J W 2012 Nat. Phys. 8 517 Google Scholar
[102]	Yang S J, Wang X J, Bao X H, Pan J W 2016 Nat. Photon. 10 381 Google Scholar
[103]	Saunders D J, Munns J H D, Champion T F M, Qiu C, Kaczmarek K T, Poem E, Ledingham P M, Walmsley A I, Nunn J 2016 Phys. Rev. Lett. 116 090501 Google Scholar
[104]	Vahlbruch H, Mehmet M, Danzmann K, Schnabel R 2016 Phys. Rev. Lett. 117 110801 Google Scholar

Cited By

图 1 偏振压缩光场制备原理图

Figure 1. Schematic of generation system of polarization squeezing.

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图 2 Stokes分量(a) ${\hat S_0}$, (b) ${\hat S_1}$, (c)${\hat S_2}$, (d) ${\hat S_3}$的量子噪声的实验测量(HWP, 二分之一波片; QWP, 四分之一波片; PBS, 偏振分束棱镜; +/−, 功率加法/减法器)

Figure 2. Measurement of quantum noise of Stokes component (a) ${\hat S_0}$, (b) ${\hat S_1}$, (c) ${\hat S_2}$, (d) ${\hat S_3}$. HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarization beam splitter; +/−, positive/negative power combiner.

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图 3 偏振压缩光Stokes分量的量子噪声^[61]　(a) ${\hat S_0}$; (b) $\hat S{}_1$; (c) ${\hat S_2}$; (d) ${\hat S_3}$

Figure 3. Quantum noises of Stokes component of polarization squeezedlight^[61]: (a) ${\hat S_0}$; (b) ${\hat S_1}$; (c) ${\hat S_2}$; (d) ${\hat S_3}$.

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图 4 偏振纠缠制备原理图

Figure 4. Schematic for the generation system of polarization entanglement.

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图 5 三组分偏振纠缠态产生方案(BS1, 光学分束器1; BS2, 光学分束器2; PBS1, 偏振分束棱镜1; PBS2, 偏振分束棱镜2; PBS3, 偏振分束棱镜3)

Figure 5. Schematic for the generation of tripartite polarization entangled state. BS1, beam splitter1; BS2, beam splitter2; PBS1, polarization beam splitter1; PBS2, polarization beam splitter2; PBS3, polarization beam splitter3.

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图 6 分析频率在1—6 MHz间测量的Stokes关联方差　(a) ${{\text{δ }}^2}({\hat S_{{2_{{d_2}}}}} - {\hat S_{{2_{{d_3}}}}})$; (b) ${{\text{δ }}^2}({g_1}{\hat S_{{3_{{d_1}}}}} + {\hat S_{{3_{{d_2}}}}} + {\hat S_{{3_{d3}}}})$; (c) ${{\text{δ }}^2}({\hat S_{{2_{{d_1}}}}} - {\hat S_{{2_{d3}}}})$; (d) ${{\text{δ }}^2}({\hat S_{{3_{{d_1}}}}} + {g_2}{\hat S_{{3_{{d_2}}}}} + {\hat S_{{3_{d3}}}})$; (e) ${{\text{δ }}^2}({\hat S_{{2_{{d_1}}}}} - {\hat S_{{2_{d2}}}})$; (f) ${{\text{δ }}^2}({\hat S_{{3_{{d_1}}}}} + {\hat S_{{3_{{d_2}}}}} + {g_3}{\hat S_{{3_{d3}}}})$

Figure 6. Measured correlation variances of (a) ${{\text{δ }}^2}({\hat S_{{2_{{d_2}}}}} - {\hat S_{{2_{{d_3}}}}})$, (b) ${{\text{δ }}^2}({g_1}{\hat S_{{3_{{d_1}}}}} + {\hat S_{{3_{{d_2}}}}} + {\hat S_{{3_{d3}}}})$, (c) ${{\text{δ }}^2}({\hat S_{{2_{{d_1}}}}} - {\hat S_{{2_{d3}}}})$, (d) ${{\text{δ }}^2}({\hat S_{{3_{{d_1}}}}} + {g_2}{\hat S_{{3_{{d_2}}}}} + {\hat S_{{3_{d3}}}})$, (e) ${{\text{δ }}^2}({\hat S_{{2_{{d_1}}}}} - {\hat S_{{2_{d2}}}})$, (f) ${{\text{δ }}^2}({\hat S_{{3_{{d_1}}}}} + {\hat S_{{3_{{d_2}}}}} + {g_3}{\hat S_{{3_{d3}}}})$ over the analysis frequency rangefrom 1 to 6 MHz.

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图 7 原子系综纠缠示意图

Figure 7. Schematic of atom-atom entanglement generation system.

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图 8 三原子系综纠缠实验装置图

Figure 8. Experimental device diagram of quantum entanglement among three distant atomic ensembles.

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图 9 信号光与控制光的时序控制图

Figure 9. Sequence control of signal and control light.

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图 10 测量的输入模式和释放模式的关联方差

Figure 10. Measured normalized correlation variances of input and released optical submodes.

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表 1 释放光模正交分量不同组合的归一化关联方差

Table 1. Values of normalized correlation variances for different combinations.

不同组合的关联方差	输入模式/dB	原子自旋波/dB	释放模式/dB
$\left\langle {{{\text{δ}}^2}({{\hat X}_2} - {{\hat X}_3})} \right\rangle $	−3.30 ± 0.05	−0.56 ± 0.03	−0.37 ± 0.03
$\left\langle {{{\text{δ}}^2}({g_1}{{\hat P}_1} + {{\hat P}_2} + {{\hat P}_3})} \right\rangle $	−2.93 ± 0.05	−0.15 ± 0.02	−0.10 ± 0.02
$\left\langle {{{\text{δ}}^2}({{\hat X}_1} - {{\hat X}_3})} \right\rangle $	−3.25 ± 0.05	−0.53 ± 0.03	−0.35 ± 0.03
$\left\langle {{{\text{δ}}^2}({{\hat P}_1} + {g_2}{{\hat P}_2} + {{\hat P}_3})} \right\rangle $	−2.91 ± 0.05	−0.15 ± 0.02	−0.10 ± 0.02
$\left\langle {{{\text{δ}}^2}({{\hat X}_1} - {{\hat X}_2})} \right\rangle $	−3.25 ± 0.05	−0.52 ± 0.03	−0.34 ± 0.03
$\left\langle {{{\text{δ}}^2}({g_1}{{\hat P}_2} + {{\hat P}_2} + {{\hat P}_3})} \right\rangle $	−2.90 ± 0.05	−0.14 ± 0.02	−0.09 ± 0.02

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[1]	Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Żukowski M 2012 Rev. Mod. Phys. 84 777 Google Scholar
[2]	Braunstein S L, van Loock P 2005 Rev. Mod. Phys. 77 513 Google Scholar
[3]	Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575 Google Scholar
[4]	Furusawa A, Sørensen J L, Braunstein S L, Fuchs C A, Kimble H J, Polzik E S 1998 Science 282 706 Google Scholar
[5]	Huo M R, Qin J L, Cheng J L, Yan Z H, Qin Z Z, Su X L, Jia X J, Xie C D, Peng K C 2018 Sci. Adv. 4 eaas9401 Google Scholar
[6]	Pan J W, Bouwmeester D, Weinfurter H, Zeilinger A 1998 Phys. Rev. Lett. 80 3891 Google Scholar
[7]	Jia X J, Su X L, Pan Q, Gao J R, Xie C D, Peng K C 2004 Phys. Rev. Lett. 93 250503 Google Scholar
[8]	Takeda S, Fuwa M, van Loock P, Furusawa A 2015 Phys. Rev. Lett. 114 100501 Google Scholar
[9]	Chen Y A, Zhang A N, Zhao Z, Zhou X Q, Lu C Y, Peng C Z, Yang T, Pan J W 2005 Phys. Rev. Lett. 95 200502 Google Scholar
[10]	Lance A M, Symul T, Bowen W P, Sanders B C, Lam P K 2004 Phys. Rev. Lett. 92 177903 Google Scholar
[11]	Zhou Y Y, Yu J, Yan Z H, Jia X J, Zhang J, Xie C D, Peng K C 2018 Phys. Rev. Lett. 121 150502 Google Scholar
[12]	Cai X D, Wu D, Su Z S, Chen M C, Wang X L, Li L, Liu N L, Lu C Y, Pan J W 2015 Phys. Rev. Lett. 114 110504 Google Scholar
[13]	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
[14]	Kimble H J 2008 Nature 453 1023 Google Scholar
[15]	Glöckl O, Heersink J, Korolkova N, Leuchs G, Lorenz S 2003 J. Opt. B: Quantum Semiclass. Opt. 5 S492 Google Scholar
[16]	Iskhakov T Sh, Agafonov I N, Chekhova M V, Leuchs G 2012 Phys. Rev. Lett. 109 150502 Google Scholar
[17]	Hosseini M, Sparkes B M, Campbell G, Lam P K, Buchler B C 2011 Nat. Commun. 2 174 Google Scholar
[18]	Parigi V, Ambrosio V, Arnold C, Marrucci L, Sciarrino F, Laurat J 2015 Nat. Commun. 6 7706 Google Scholar
[19]	Yan Z H, Jia X J 2017 Quantum Sci. Technol. 2 024003 Google Scholar
[20]	Pu Y F, Jiang N, Chang W, Yang H X, Li C, Duan L M 2017 Nat. Commun. 8 15359 Google Scholar
[21]	Colangelo G, Ciurana F M, Bianchet L C, Sewell R J, Mitchell M W 2017 Nature 543 525 Google Scholar
[22]	Specht H P, Nolleke C, Reiserer A, Uphoff M, Figueroa E, Ritter S, Rempe G 2011 Nature 473 190 Google Scholar
[23]	Facon A, Dietsche E K, Grosso D, Haroche S, Raimond J M, Brune M, Gleyzes S 2016 Nature 535 262 Google Scholar
[24]	Stute A, Casabone B, Schindler P, Monz T, Schmidt P O, Brandstätter B, Northup T E, Blatt R 2012 Nature 485 482 Google Scholar
[25]	Hucul D, Inlek I V, Vittorini G, Crocker C, Debnath S, Clark S M, Monroe C 2014 Nat. Phys. 11 37 Google Scholar
[26]	Fiore V, Yang Y, Kuzyk M C, Barbour R, Tian L, Wang H 2011 Phys. Rev. Lett. 107 133601 Google Scholar
[27]	Lee H, Suh M G, Chen T, Li J, Diddams S A, Vahala K J 2013 Nat. Commun. 4 2468 Google Scholar
[28]	Riedinger R, Hong S, Norte R A, Slater J A, Shang J, Krause A G, Anant V, Aspelmeyer M, Gröblacher S 2016 Nature 530 313 Google Scholar
[29]	Kiesewetter S, Teh R Y, Drummond P D, Reid M D 2017 Phys. Rev. Lett. 119 023601 Google Scholar
[30]	Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys. Rev. Lett. 114 090503 Google Scholar
[31]	Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussieres F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512 Google Scholar
[32]	Zhong M, Hedges M P, Ahlefeldt R L, Bartholomew J G, Beavan S E, Wittig S E, Longdell J J, Sellars M J 2015 Nature 517 177 Google Scholar
[33]	Gao W B, Fallahi P, Togan E, Miguel-Sanchez J, Imamoglu A 2012 Nature 491 426 Google Scholar
[34]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413 Google Scholar
[35]	Chou C W, de Riedmatten H, Felinto D, Polyakov S V, van Enk S J, Kimble H J 2005 Nature 438 828 Google Scholar
[36]	Yuan Z S, Chen Y A, Zhao B, Chen S, Schmiedmayer J, Pan J W 2008 Nature 454 1098 Google Scholar
[37]	Choi K S, Deng H, Laurat J, Kimble H J 2008 Nature 452 67 Google Scholar
[38]	Zhang W, Ding D S, Dong M X, Shi S, Wang K, Liu S L, Li Y, Zhou Z Y, Shi B S, Guo G C 2016 Nat. Commun. 7 13514 Google Scholar
[39]	Choi K S, Goban A, Papp S B, van Enk S J, Kimble H J 2010 Nature 468 412 Google Scholar
[40]	Julsgaard B, Kozhekin A E, Polzik E S 2001 Nature 413 400 Google Scholar
[41]	Krauter H, Muschik C A, Jensen K, Wasilewski W, Petersen J M, Cirac J I, Polzik E S 2011 Phys. Rev. Lett. 107 080503 Google Scholar
[42]	Ou Z Y 2008 Phys. Rev. A 78 023819 Google Scholar
[43]	Yang X H, Zhou Y Y, Xiao M 2013 Sci. Rep. 3 3479 Google Scholar
[44]	Liu Y H, Yan Z H, Jia X J, Xie C D 2016 Sci. Rep. 6 25715 Google Scholar
[45]	Yadsanappleby H, Serafini A 2011 Phys. Lett. A 375 1864 Google Scholar
[46]	Tikhonov K S, Golubeva T Y, Golubev Y M 2015 Opt. Spectrosc. 118 773 Google Scholar
[47]	Honda K, Akamatsu D, Arikawa M, Yokoi Y, Akiba K, Nagatsuka S, Tanimura T, Furusawa A, Kozuma M 2008 Phys. Rev. Lett. 100 093601 Google Scholar
[48]	Appel J, Figueroa E, Korystov D, Lobino M, Lvovsky A I 2008 Phys. Rev. Lett. 100 093602 Google Scholar
[49]	Jensen K, Wasilewski W, Krauter H, Fernholz T, Nielsen B M, Owari M, Plenio M B, Serafini A, Wolf M M, Polzik E S 2011 Nat. Phys. 7 13 Google Scholar
[50]	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 Google Scholar
[51]	Grangien P, Slusheg R E, Yurke B, LaPorta A 1987 Phys. Rev. Lett. 59 2153 Google Scholar
[52]	Polzik E S, Carri J, Kimble H J 1992 Phys. Rev. Lett. 68 3020 Google Scholar
[53]	孙恒信, 刘奎, 张俊香, 郜江瑞 2015 64 234210 Google Scholar Sun H X, Liu K, Zhang J X, Gao J R 2015 Acta Phys. Sin. 64 234210 Google Scholar
[54]	左小杰, 孙颍榕, 闫智辉, 贾晓军 2018 67 134202 Google Scholar Zuo X J, Sun Y R, Yan Z H, Jia X J 2018 Acta Phys. Sin. 67 134202 Google Scholar
[55]	Vahlbruch H, Chelkowski S, Hage B 2006 Phys. Rev. Lett. 97 011101 Google Scholar
[56]	万振菊, 冯晋霞, 孙志妮, 要立婷, 张宽收 2014 量子光学学报 20 271 Google Scholar Wan Z J, Feng J X, Sun Z N, Yao L T, Zhang K S 2014 Acta Sin. Quantum Opt. 20 271 Google Scholar
[57]	Korolkova N, Leuchs G, Loudon R, Ralph T C, Silberhorn C 2002 Phys. Rev. A 65 052306 Google Scholar
[58]	Peuntinger C, Heim B, Müller C R, Gabriel C, Marquardt C, Leuchs G 2014 Phys. Rev. Lett. 113 060502 Google Scholar
[59]	Josse V, Dantan A, Vernac L, Bramati A, Pinard M, Giacobino E 2003 Phys. Rev. Lett. 91 103601 Google Scholar
[60]	Bowen W P, Schnabel R, Bachor H A, Lam P K 2002 Phys. Rev. Lett. 88 093601 Google Scholar
[61]	Wu L, Liu Y H, Deng R J, Yan Z H, Jia X J, Peng K C 2016 J. Opt. Soc. Am. B 33 2296 Google Scholar
[62]	Josse V, Dantan A, Vernac L, Bramati A, Pinard M, Giacobino E 2004 Phys. Rev. Lett. 92 123601 Google Scholar
[63]	闫智辉, 贾晓军, 谢常德, 彭堃墀 2012 61 014206 Google Scholar Yan Z H, Jia X J, Xie C D, Peng K C 2012 Acta Phys. Sin. 61 014206 Google Scholar
[64]	Jia X J, Yan Z H, Duan Z Y, Su X L, Wang H, Xie C D, Peng K C 2012 Phys. Rev. Lett. 109 253604 Google Scholar
[65]	Su X L, Zhao Y P, Hao S H, Jia X J, Xie C D, Peng K C 2012 Opt. Lett. 37 5178 Google Scholar
[66]	Yan Z H, Jia X J 2015 J. Opt. Soc. Am. B 32 2139 Google Scholar
[67]	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 Google Scholar
[68]	Teh R Y, Reid M D 2014 Phys. Rev. A 90 062337 Google Scholar
[69]	Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev. Lett. 84 2722 Google Scholar
[70]	Bowen W P, Treps N, Schnabel R, Lam P K 2002 Phys. Rev. Lett. 89 253601 Google Scholar
[71]	van Loock P, Furusawa A 2003 Phys. Rev. A 67 052315 Google Scholar
[72]	Hofmann H F, Takeuchi S 2003 Phys. Rev. A 68 032103 Google Scholar
[73]	Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633 Google Scholar
[74]	Lvovsky A I, Sander B C, Tittel W 2009 Nat. Photon. 3 706 Google Scholar
[75]	Duan L M, Monroe C 2010 Rev. Mod. Phys. 82 1209 Google Scholar
[76]	Hammerer K, Sørensen A S, Polzik E S 2010 Rev. Mod. Phys. 82 1041 Google Scholar
[77]	Sangouard N, Simon C, de Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33 Google Scholar
[78]	Wootton J R 2012 J. Mod. Opt. 59 1717 Google Scholar
[79]	Bussières F, Sangouard N, Afzelius M, de Riedmatten H, Simon C, Tittel W 2013 J. Mod. Opt. 60 1519 Google Scholar
[80]	Northup T E, Blatt R 2014 Nat. Photon. 8 356 Google Scholar
[81]	Phillips D F, Fleischhauer A, Mair A, Walsworth R L 2001 Phys. Rev. Lett. 86 783 Google Scholar
[82]	Fleischhayer M, Lukin M 2002 Phys. Rev. A 65 022314 Google Scholar
[83]	邓瑞婕, 闫智辉, 贾晓军 2017 66 074201 Google Scholar Deng R J, Yan Z H, Jia X J 2017 Acta Phys. Sin. 66 074201 Google Scholar
[84]	Julsgaard B, Sherson J, Cirac J I, Fiurasek J, Polzik E S 2004 Nature 432 482 Google Scholar
[85]	Hétet G, Longdell J J, Sellars M J, Lam P K, Buchler B C 2008 Phys. Rev. Lett. 101 203601 Google Scholar
[86]	Moiseev S, Kröll S 2001 Phys. Rev. Lett. 87 173601 Google Scholar
[87]	Fleischhauer M, Lukin M D 2000 Phys. Rev. Lett. 84 5094 Google Scholar
[88]	杨胜军 2014 博士学位论文 (合肥: 中国科学技术大学) Yang S J 2014 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[89]	Alexander A L, Longdell J J, Sellars M J, Manson N B 2006 Phys. Rev. Lett. 96 043602 Google Scholar
[90]	Ding D S, Zhang W, Zhou Z Y, Shi S, Xiang G Y, Wang X S, Jiang Y K, Shi B S, Guo G C 2015 Phys. Rev. Lett. 114 050502 Google Scholar
[91]	Simon R 2000 Phys. Rev. Lett. 84 2726 Google Scholar
[92]	温馨, 韩亚帅, 刘金玉, 白乐乐, 何军, 王军民 2018 67 024207 Google Scholar Wen X, Han Y S, Liu J Y, Bai L L, He J, Wang J M 2018 Acta Phys. Sin. 67 024207 Google Scholar
[93]	吴量, 刘艳红, 邓瑞婕, 闫智辉, 贾晓军 2017 光学学报 37 0527001 Google Scholar Wu L, Liu Y H, Deng R J, Yan Z H, Jia X J 2017 Acta Opt. Sin. 37 0527001 Google Scholar
[94]	Yokoyama S, Ukai R, Armstrong S C, Sornphiphatphong C, Kaji T, Suzuki S, Yoshikawa J, Yonezawa H, Menicucci N C, Furusawa A 2013 Nat. Photon. 7 982 Google Scholar
[95]	Roslund J, Medeiros R, Jiang S, Fabre C, Treps N 2014 Nat. Photon. 8 109 Google Scholar
[96]	Phillips N B, Gorshkov A V, Novikova I 2011 Phys. Rev. A 83 063823 Google Scholar
[97]	Lobino M, Kupchak C, Figueroa E, Lvovsky A I 2009 Phys. Rev. Lett. 102 203601 Google Scholar
[98]	Lauk N, O’Brien C, Fleischhauer M 2013 Phys. Rev. A 88 013823 Google Scholar
[99]	Barrett S D 2010 New J. Phys. 12 093032 Google Scholar
[100]	Datta A, Zhang L J, Nunn J, Langford N K, Feito A, Plenio M B, Walmsley I A 2012 Phys. Rev. Lett. 108 060502 Google Scholar
[101]	Bao X H, Reingruber A, Dietrich P, Rui J, Dück A, Strassel T, Li L, Liu N L, Zhao B, Pan J W 2012 Nat. Phys. 8 517 Google Scholar
[102]	Yang S J, Wang X J, Bao X H, Pan J W 2016 Nat. Photon. 10 381 Google Scholar
[103]	Saunders D J, Munns J H D, Champion T F M, Qiu C, Kaczmarek K T, Poem E, Ledingham P M, Walmsley A I, Nunn J 2016 Phys. Rev. Lett. 116 090501 Google Scholar
[104]	Vahlbruch H, Mehmet M, Danzmann K, Schnabel R 2016 Phys. Rev. Lett. 117 110801 Google Scholar

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