Research progress of Rydberg many-body interaction

Zhang Zheng-Yuan; Zhang Tian-Yi; Liu Zong-Kai; Ding Dong-Sheng; Shi Bao-Sen

doi:10.7498/aps.69.20200649

Abstract

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:

Authors and contacts

CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Ding Dong-Sheng, dds@ustc.edu.cn

FullText HTML : translate this paragraph

References

[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 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

Cited By

图 1 激光激发两原子体系能级示意图

Figure 1. Energy level of two-atoms system excited by one laser.

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

图 3 多体态的空间有序分布图^[3]　(a) 直接成像结果; (b) 多次叠加结果; (c) 预测结果

Figure 3. Spatially ordered components of the many-body states^[3]: (a) Directly imaging result; (b) accumulative result of many measurements; (c) predicted result.

DownLoad: Full-Size Img PowerPoint

图 4 (a)一维Ising模型配分函数的张量网络表示; (b) 二维Ising模型配分函数的张量元; (c) 二维Ising模型配分函数的张量网络表示^[26]

Figure 4. (a) Tensor network form of the partition function for 1D Ising model; (b) tensor element for the partition function of 2D Ising model; (c) tensor network form of the partition function for 2D Ising model^[26]

DownLoad: Full-Size Img PowerPoint

图 5 二维Ising模型的比热随温度倒数的变化^[27]

Figure 5. Relationship between the specific heat and the reciprocal of the temperature^[27].

DownLoad: Full-Size Img PowerPoint

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]

Figure 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].

DownLoad: Full-Size Img PowerPoint

图 7 量子存储性质随入射光子数N_in变化^[47]　(a) 存储效率与存储时间关系; (b) 存储效率与Rydberg态关系

Figure 7. Properties of quantum storage with different number of input photons N_in^[47]: (a) Storage efficiency as a function of storage time; (b) storage efficiency as a function of Rydberg states.

DownLoad: Full-Size Img PowerPoint

图 8 基态与激发态结合能级示意图^[4]　(a) 写入过程; (b) 基态存储; (c) 读出过程

Figure 8. Schematic of energy levels combined exciting state with ground state^[4]: (a) Procedure of writing; (b) storage in the ground state; (c) procedure of read.

DownLoad: Full-Size Img PowerPoint

图 9 成像示意图与模拟结果^[6]　(a) 单原子成像过程示意图; (b) 没有控制光情况下的探测光吸收图; (c) 有控制光情况下的探测光吸收图

Figure 9. Scheme of imaging process and simulated results^[6]: (a) Scheme of single-atom imaging process; (b) absorption of probe light without control light; (c) absorption of probe light with control light.

DownLoad: Full-Size Img PowerPoint

图 10 (a) 不同源光子数情况下, 恢复门光子数与存储门光子数关系^[7]; (b) 最佳减法效率对比^[7]

Figure 10. (a) Number of retrial gate photons ${\bar a_{\rm g}}$ as a function of number of stored gate photons ${a_{\rm s}}$ with different number of source photons ${a_{\rm s}}$^[7]; (b) contrast of optimal efficiency of subtraction^[7].

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

DownLoad: CSV

map

[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 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

[1]	Zhao Ling-Yi, Liu Jin-Lei, Jiang Tao, Lang Yue, Zhao Zeng-Xiu. Envelope effect of Rydberg States Generation in Strong Laser Pulses. Acta Physica Sinica, 2024, 73(23): 1-6. doi: 10.7498/aps.73.20241222
[2]	Zhou Fei, Jia Feng-Dong, Liu Xiu-Bin, Zhang Jian, Xie Feng, Zhong Zhi-Ping. Measurement of microwave electric field based on electromagnetically induced transparency by using cold Rydberg atoms. Acta Physica Sinica, 2023, 72(4): 045204. doi: 10.7498/aps.72.20222059
[3]	Liao Qiu-Yu, Hu Heng-Jie, Chen Mao-Wei, Shi Yi, Zhao Yuan, Hua Chun-Bo, Xu Si-Liu, Fu Qi-Dong, Ye Fang-Wei, Zhou Qin. Two-dimensional spatial optical solitons in Rydberg cold atomic system under the action of optical lattice. Acta Physica Sinica, 2023, 72(10): 104202. doi: 10.7498/aps.72.20230096
[4]	Wang Xin, Ren Fei-Fan, Han Song, Han Hai-Yan, Yan Dong. Perfect optomechanically induced transparency and slow light in an Rydberg atom-assisted optomechanical system. Acta Physica Sinica, 2023, 72(9): 094203. doi: 10.7498/aps.72.20222264
[5]	Li Yan. Effects of long-range inter-particle interactions and isolated defect on quantum walks of two hard-core bosons in one-dimensional lattices. Acta Physica Sinica, 2023, 72(17): 170501. doi: 10.7498/aps.72.20230642
[6]	Pei Si-Hui, Song Zi-Xuan, Lin Xing, Fang Wei. Interaction between light and single quantum-emitter in open Fabry-Perot microcavity. Acta Physica Sinica, 2022, 71(6): 060201. doi: 10.7498/aps.71.20211970
[7]	Jin Zhao, Li Rui, Gong Wei-Jiang, Qi Yang, Zhang Shou, Su Shi-Lei. Implementation of the Rydberg double anti-blockade regime and the quantum logic gate based on resonant dipole-dipole interactions. Acta Physica Sinica, 2021, 70(13): 134202. doi: 10.7498/aps.70.20210059
[8]	Li Jing-Kui, Yang Wen-Guang, Song Zhen-Fei, Zhang Hao, Zhang Lin-Jie, Zhao Jian-Ming, Jia Suo-Tang. Two-photon radio frequency spectroscopy of 49S Rydberg state. Acta Physica Sinica, 2015, 64(16): 163201. doi: 10.7498/aps.64.163201
[9]	Huang Wei, Liang Zhen-Tao, Du Yan-Xiong, Yan Hui, Zhu Shi-Liang. Rydberg-atom-based electrometry. Acta Physica Sinica, 2015, 64(16): 160702. doi: 10.7498/aps.64.160702
[10]	Wu Hai-Na, Sun Xue, Gong Wei-Jiang, Yi Guang-Yu. Influences of electron-phonon interaction on the thermoelectric effect in a parallel double quantum dot system. Acta Physica Sinica, 2015, 64(7): 077301. doi: 10.7498/aps.64.077301
[11]	Han Xiao-Xuan, Zhao Jian-Ming, Li Chang-Yong, Jia Suo-Tang. Potentials of long-range cesium Rydberg molecule. Acta Physica Sinica, 2015, 64(13): 133202. doi: 10.7498/aps.64.133202
[12]	Zhao Jian-Dong, Xin Jie. Van der Waals interaction between high excited states. Acta Physica Sinica, 2014, 63(13): 133201. doi: 10.7498/aps.63.133201
[13]	Li Chang-Yong, Zhang Lin-Jie, Zhao Jian-Ming, Jia Suo-Tang. Measurement and theoretical calculation for Stark energy and electric dipole moment of Cs Rydberg state. Acta Physica Sinica, 2012, 61(16): 163202. doi: 10.7498/aps.61.163202
[14]	Zhang Wang, Xu Fa-Qiang, Wang Guo-Dong, Zhang Wen-Hua, Li Zong-Mu, Wang Li-Wu, Chen Tie-Xin. Thickness dependence of the interfacial interaction for the Fe/ZnO (0001) system studied by photoemission. Acta Physica Sinica, 2011, 60(1): 017104. doi: 10.7498/aps.60.017104
[15]	Li Jia-Liang, Lei Shu-Guo. Study of the XY chain with long-range interactions. Acta Physica Sinica, 2008, 57(9): 5944-5950. doi: 10.7498/aps.57.5944
[16]	Yan Li-Fen, Wang Hong-Cheng, She Wei-Long. Influence of diffusion on the interaction between photovoltaic spatial solitons. Acta Physica Sinica, 2006, 55(10): 5257-5262. doi: 10.7498/aps.55.5257
[17]	MA JIN-YI, QIU XI-JUN. INTERACTION BETWEEN AN ELECTRONIC SYSTEM AND MULTIPHOTONS IN A STRONG LASER FIELD. Acta Physica Sinica, 2001, 50(3): 416-421. doi: 10.7498/aps.50.416
[18]	ZHANG SEN, QIU JI-ZHEN, WANG GANG. LEVEL STRUCTURE OF THE RYDBERG STATES OF CALCIUM ATOM IN ELECTRIC FIELD. Acta Physica Sinica, 1989, 38(3): 481-486. doi: 10.7498/aps.38.481
[19]	HE XING-HONG, LI BAI-WEN, ZHANG CHENG-XIU. POLARIZABILITIES OF HIGH RYDBERG ALKALI ATOMS. Acta Physica Sinica, 1989, 38(10): 1717-1722. doi: 10.7498/aps.38.1717
[20]	ZHANG SEN, QIU JI-ZHEN, HU SU-FEN, LU JIE, ZHONG JIAN-WEI, LIANG YI, SUN JIA-ZHEN. ELECTRIC FIELD EFFECTS ON Sr ATOM RYDBERG STATES. Acta Physica Sinica, 1988, 37(6): 983-988. doi: 10.7498/aps.37.983

Catalog

Vol. 69, Issue 18 - 2020-09-20

Metrics

Abstract views: 16370
PDF Downloads: 864
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板