Establishing of quantum entanglement among three atomic nodes via spontanenous Raman scattering

Liu Yan-Hong; Zhou Yao-Yao; Yan Zhi-Hui; Jia Xiao-Jun

doi:10.7498/aps.70.20201299

Abstract

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.

Keywords:

Authors and contacts

1.
Department of Physics, Taiyuan Normal University, Jinzhong 030619, China
2.
Institute of Computational and Applied Physics, Taiyuan Normal University, Jinzhong 030619, China
3.
Institute of Opto-Electronics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan 030006, China
4.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

Corresponding author: Liu Yan-Hong, 15135111277@163.com

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0301402), the National Natural Science Foundation of China (Grant Nos. 61775127, 61925503, 11904218, 11804246, 12004276), the Scientific and Technological Programs of Higher Education Institutions in Shanxi, China (Grant No. 2020L0516), the Program for Sanjin Scholars of Shanxi Province, China, the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, China, the Fund for Shanxi “1331Project” Key Subjects Construction, China, and the Natural Science Foundation of Shanxi Province, China (Grant No. 201901D111293)

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References

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[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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[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

Cited By

图 1 三个原子系综确定性纠缠产生原理图

Figure 1. Schematic diagram of deterministic entanglement generation among three atomic ensembles.

DownLoad: Full-Size Img PowerPoint

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}}$

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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}}$.

DownLoad: Full-Size Img PowerPoint

map

[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 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 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 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
[30]	Eisaman M D, André A, Massou F, Fleischhauer M, Zibrov A S, Lukin M D 2005 Nature 438 837 Google Scholar
[31]	Ritter S, Nölleke C, Hahn C, Reiserer A, Neuzner A, Upho M, Mücke M, Figueroa E, Bochmann J, Rempe G 2012 Nature 484 195 Google Scholar
[32]	Moehring D L, Maunz P, Olmschenk S, Younge K C, Matsukevich D N, Duan L M, Monroe C 2007 Nature 449 68 Google Scholar
[33]	Usmani I, Clausen C, Bussières F, Sangouard N, Afzelius M, Gisin N 2012 Nature Photon. 6 234 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
[41]	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
[42]	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
[43]	周瑶瑶, 田剑锋, 闫智辉, 贾晓军 2019 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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