-
多体量子系统的相互作用是研究量子信息科学必须要解决的瓶颈性问题之一. 里德堡(Rydberg)原子具有很大的电偶极矩, 使得它可以实现长程的相互作用, 为研究多体量子物理提供了有力的技术手段. 因而Rydberg原子多体系统是多体相互作用探究的理想平台, Rydberg原子多体相互作用的研究对多体量子系统的相互作用的性质研究和应用探究有着重要意义. 本文综述了关于Rydberg原子多体相互作用方面的研究, 介绍了由Rydberg原子的多体相互作用引起的Rydberg阻塞效应、Rydberg原子多体系统拉比频率的变化以及Rydberg原子多体系统呈现的特别的空间构型; 同时介绍了利用Rydberg原子多体相互作用实现一些应用的工作, 如实现单光子源、量子存储、实时单原子成像以及量子模拟等, 并讨论了Rydberg原子多体系统的研究方向和应用前景.The interaction of many-body quantum system is a critical problem to be solved in the field of quantum information science. Rydberg atoms have large dipole moment, enabling them to interact with others in a long range, thereby offering us a powerful tool for studying many-body quantum physics. Meanwhile, atoms in the ground state are stable, which makes it easy to manipulate them. Therefore, Rydberg-atom many-body system is an ideal platform for studying the interaction of many-body quantum system. Studies of Rydberg-atom many-body system may contribute to understanding the properties of many-body system and putting the interaction of many-body quantum system into practical applications. In this review, we introduce some studies of properties of interaction of Rydberg-atom many-body system, including the Rydberg excitation blockade, the variation of Rabi frequencies of the many-body system and special spatial distribution of Rydberg atoms in a many-body system. Firstly, the Rydberg excitation blockade, the most important property in the Rydberg-atom many-body system, indicates that atoms’ excitation will be suppressed in a certain range around one Rydberg excitation because the interaction between the Rydberg excitation and atoms leads the energy level to shift so that atoms cannot be excited by the same pulse. Secondly, there is a collective Rabi frequency in the system, which is proportional to the square of the number of atoms in the suppressed area. And additionally, because of the Rydberg blockade effect, Rydberg excitations in the ensemble cannot be at casual positions but a regular distribution is formed. Besides the studies of properties, several researches on the applications of interaction of Rydberg-atom many-body system are introduced, including single-photon source, quantum storage, single-atom imaging, quantum simulation, etc. These applications contribute to the development of quantum community and quantum computing, which may bring us a quantum-technology time. Finally, we discuss the future development of Rydberg-atom many-body system and its further applications. Further development includes the development of many-body system with a larger number of atoms, the development of many-body system of atoms with more than one electron, and some other specific subjects based on many-system, such as Rydberg dimer and topological phase. Also some promising applications such as in studying optimization problem by quantum annealing, may become true.
-
Keywords:
- Rydberg /
- many-body system /
- long-range interaction /
- excitation blockade
[1] Gaëtan A, Miroshnychenko Y, Wilk T, Chotia A, Viteau M, Comparat D, Pillet P, Browaeys A, Grangier P 2009 Nat. Phys. 5 115
Google Scholar
[2] Dudin Y O, Li L, Bariani F, Kuzmich A 2012 Nat. Phys. 8 790
Google Scholar
[3] Schauß P, Cheneau M, Endres M, Fukuhara T, Hild S, Omran A, Pohl T, Gross C, Kuhr S, Bloch I 2012 Nature 491 87
Google Scholar
[4] Li L, Kuzmich A 2016 Nat. Commun. 7 13618
Google Scholar
[5] Maxwell D, Szwer D J, Paredes-Barato D, Busche H, Pritchard J D, Gauguet A, Weatherill K J, Jones M P A, Adams C S 2013 Phys. Rev. Lett. 110 103001
Google Scholar
[6] Günter G, Robert-de-Saint-Vincent M, Schempp H, Hofmann C S, Whitlock S, Weidemüller M 2012 Phys. Rev. Lett. 108 013002
Google Scholar
[7] Murray C R, Mirgorodskiy I, Tresp C, Braun C, Paris-Mandoki A, Gorshkov A V, Hofferberth S, Pohl T 2018 Phys. Rev. Lett. 120 113601
Google Scholar
[8] Keesling A, Omran A, Levine H, Bernien H, Pichler H, Choi S, Samajdar R, Schwartz S, Silvi P, Sachdev S, Zoller P, Endres M, Greiner M, Vuletić V, Lukin M D 2019 Nature 568 207
Google Scholar
[9] Bernien H, Schwartz S, Keesling A, Levine H, Omran A, Pichler H, Choi S, Zibrov A S, Endres M, Greiner M, Vuletić V, Lukin M D 2017 Nature 551 579
Google Scholar
[10] Ding D S, Busche H, Shi B S, Guo G C, Adams C S 2020 Phys. Rev. X 10 021023
[11] Gallagher T F 1994 Rydberg Atoms (Cambridge: Cambridge University Press) p25
[12] Christoph T 2017 Ph. D. Dissertation (Stuttgart: University of Stuttgart. Physical Institute)
[13] Gallagher T F 1988 Rep. Prog. Phys. 51 143
[14] Gallagher T F, Cooke W E 1979 Phys. Rev. Lett. 42 835
Google Scholar
[15] Cooke W E, Gallagher T F 1980 Phys. Rev. A 21 588
[16] Born M, Oppenheimer J R 1927 Ann. Phys. 84 457
[17] Thomas A 2008 Ph. D. Dissertation (Freiburg city: Faculty of Mathematics and Physics Albert Ludwigs University of Freiburg)
[18] Browaeys A, Lahaye T 2020 Nat. Phys. 16 132
Google Scholar
[19] Balewski J B, Krupp A T, Gaj A, Hofferberth S, Löw R, Pfau T 2014 New J. Phys. 16 063012
Google Scholar
[20] Zeiher J, Schauß P, Hild S, Macrì T, Bloch I, Gross C 2015 Phys. Rev. X 5 031015
[21] Tuchendler C, Lance A M, Browaeys A, Sortais Y R P, Grangier P 2018 arXiv:0805.3510 v2 [quant-ph]
[22] Labeyrie G, Muller C A, Delande D, Miniatura C, Wilkowski D, Kaiser R 2003 Phys. Rev. Lett. 91 223904
Google Scholar
[23] Robicheaux F, Hernández J V 2005 Phys. Rev. A 72 063403
Google Scholar
[24] 马文淦 2001 计算物理学 (合肥: 中国科学技术大学出版社) 第59页
Ma W G 2001 Computational Physics (Hefei: Press of University of Science and Technology of China) p59
[25] White S R 1992 Phys. Rev. Lett. 69 2863
Google Scholar
[26] TRG Algorithm, Hubig C, Schollwöck U http://tensornetwork. org/trg/ [2020-8-10]
[27] Liao H J, Liu J G, Wang L, Xiang T 2019 Phys. Rev. X 9 031041
[28] Wang H, He Y M, Chung T H, Hu H, Ying Y, Chen S, Ding X, Chen M C, Qin J, Yang X, Liu R Z, Duan Z C, Li J P, Gerhardt S, Winkler K, Jurkat J, Wang L J, Gregersen N, Huo Y H, Dai Q, Yu S, Höfling S, Lu Z Y, Pan J W 2019 Nat. Photonics 13 770
Google Scholar
[29] Chen S, Chen Y A, Strassel T, Yuan Z S, Zhao B, Schmiedmayer J, Pan J W 2006 Phys. Rev. Lett. 97 173004
Google Scholar
[30] Dudin Y O, Kuzmich A 2012 Science 336 887
Google Scholar
[31] Liu J, Zhou Y, Wang W, Liu R, He K, Li F, Xu Z 2013 Opt. Express 21 19209
Google Scholar
[32] Barbieri M, Roccia E, Mancino L, Sbroscia M, Gianani I, Sciarrino F 2017 Sci. Rep. 7 7247
Google Scholar
[33] Lvovsky A I, Sanders B C, Tittel W 2009 Nat. Photonics 3 706
Google Scholar
[34] Hua Y L, Zhou Z Q, Li C F, Guo G C 2018 Chin. Phys. B 27 020303
Google Scholar
[35] 窦建鹏, 李航, 庞晓玲, 张超妮, 杨天怀, 金贤敏 2019 物理学报 68 030307
Google Scholar
Dou J P, Li H, Pang X L, Zhang C N, Yang T H, Jin X M 2019 Acta Phys. Sin. 68 030307
Google Scholar
[36] Gisin N, Thew R 2007 Nat. Photonics 1 165
Google Scholar
[37] Jin X M, Ren J G, Yang B, Yi Z H, Zhou F, Xu X F, Wang S K, Yang D, Hu Y F, Jiang S, Yang T, Yin H, Chen K, Peng C Z, Pan J W 2010 Nat. Photonics 4 376
Google Scholar
[38] Yuan Z S, Chen Y A, Zhao B, Chen S, Schmiedmayer J, Pan J W 2008 Nature 454 1098
Google Scholar
[39] Bernien H, Hensen B, Pfaff W, Koolstra G, Blok M S, Robledo L, Taminian T H, Markham M, Twitchen D J, Childress L, Hanson R 2013 Nature 497 86
Google Scholar
[40] Wasilewski W, Jensen K, Krauter H, Renema J J, Balabas M V, Polzik E S 2010 Phys. Rev. Lett. 104 133601
Google Scholar
[41] Biedermann G W, McGuinness H J, Rakholia A V, Jau Y Y, Wheeler D R, Sterk J D, Burns G R 2017 Phys. Rev. Lett. 118 163601
Google Scholar
[42] Zhang H, Jin X M, Yang J, Dai H N, Yang S J, Zhao T M, Rui J, He Y, Jiang X, Yang F, Pan G S, Yuan Z S, Deng Y J, Chen Z B, Bao X H, Chen S, Zhao B, Pan J W 2011 Nat. Photonics 5 628
Google Scholar
[43] Chen Y H, Lee M J, Wang I C, Du S W, Chen Y F, Chen Y C, Yu I A 2013 Phys. Rev. Lett. 110 083601
Google Scholar
[44] Fleischhauer M, Lukin M D 2002 Phys. Rev. A 65 022314
Google Scholar
[45] Fleischhauer M, Imamogu A, Marrangos J P 2005 Rev. Mod. Phys. 77 633
Google Scholar
[46] Mirgorodskiy I, Christaller F, Braun C, Paris-Mandoki A, Tresp C, Hofferberth S 2017 Phys. Rev. A 96 011402
Google Scholar
[47] Distante E, Padrón-Brito A, Cristiani M, Paredes-Barato D, Riedmatten H 2016 Phys. Rev. Lett. 117 113001
Google Scholar
[48] Betzig E, Chichester R J 1993 Science 262 1422
Google Scholar
[49] Pan S H, Hudson E W, Lang K M, Eisaki H, Uchida S, Davis J C 2000 Nature 403 746
Google Scholar
[50] Häffner H, Hänsel W, Roos C F, Benhelm J, Chen-al-kar D, Chwalla M, Körber T, Rapol U D, Riebe M, Schmidt P O, Becher C, Gühne O, Dür W, Blatt R 2005 Nature 438 643
Google Scholar
[51] Nelson K D, Li X, Weiss D S 2007 Nat. Phys. 3 556
Google Scholar
[52] Bakr W S, Gillen J I, Peng A, Fölling S, Greiner M 2009 Nature 462 74
Google Scholar
[53] Sherson J F, Weitenberg C, Endres M, Cheneau M, Bloch I, Kuhr S 2010 Nature 467 68
Google Scholar
[54] Brahms N, Purdy T P, Brooks D W C, Botter T, Stamper-Kurn D M 2011 Nat. Phys. 7 604
Google Scholar
[55] Gericke T, Würtz P, Reitz D, Langen T, Ott H 2008 Nat. Phys. 4 949
Google Scholar
[56] Zipkes C, Palzer S, Sias C, Köhl M 2010 Nature 464 388
Google Scholar
[57] Verstraete F, Wolf M M, Ciac J I 2009 Nat. Phys. 5 633
Google Scholar
[58] Barreiro J T, Müller M, Schindler P, Nigg D, Monz T, Chwalla M, Hennrich M, Roos C F, Zoller P, Blatt R 2011 Nature 470 486
Google Scholar
[59] Lim K, Suh C, Rhee J K K 2019 Quantum Inf. Process 18 73
Google Scholar
[60] Tresp C, Zimmer C, Mirgorodskiy I, Gorniaczyk H, Paris-Mandoki A, Hofferberth S 2016 Phys. Rev. Lett. 117 223001
Google Scholar
[61] Honer J, Löw R, Weimer H, Pfau T, Büchler H P 2011 Phys. Rev. Lett. 107 093601
Google Scholar
[62] Trenkwalder A, Spagnolli G, Semeghini G, Coop S, Landini M, Castilho P, Pezzè L, Modugno G, Inguscio M, Smerzi A, Fattori M 2016 Nat. Phys. 12 826
Google Scholar
[63] Labuhn H, Barredo D, Ravets S, Léséleuc S, Macri T, Lahaye T, Browaeys A 2016 Nature 534 667
Google Scholar
[64] Helmrich S, Arias A, Lochead G, Wintermatel T M, Bochhold M, Diehl S, Whitlock S 2020 Nature 577 481
Google Scholar
[65] Bloch I, Dalibard J, Nascimbène S 2012 Nat. Phys. 8 267
Google Scholar
[66] Yan B, Moses S A, Gadway B, Covey J P, Hazzard K R A, Rey A M, Jin D S, Ye J 2013 Nature 501 521
Google Scholar
[67] Blatt R, Roos C F 2012 Nat. Phys. 8 277
Google Scholar
[68] Lucas A 2014 Front. Phys. 2 5
[69] O’Shea D, Junge C, Volz J, Rauschenbeutel A 2013 Phys. Rev. Lett. 111 193601
Google Scholar
[70] Bajcsy M, Hofferberth S, Balic V, Peyronel T, Hafezi M, Zibrov A S, Vuletic V, Lukin M D 2009 Phys. Rev. Lett. 102 203902
Google Scholar
[71] Chen W, Beck K M, Gullans M, Lukin M D, Tanji-Suzuki H, Vuletic V 2013 Science 341 768
Google Scholar
[72] Volz T, Reinhard A, Winger M, Badolato A, Hennessy K J, Hu E L, Imamoglu A 2012 Nat. Photonics 6 76
Google Scholar
[73] Garcia-Escartin J C, Chamorro-Posada P 2012 Phys. Rev. A 85 032309
Google Scholar
[74] Baur S, Tiarks D, Rempe G, Dürr S 2014 Phys. Rev. Lett. 112 073901
Google Scholar
[75] Li W, Lesanovsky I 2015 Phys. Rev. A 92 043828
[76] Yu Y C, Dong M X, Ye Y H, Guo G C, Ding D S, Shi B S 2020 Sci. China Phys. Mech. Astron. 63 110312
[77] Chang D E, Sørensen A S, Demler E A, Lukin M D 2007 Nat. Phys. 3 807
Google Scholar
[78] Tiarks D, Baur S, Schneider K, Dürr S, Rempe G 2014 Phys. Rev. Lett. 113 053602
Google Scholar
[79] Gorniaczyk H, Tresp C, Schmidt J, Fedder H, Hofferberth S 2014 Phys. Rev. Lett. 113 053601
Google Scholar
[80] Gorniaczyk H, Tresp C, Bienias P, Paris-Mandoki A, Li W, Mirgorodskiy I, Büchler H P, Lesanovsky I, Hofferberth S 2016 Nat. Commun. 7 12480
Google Scholar
[81] Hao Y M, Lin G W, Lin X M, Niu Y P, Gong S Q 2019 Sci. Rep. 9 4723
[82] Norcia M A, Young A W, Kaufman A M 2018 Phys. Rev. X 8 041054
[83] Saskin S, Wilson J T, Grinkenmeyer B, Tomson J D 2019 Phys. Rev. Lett. 122 143002
Google Scholar
[84] Bendkowsky V, Butscher B, Nipper J, Shaffer J P, Löw R, Pfau T 2009 Nature 458 1005
Google Scholar
[85] Tallant J, Rittenhouse S T, Booth D, Sadeghpour H R, Shaffer J P 2012 Phys. Rev. Lett. 109 173202
Google Scholar
[86] Desalvo B J, Aman J A, Dunning F B, Killian T C, Sadeghpour H R, Yoshida S, Burgdörfer J 2015 Phys. Rev. A 92 031403
Google Scholar
[87] Dauphin A, Müller M, Martin-Delgado M A 2012 Phys. Rev. A 86 053618
Google Scholar
[88] Li X, Sarma S D 2015 Nat. Commun. 6 7137
Google Scholar
[89] Gorshkov A V, Nath R, Pohl T 2013 Phys. Rev. Lett. 110 153601
Google Scholar
[90] Otterbach J, Moos M, Muth D, Fleischhauer M 2013 Phys. Rev. Lett. 111 113001
Google Scholar
[91] Glaetzle A W, van Bijnen R M W, Zoller P, Lechner W A 2017 Nat. Commun. 8 15813
Google Scholar
[92] Pichler H, Wang S, Zhou L, Choi S, Lukin M D 2018 arXiv:1808.10816 [quant-ph]
[93] Kokail C, Maier C, Bijnen R, Brydges T, Joshi M K, Jurcevic P, Muschik C A, Silvi P, Blatt R, Roos C F, Zoller P 2019 Nature 569 355
Google Scholar
-
图 2 存在频率失谐时的双原子系统能量示意图 (a) 当
$\varDelta > 0$ 且${\rm d}U/{\rm d}R > 0$ 时双原子系统的能量; (b) 不同频率失谐和势能情况下双原子系统的能量[19]Fig. 2. Schematic of binary Rydberg energy with detuning: (a) The energy of a pair of atoms with
$\varDelta > 0$ and${\rm d}U/{\rm d}R > 0$ ; (b) the energy of a pair of atoms with different detuning and potentials[19].图 6 单光子源性质参数 (a)
${g^{\left( 2 \right)}}\left( 0 \right)$ 与有效主量子数n*关系[30], 内插图为重合光子计数与延时关系[30]; (b) 量子点方案中归一化的重合光子计数与延时关系[28]; (c) 量子点方案中平行和交叉极化情况下Hong-Ou-Mandel干涉归一化的重合光子计数与延时关系[28]Fig. 6. Parameters of single-photon source: (a)
${g^{\left( 2 \right)}}\left( 0 \right)$ as a function of effective principle quantum number[30]. Coincidence count as a function of time decay is showed in the inset[30]; (b) normalized coincidence count as a function of time decay using quantum dots[28]; (c) normalized coincidence count of Hong-Ou-Mandel interference as a function of time decay with parallel and cross polarization respectively using quantum dots[28].图 11 相图[10]和自组织行为[64] (a) Rydberg原子密度相图; (b) 没有控制光时EIT相图; (c) 自组织演化; (d) 自组织定态规律
Fig. 11. phase diagram[10] and self-organized behaviors[64]: (a) Phase diagram of density of Rydberg atom; (b) EIT phase diagram without control light; (c) evolution in the self-organized process; (d) regulation of self-organized stationary states.
图 12 二维量子模拟[63] (a) 不同原子数的集体拉比振荡; (b) 20个原子系统的Rydberg分数
${f_{\rm R}}$ 变化; (c) 28个原子系统的Rydberg分数${f_{\rm R}}$ 变化Fig. 12. Quantum simulation in two dimensions[63]: (a) Collective Rabi oscillation with different number of atoms; (c) Rydberg fraction of the systems with 20 atoms; (d) Rydberg fraction of the systems with 28 atoms.
图 13 一维多原子量子模拟[9] (a) 不同相互作用强度的演化理论结果; (b) 不同相互作用强度的演化实验结果; (c) 基态概率与系统大小的关系; (d) 出现次数的状态数的统计
Fig. 13. Many-atom quantum simulation in one dimension[9]: (a) Predicted results of evolution with different interaction; (b) experimental results of evolution with different interaction; (c) ground-state probability as a function of system size; (d) number of states with identical number of occurrences.
表 1 Rydberg原子的性质和主量子数的关系[11].
Table 1. Relation between the properties of Rydberg atom and its principal quantum number[11].
性质 与主量子数关系 Na(10 d) 束缚能 n–2 0.14 eV 相邻n态间的能量差 n–3 0.023 eV 轨道半径 n2 147a0 几何截面 n4 68000$a_0^2$ 偶极矩$\left\langle {nd\left| {er} \right|\left. {nf} \right\rangle } \right.$ n2 143ea0 极化率 n7 0.21 MHz·cm2·V–2 辐射寿命 n3 1.0 μs 精细结构间隔 n–3 –92 MHz -
[1] Gaëtan A, Miroshnychenko Y, Wilk T, Chotia A, Viteau M, Comparat D, Pillet P, Browaeys A, Grangier P 2009 Nat. Phys. 5 115
Google Scholar
[2] Dudin Y O, Li L, Bariani F, Kuzmich A 2012 Nat. Phys. 8 790
Google Scholar
[3] Schauß P, Cheneau M, Endres M, Fukuhara T, Hild S, Omran A, Pohl T, Gross C, Kuhr S, Bloch I 2012 Nature 491 87
Google Scholar
[4] Li L, Kuzmich A 2016 Nat. Commun. 7 13618
Google Scholar
[5] Maxwell D, Szwer D J, Paredes-Barato D, Busche H, Pritchard J D, Gauguet A, Weatherill K J, Jones M P A, Adams C S 2013 Phys. Rev. Lett. 110 103001
Google Scholar
[6] Günter G, Robert-de-Saint-Vincent M, Schempp H, Hofmann C S, Whitlock S, Weidemüller M 2012 Phys. Rev. Lett. 108 013002
Google Scholar
[7] Murray C R, Mirgorodskiy I, Tresp C, Braun C, Paris-Mandoki A, Gorshkov A V, Hofferberth S, Pohl T 2018 Phys. Rev. Lett. 120 113601
Google Scholar
[8] Keesling A, Omran A, Levine H, Bernien H, Pichler H, Choi S, Samajdar R, Schwartz S, Silvi P, Sachdev S, Zoller P, Endres M, Greiner M, Vuletić V, Lukin M D 2019 Nature 568 207
Google Scholar
[9] Bernien H, Schwartz S, Keesling A, Levine H, Omran A, Pichler H, Choi S, Zibrov A S, Endres M, Greiner M, Vuletić V, Lukin M D 2017 Nature 551 579
Google Scholar
[10] Ding D S, Busche H, Shi B S, Guo G C, Adams C S 2020 Phys. Rev. X 10 021023
[11] Gallagher T F 1994 Rydberg Atoms (Cambridge: Cambridge University Press) p25
[12] Christoph T 2017 Ph. D. Dissertation (Stuttgart: University of Stuttgart. Physical Institute)
[13] Gallagher T F 1988 Rep. Prog. Phys. 51 143
[14] Gallagher T F, Cooke W E 1979 Phys. Rev. Lett. 42 835
Google Scholar
[15] Cooke W E, Gallagher T F 1980 Phys. Rev. A 21 588
[16] Born M, Oppenheimer J R 1927 Ann. Phys. 84 457
[17] Thomas A 2008 Ph. D. Dissertation (Freiburg city: Faculty of Mathematics and Physics Albert Ludwigs University of Freiburg)
[18] Browaeys A, Lahaye T 2020 Nat. Phys. 16 132
Google Scholar
[19] Balewski J B, Krupp A T, Gaj A, Hofferberth S, Löw R, Pfau T 2014 New J. Phys. 16 063012
Google Scholar
[20] Zeiher J, Schauß P, Hild S, Macrì T, Bloch I, Gross C 2015 Phys. Rev. X 5 031015
[21] Tuchendler C, Lance A M, Browaeys A, Sortais Y R P, Grangier P 2018 arXiv:0805.3510 v2 [quant-ph]
[22] Labeyrie G, Muller C A, Delande D, Miniatura C, Wilkowski D, Kaiser R 2003 Phys. Rev. Lett. 91 223904
Google Scholar
[23] Robicheaux F, Hernández J V 2005 Phys. Rev. A 72 063403
Google Scholar
[24] 马文淦 2001 计算物理学 (合肥: 中国科学技术大学出版社) 第59页
Ma W G 2001 Computational Physics (Hefei: Press of University of Science and Technology of China) p59
[25] White S R 1992 Phys. Rev. Lett. 69 2863
Google Scholar
[26] TRG Algorithm, Hubig C, Schollwöck U http://tensornetwork. org/trg/ [2020-8-10]
[27] Liao H J, Liu J G, Wang L, Xiang T 2019 Phys. Rev. X 9 031041
[28] Wang H, He Y M, Chung T H, Hu H, Ying Y, Chen S, Ding X, Chen M C, Qin J, Yang X, Liu R Z, Duan Z C, Li J P, Gerhardt S, Winkler K, Jurkat J, Wang L J, Gregersen N, Huo Y H, Dai Q, Yu S, Höfling S, Lu Z Y, Pan J W 2019 Nat. Photonics 13 770
Google Scholar
[29] Chen S, Chen Y A, Strassel T, Yuan Z S, Zhao B, Schmiedmayer J, Pan J W 2006 Phys. Rev. Lett. 97 173004
Google Scholar
[30] Dudin Y O, Kuzmich A 2012 Science 336 887
Google Scholar
[31] Liu J, Zhou Y, Wang W, Liu R, He K, Li F, Xu Z 2013 Opt. Express 21 19209
Google Scholar
[32] Barbieri M, Roccia E, Mancino L, Sbroscia M, Gianani I, Sciarrino F 2017 Sci. Rep. 7 7247
Google Scholar
[33] Lvovsky A I, Sanders B C, Tittel W 2009 Nat. Photonics 3 706
Google Scholar
[34] Hua Y L, Zhou Z Q, Li C F, Guo G C 2018 Chin. Phys. B 27 020303
Google Scholar
[35] 窦建鹏, 李航, 庞晓玲, 张超妮, 杨天怀, 金贤敏 2019 物理学报 68 030307
Google Scholar
Dou J P, Li H, Pang X L, Zhang C N, Yang T H, Jin X M 2019 Acta Phys. Sin. 68 030307
Google Scholar
[36] Gisin N, Thew R 2007 Nat. Photonics 1 165
Google Scholar
[37] Jin X M, Ren J G, Yang B, Yi Z H, Zhou F, Xu X F, Wang S K, Yang D, Hu Y F, Jiang S, Yang T, Yin H, Chen K, Peng C Z, Pan J W 2010 Nat. Photonics 4 376
Google Scholar
[38] Yuan Z S, Chen Y A, Zhao B, Chen S, Schmiedmayer J, Pan J W 2008 Nature 454 1098
Google Scholar
[39] Bernien H, Hensen B, Pfaff W, Koolstra G, Blok M S, Robledo L, Taminian T H, Markham M, Twitchen D J, Childress L, Hanson R 2013 Nature 497 86
Google Scholar
[40] Wasilewski W, Jensen K, Krauter H, Renema J J, Balabas M V, Polzik E S 2010 Phys. Rev. Lett. 104 133601
Google Scholar
[41] Biedermann G W, McGuinness H J, Rakholia A V, Jau Y Y, Wheeler D R, Sterk J D, Burns G R 2017 Phys. Rev. Lett. 118 163601
Google Scholar
[42] Zhang H, Jin X M, Yang J, Dai H N, Yang S J, Zhao T M, Rui J, He Y, Jiang X, Yang F, Pan G S, Yuan Z S, Deng Y J, Chen Z B, Bao X H, Chen S, Zhao B, Pan J W 2011 Nat. Photonics 5 628
Google Scholar
[43] Chen Y H, Lee M J, Wang I C, Du S W, Chen Y F, Chen Y C, Yu I A 2013 Phys. Rev. Lett. 110 083601
Google Scholar
[44] Fleischhauer M, Lukin M D 2002 Phys. Rev. A 65 022314
Google Scholar
[45] Fleischhauer M, Imamogu A, Marrangos J P 2005 Rev. Mod. Phys. 77 633
Google Scholar
[46] Mirgorodskiy I, Christaller F, Braun C, Paris-Mandoki A, Tresp C, Hofferberth S 2017 Phys. Rev. A 96 011402
Google Scholar
[47] Distante E, Padrón-Brito A, Cristiani M, Paredes-Barato D, Riedmatten H 2016 Phys. Rev. Lett. 117 113001
Google Scholar
[48] Betzig E, Chichester R J 1993 Science 262 1422
Google Scholar
[49] Pan S H, Hudson E W, Lang K M, Eisaki H, Uchida S, Davis J C 2000 Nature 403 746
Google Scholar
[50] Häffner H, Hänsel W, Roos C F, Benhelm J, Chen-al-kar D, Chwalla M, Körber T, Rapol U D, Riebe M, Schmidt P O, Becher C, Gühne O, Dür W, Blatt R 2005 Nature 438 643
Google Scholar
[51] Nelson K D, Li X, Weiss D S 2007 Nat. Phys. 3 556
Google Scholar
[52] Bakr W S, Gillen J I, Peng A, Fölling S, Greiner M 2009 Nature 462 74
Google Scholar
[53] Sherson J F, Weitenberg C, Endres M, Cheneau M, Bloch I, Kuhr S 2010 Nature 467 68
Google Scholar
[54] Brahms N, Purdy T P, Brooks D W C, Botter T, Stamper-Kurn D M 2011 Nat. Phys. 7 604
Google Scholar
[55] Gericke T, Würtz P, Reitz D, Langen T, Ott H 2008 Nat. Phys. 4 949
Google Scholar
[56] Zipkes C, Palzer S, Sias C, Köhl M 2010 Nature 464 388
Google Scholar
[57] Verstraete F, Wolf M M, Ciac J I 2009 Nat. Phys. 5 633
Google Scholar
[58] Barreiro J T, Müller M, Schindler P, Nigg D, Monz T, Chwalla M, Hennrich M, Roos C F, Zoller P, Blatt R 2011 Nature 470 486
Google Scholar
[59] Lim K, Suh C, Rhee J K K 2019 Quantum Inf. Process 18 73
Google Scholar
[60] Tresp C, Zimmer C, Mirgorodskiy I, Gorniaczyk H, Paris-Mandoki A, Hofferberth S 2016 Phys. Rev. Lett. 117 223001
Google Scholar
[61] Honer J, Löw R, Weimer H, Pfau T, Büchler H P 2011 Phys. Rev. Lett. 107 093601
Google Scholar
[62] Trenkwalder A, Spagnolli G, Semeghini G, Coop S, Landini M, Castilho P, Pezzè L, Modugno G, Inguscio M, Smerzi A, Fattori M 2016 Nat. Phys. 12 826
Google Scholar
[63] Labuhn H, Barredo D, Ravets S, Léséleuc S, Macri T, Lahaye T, Browaeys A 2016 Nature 534 667
Google Scholar
[64] Helmrich S, Arias A, Lochead G, Wintermatel T M, Bochhold M, Diehl S, Whitlock S 2020 Nature 577 481
Google Scholar
[65] Bloch I, Dalibard J, Nascimbène S 2012 Nat. Phys. 8 267
Google Scholar
[66] Yan B, Moses S A, Gadway B, Covey J P, Hazzard K R A, Rey A M, Jin D S, Ye J 2013 Nature 501 521
Google Scholar
[67] Blatt R, Roos C F 2012 Nat. Phys. 8 277
Google Scholar
[68] Lucas A 2014 Front. Phys. 2 5
[69] O’Shea D, Junge C, Volz J, Rauschenbeutel A 2013 Phys. Rev. Lett. 111 193601
Google Scholar
[70] Bajcsy M, Hofferberth S, Balic V, Peyronel T, Hafezi M, Zibrov A S, Vuletic V, Lukin M D 2009 Phys. Rev. Lett. 102 203902
Google Scholar
[71] Chen W, Beck K M, Gullans M, Lukin M D, Tanji-Suzuki H, Vuletic V 2013 Science 341 768
Google Scholar
[72] Volz T, Reinhard A, Winger M, Badolato A, Hennessy K J, Hu E L, Imamoglu A 2012 Nat. Photonics 6 76
Google Scholar
[73] Garcia-Escartin J C, Chamorro-Posada P 2012 Phys. Rev. A 85 032309
Google Scholar
[74] Baur S, Tiarks D, Rempe G, Dürr S 2014 Phys. Rev. Lett. 112 073901
Google Scholar
[75] Li W, Lesanovsky I 2015 Phys. Rev. A 92 043828
[76] Yu Y C, Dong M X, Ye Y H, Guo G C, Ding D S, Shi B S 2020 Sci. China Phys. Mech. Astron. 63 110312
[77] Chang D E, Sørensen A S, Demler E A, Lukin M D 2007 Nat. Phys. 3 807
Google Scholar
[78] Tiarks D, Baur S, Schneider K, Dürr S, Rempe G 2014 Phys. Rev. Lett. 113 053602
Google Scholar
[79] Gorniaczyk H, Tresp C, Schmidt J, Fedder H, Hofferberth S 2014 Phys. Rev. Lett. 113 053601
Google Scholar
[80] Gorniaczyk H, Tresp C, Bienias P, Paris-Mandoki A, Li W, Mirgorodskiy I, Büchler H P, Lesanovsky I, Hofferberth S 2016 Nat. Commun. 7 12480
Google Scholar
[81] Hao Y M, Lin G W, Lin X M, Niu Y P, Gong S Q 2019 Sci. Rep. 9 4723
[82] Norcia M A, Young A W, Kaufman A M 2018 Phys. Rev. X 8 041054
[83] Saskin S, Wilson J T, Grinkenmeyer B, Tomson J D 2019 Phys. Rev. Lett. 122 143002
Google Scholar
[84] Bendkowsky V, Butscher B, Nipper J, Shaffer J P, Löw R, Pfau T 2009 Nature 458 1005
Google Scholar
[85] Tallant J, Rittenhouse S T, Booth D, Sadeghpour H R, Shaffer J P 2012 Phys. Rev. Lett. 109 173202
Google Scholar
[86] Desalvo B J, Aman J A, Dunning F B, Killian T C, Sadeghpour H R, Yoshida S, Burgdörfer J 2015 Phys. Rev. A 92 031403
Google Scholar
[87] Dauphin A, Müller M, Martin-Delgado M A 2012 Phys. Rev. A 86 053618
Google Scholar
[88] Li X, Sarma S D 2015 Nat. Commun. 6 7137
Google Scholar
[89] Gorshkov A V, Nath R, Pohl T 2013 Phys. Rev. Lett. 110 153601
Google Scholar
[90] Otterbach J, Moos M, Muth D, Fleischhauer M 2013 Phys. Rev. Lett. 111 113001
Google Scholar
[91] Glaetzle A W, van Bijnen R M W, Zoller P, Lechner W A 2017 Nat. Commun. 8 15813
Google Scholar
[92] Pichler H, Wang S, Zhou L, Choi S, Lukin M D 2018 arXiv:1808.10816 [quant-ph]
[93] Kokail C, Maier C, Bijnen R, Brydges T, Joshi M K, Jurcevic P, Muschik C A, Silvi P, Blatt R, Roos C F, Zoller P 2019 Nature 569 355
Google Scholar
计量
- 文章访问数: 14918
- PDF下载量: 793
- 被引次数: 0