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量子纠缠是一种关键的量子资源. 随着量子信息技术的发展, 由量子通道和量子节点组成的量子网络成为研究的热点. 量子信息网络的建立需要在多个远距离的量子节点间建立纠缠, 它在分步式量子计算及量子因特网等方面有很重要的应用价值. 本文在光和原子混合纠缠的基础上, 提出了结合前馈网络建立三个独立的远程原子系综之间的连续变量确定性纠缠. 三个原子系综分别放置在三个远程的节点中, 每个节点首先通过自发拉曼散射过程制备光和原子的混合纠缠; 然后, 利用平衡零拍探测器测量三束Stokes光场干涉后的量子噪声, 并将测量的结果前馈到原子系综, 在三个独立的远距离的原子系综间建立纠缠; 最后, 利用来自三个原子系综的三束反斯托克斯光束的关联方差通过三组份不可分判据验证三个原子系综的纠缠. 该方案简单可行, 可以拓展到基于不同物理系统的量子节点, 甚至实现更多原子节点的纠缠, 从而实现大规模量子信息网络.Quantum entanglement is an essential quantum resource. With the development of quantum information science, quantum network consisting of quantum nodes and quantum channels has attracted extensive attention. The development of quantum information network requires the capability of generating, storing and distributing quantum entanglement among multiple quantum nodes. It is significant to construct the quantum information, and it has very important applications in the distributed quantum computation and quantum internet. Here we propose a simple and feasible scheme to deterministically entangle three distant atomic ensembles via the interference and feedforward network of the light-atom mixed entanglement. Firstly, three atomic ensembles placed at three remote nodes in a quantum network are prepared into the mixed entangled state of light and atomic ensembles via the spontaneous Raman scattering (SRS) process. Then, the first and second Stokes optical field are interfered on an R1∶T1 optical beam splitter (BS1), and one of the output optical fields from the first optical beam splitter is interfered with the third Stokes field on the second R2∶T2 optical beam splitter (BS2). The quantum fluctuations of the amplitude and phase quadratures of these three output optical fields from BS1 and BS2 are detected by three sets of balanced homodyne detectors, respectively. Finally, the detected signals of the amplitude and phase quadratures are fed to the three atomic ensembles via the radio frequency coils to establish the entanglement among three remote atomic ensembles. At the user-controlled time, three read optical pulses can be applied to these three atomic ensembles to convert the stored entangled state from the atomic spin waves into the anti-Stokes optical fields via the SRS process. According to the tripartite inseparability criterion, the correlation variance combinations of these three anti-Stokes optical fields can be used to verify the performance of entanglement of three atomic ensembles. This scheme can be extended to larger-scale quantum information network with different physical systems and more atomic nodes. Moreover, the entanglement distillation can be combined with this scheme to realize the entanglement among longer distance quantum nodes.
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图 1 三个原子系综确定性纠缠产生原理图
Fig. 1. Schematic diagram of deterministic entanglement generation among three atomic ensembles.
图 2 原子系综关联方差之和E1, E2, E3随光学分束片BS2的反射率R2的变化曲线 (a), (c), (e) BS1的反射率
${R_1} = 0.1,\; 0.2,\; $ $ 0.3,\; 0.5$ ; (b), (d), (f) BS1的反射率${R_1} = 0.5, {{0}}{{.7, 0}}{{.9}}$ Fig. 2. Dependence of the correlation variance combinations of atomic ensembles E1, E2, E3 on the reflectivity R2 of the second optical beam splitter BS2: (a), (c), (e) Reflectivity
${R_1} = 0.1,\; 0.2,\; 0.3, \;0.5$ of BS1; (b), (d), (f) reflectivity${R_1} = 0.5, 0.7, 0.9$ of BS1.
图 3 原子系综关联方差之和E1, E2, E3与前馈增益因子
${g_2}$ 的变化曲线 (a)${g_1} = 0.7, \;0.{8},\; 0.9, \;1.{{0}}$ 时, E1的变化曲线; (b)${g_3} = 0.{{7}},\; 0.{8},\; {{0}}{{.9}},\; 1.{{0}}$ 时, E3曲线; (c)${g_1} = 0.{{7}},\; $ $ 0.{8},\; {{0}}{{.9}},\; 1.{{0}}$ 时, E2的变化Fig. 3. Correlation variance combinations E1, E2 and E3 versus the feedforward gain factor
${g_2}$ : (a) The correlation variance combination E1 versus${g_2}$ when${g_1} = 0.{{7}},\; $ $ 0.{8}, \;{{0}}{{.9}},\; 1.{{0}}$ ; (b) the correlation variance combinations E3 versus${g_2}$ when${g_3} = 0.{{7}},\; 0.{8}, \;{{0}}{{.9}},\; 1.{{0}}$ ; (c) the correlation variance combinations E2 versus${g_2}$ when${g_{1}} = 0.{{7}},\; 0.{8}, $ $ {{0}}{{.9}},\; 1.{{0}}$ . -
[1] Braunstein S L, van Loock P 2005 Rev. Mod. Phys. 77 513
Google Scholar
[2] Pan J W, Chen Z B, Lu C Y, Weinfurter H, Zeilinger A, Żukowski M 2012 Rev. Mod. Phys. 84 777
Google Scholar
[3] Kimble H J 2008 Nature 453 1023
Google Scholar
[4] Hosseini M, Sparkes B M, Campbell G, Lam P K, Buchler B C 2011 Nat. Commun. 2 174
Google Scholar
[5] Parigi V, D'Ambrosio V, Arnold C, Marrucci L, Sciarrino F, Laurat J 2015 Nat. Commun. 6 7706
Google Scholar
[6] Yan Z H, Jia X J 2017 Quantum Sci. Technol. 2 024003
Google Scholar
[7] 邓瑞婕, 闫智辉, 贾晓军 2017 物理学报 66 074201
Google Scholar
Deng R J, Yan Z H, Jia X J 2017 Acta Phys. Sin. 66 074201
Google Scholar
[8] 刘艳红, 吴量, 闫智辉, 贾晓军, 彭堃墀 2019 物理学报 68 034202
Google Scholar
Liu Y H, Wu L, Yan Z H, Jia X J, Peng K C 2019 Acta Phys. Sin. 68 034202
Google Scholar
[9] Pu Y F, Jiang N, Chang W, Yang H X, Li C, Duan L M 2017 Nat. Commun. 8 15359
Google Scholar
[10] 闫妍, 李淑静, 田龙, 王海 2016 物理学报 65 014205
Google Scholar
Yan Y, Li S J, Tian L, Wang H 2016 Acta Phys. Sin. 65 014205
Google Scholar
[11] Specht H P, Nölleke C, Reiserer A, Uphoff M, Figueroa E, Ritter S, Rempe G 2011 Nature 473 190
Google Scholar
[12] Facon A, Dietsche E K, Grosso D, Haroche S, Raimond J M, Brune M, Gleyzes S 2016 Nature 535 262
Google Scholar
[13] Langer C, Ozeri R, Jost J D, Chiaverini J, DeMarco B, Ben-Kish A, Blakestad R B, Britton J, Hume D B, Itano W M, Leibfried D, Reichle R, Rosenband T, Schaetz T, Schmidt P O, Wineland D J 2005 Phys. Rev. Lett. 95 060502
Google Scholar
[14] Stute A, Casabone B, Schindler P, Monz T, Schmidt P O, Brandstätter B, Northup T E, Blatt R 2012 Nature 485 482
Google Scholar
[15] Hucul D, Inlek I V, Vittorini G, Crocker C, Debnath S, Clark S M, Monroe C 2015 Nature Phys. 11 37
Google Scholar
[16] Fiore V, Yang Y, Kuzyk M C, Barbour R, Tian L, Wang H 2011 Phys. Rev. Lett. 107 133601
Google Scholar
[17] Lee H, Suh M G, Chen T, Li J, Diddams S A, Vahala K J 2013 Nat. Commun. 4 2468
Google Scholar
[18] 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
[19] Riedinger R, Wallucks A, Marinković I, Löschnauer C, Aspelmeyer M, Hong S, Gröblacher S 2018 Nature 556 473
Google Scholar
[20] Kiesewetter S, Teh R Y, Drummond P D, Reid M D 2017 Phys. Rev. Lett. 119 023601
Google Scholar
[21] Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys. Rev. Lett. 114 090503
Google Scholar
[22] Axline C J, Burkhart L D, Pfaff W, Zhang M Z, Chou K, Campagne-Ibarcq P, Reinhold P, Frunzio L, Girvin S M, Jiang L, Devoret M H, Schoelkopf R J 2018 Nature Phys. 14 705
Google Scholar
[23] Kurpiers P, Magnard P, Walter T, Royer B, Pechal M, Heinsoo J, Salathé Y, Akin A, Storz S, Besse J C, Gasparinetti S, Blais A, Wallraff A 2018 Nature 558 264
Google Scholar
[24] Clausen C, Usmani I, Bussières F, Sangouard N, Afzelius M, de Riedmatten H, Gisin N 2011 Nature 469 508
Google Scholar
[25] Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussières F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512
Google Scholar
[26] Zhong M, Hedges M P, Ahlefeldt R L, Bartholomew J G, Beavan S E, Wittig S M, Longdell J J, Sellars M J 2015 Nature 517 177
Google Scholar
[27] Gao W B, Fallahi P, Togan E, Miguel-Sanchez J, Imamoglu A 2012 Nature 491 426
Google Scholar
[28] Chou C W, de Riedmatten H, Felinto D, Polyakov S V, van Enk S J, Kimble H J 2005 Nature 438 828
Google Scholar
[29] Chanelière T, Matsukevich D N, Jenkins S D, Lan S Y, Kennedy T A B, Kuzmich A 2005 Nature 438 833
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[34] Pfaff W, Hensen B J, Bernien H, van Dam S B, Blok M S, Taminiau T H, Tiggelman M J, Schouten R N, Markham M, Twitchen D J, Hanson R 2014 Science 345 532
Google Scholar
[35] Yuan Z S, Chen Y A, Zhao B, Chen S, Schmiedmayer J, Pan J W 2008 Nature 454 1098
Google Scholar
[36] Julsgaard B, Kozhekin A, Polzik E S 2001 Nature 413 400
Google Scholar
[37] 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
[38] Liu Y H, Yan Z H, Jia X J, Xie C D 2016 Sci. Rep. 6 25715
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] Jing B, Wang X J, Yu Y, Sun P F, Jiang Y, Yang S J, Jiang W H, Luo X Y, Zhang J, Jiang X, Bao X H, Pan J W 2019 Nature Photon. 13 210
Google Scholar
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Google Scholar
[42] 闫智辉, 贾晓军, 谢常德, 彭堃墀 2012 物理学报 61 014206
Google Scholar
Yan Z H, Jia X J, Xie C D, Peng K C 2012 Acta Phys. Sin. 61 014206
Google Scholar
[43] 周瑶瑶, 田剑锋, 闫智辉, 贾晓军 2019 物理学报 68 064205
Google Scholar
Zhou Y Y, Tian J F, Yan Z H, Jia X J 2019 Acta Phys. Sin. 68 064205
Google Scholar
[44] Duan L M, Giedke G, Cirac J I, Zoller P 2000 Phys. Rev. Lett. 84 2722
Google Scholar
[45] Simon R 2000 Phys. Rev. Lett. 84 2726
Google Scholar
[46] Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413
Google Scholar
[47] Yang S J, Wang X J, Bao X H, Pan J W 2016 Nature Photon. 10 381
Google Scholar
[48] Maring N, Farrera P, Kutluer K, Mazzera M, Heinze G, de Riedmatten H 2017 Nature 551 485
Google Scholar
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