微纳尺度稀土掺杂晶体的量子相干性能及其应用研究进展

郭牧城; 汪福东; 胡肇高; 任苗苗; 孙伟业; 肖婉婷; 刘书萍; 钟满金

doi:10.7498/aps.72.20222166

摘要

稀土离子掺杂晶体具有稳定的固态物性和出色的能级跃迁相干特性, 在量子信息应用研究, 尤其是发展量子存储设备方面独具潜力. 除了宏观的块状稀土离子单晶, 微纳尺度稀土离子晶体在高度集成的杂化量子系统和微型化量子设备方面也具有广泛的应用前景, 且其制备难度较低, 在体积、形状和组分调控上更具灵活性. 因此, 开发高性能的微纳尺度稀土离子晶体系统, 并对其量子态进行精密探测与操控, 已成为量子信息领域的重要研究方向之一. 本文结合稀土离子晶体的高分辨和相干光谱学表征技术, 综述了近年来微纳尺度稀土离子晶体在材料制备加工、量子相干性能测量、物理机理探索以及量子器件开发等方面的研究进展, 对其在量子存储、量子频率转换、量子单光子源以及量子逻辑门等方面取得的最新研究进展进行了总结. 最后, 对微纳尺度稀土晶体材料及其信息器件研究过程中可能的改进方向和策略进行了讨论.

关键词:

Abstract

Rare-earth ion doped crystals possess stable solid state physicochemical properties and long optical coherence time and spin coherence time, thus showing important development prospect in quantum information science and technology area. Investigations on macroscopic bulk rare-earth single crystals have obtained many promising results, especially in the field of optical quantum memory. With the rapid development of quantum information science, a variety of new functions or multifunctional integrations are found in rare earth crystal systems, such as on chip quantum storage, microwave to optical frequency conversion, scalable quantum single photon sources, and quantum logic gates. As a result, beyond the macroscopic bulk rare-earth single crystals, micro/nano-scale rare-earth crystals have received much attention in recent years and they are regarded as promising candidates in highly integrated hybrid quantum systems and miniaturized quantum devices. Moreover, wet chemical method synthesized micro/nano-scale rare-earth crystals have lower growth difficulty and more flexible manipulation in volume, shape and composition. Therefore, exploring high-performance micro/nano-scale rare-earth crystals and precisely manipulating their quantum states have become one of the important directions in today’s quantum information science and technology research. In this review, we first briefly introduce the basic concepts and high resolution spectroscopic techniques that are commonly used in rare earth ion doped crystals for quantum information science and technologies, such as hole burning technique and photon echo technique. Then we summarize comprehensively recent research status and development trends of rare earth ion doped polycrystalline nanoparticles, thin films, single crystal based micro systems, and some other micro/nano-scale rare earth platforms in terms of material fabrication, quantum coherence property, dephasing mechanisms, and also quantum device explorations. The latest research advances in quantum information applications such as quantum storage, quantum frequency conversion, quantum single photon sources and quantum logic gates are given. Finally, we discuss the possible optimization directions and strategies to improve the component design, material synthesis and quantum performance of micro/nano-scale rare earth crystals and their related quantum devices. This review highlights that the micro/nano-scale rare earth crystals may offer many new possibilities for designing quantum light-matter interfaces, thus are promising quantum systems to develop scalable and integrated quantum devices in the future.

Keywords:

作者及机构信息

1.
南方科技大学深圳量子科学与工程研究院, 深圳　518055

2.
深圳国际量子研究院, 深圳　518048

3.
南方科技大学, 广东省量子科学与工程重点实验室, 深圳　518055

通信作者: 刘书萍, liusp@sustech.edu.cn ; 钟满金, Zhongmj@sustech.edu.cn

基金项目: 国家自然科学基金(批准号: 11904159, 12004168)、广东省基础与应用基础研究基金(批准号: 2021A1515110191)、广东省“珠江人才计划”引进创新创业团队(批准号: 2019ZT08X324)和广东省量子科学与工程重点实验室(批准号: 2019B121203002)资助的课题

Authors and contacts

1.
Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China

2.
Shenzhen International Quantum Academy (SIQA), Shenzhen 518048, China

3.
Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China

Corresponding author: Liu Shu-Ping, liusp@sustech.edu.cn ; Zhong Man-Jin, Zhongmj@sustech.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11904159, 12004168), the Basic and Applied Basic Research Foundation of Guangdong Province, China (Grant No. 2021A1515110191), the “Pearl River Talent Plan” Innovative and Entrepreneurial Research Team Program of Guangdong Province, China (Grant No. 2019ZT08X324), and the Guangdong Provincial Key Laboratory of Quantum Science and Engineering, China (Grant No. 2019B121203002)

文章全文 : translate this paragraph

参考文献

[1]	Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002 Google Scholar
[2]	Sangouard N, Simon C, de Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33 Google Scholar
[3]	Kimble H J 2008 Nature 453 1023 Google Scholar
[4]	Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 797 Google Scholar
[5]	Wehner S, Elkouss D, Hanson R 2018 Science 362 eaam9288 Google Scholar
[6]	Paesani S, Borghi M, Signorini S, Mainos A, Pavesi L, Laing A 2020 Nat. Commun. 11 2502 Google Scholar
[7]	Hedges M P, Longdell J J, Li Y, Sellars M J 2010 Nature 465 1052 Google Scholar
[8]	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
[9]	Saglamyurek E, Jin J, Verma V B, Shaw M D, Marsili F, Nam S W, Oblak D, Tittel W 2015 Nat. Photonics 9 83 Google Scholar
[10]	Guo M C, Liu S P, Sun W Y, Ren M M, Wang F D, Zhong M J 2023 Front. Phys. 18 21303
[11]	Dutt M V G, Childress L, Jiang L, Togan E, Maze J, Jelezko F, Zibrov A, Hemmer P R, Lukin M D 2007 Science 316 1312 Google Scholar
[12]	Taminiau T H, Cramer J, van der Sar T, Dobrovitski V V, Hanson R 2014 Nat. Nanotechnol. 9 171 Google Scholar
[13]	O’Brien C, Lauk N, Blum S, Morigi G, Fleischhauer M 2014 Phys. Rev. Lett. 113 063603 Google Scholar
[14]	Degen C L, Reinhard F, Cappellaro P 2017 Rev. Mod. Phys. 89 035002 Google Scholar
[15]	Wolfowicz G, Heremans F J, Anderson C P, Kanai S, Seo H, Gali A, Galli G, Awschalom D D 2021 Nat. Rev. Mater. 6 906 Google Scholar
[16]	Thiel C W, Böttger T, Cone R L 2011 J. Lumin. 131 353 Google Scholar
[17]	Hull R, Parisi J, Osgood R M, Warlimont H, Liu G, Jacquier B 2005 Spectroscopic Properties of Rare Earth in Optical Materials (Vol. 1) (Berlin: Springer-Verla) pp204–213
[18]	Macfarlane R M 2002 J. Lumin. 100 1 Google Scholar
[19]	Könz F, Sun Y, Thiel C W, Cone R L, Equall R W, Hutcheson R L, Macfarlane R M 2003 Phys. Rev. B 68 085109 Google Scholar
[20]	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
[21]	Tittel W, Afzelius M, Chaneliére T, Cone R L, Kröll S A, Moiseev S, Sellars M 2010 Laser Photonics Rev. 4 244 Google Scholar
[22]	Ortu A, Holzäpfel A, Etesse J, Afzelius M 2022 npj Quantum Inf. 8 29 Google Scholar
[23]	Simon C, Afzelius M, Appel J, de la Giroday A B, Dewhurst S J, Gisin N, Hu C Y, Jelezko F, Kröll S, Müller J H, Nunn J, Polzik E S, Rarity J G, de Riedmatten H, Rosenfeld W, Shields A J, Sköld N, Stevenson R M, Thew R, Walmsley I A, Weber M C, Weinfurter H, Wrachtrup J, Young R J 2010 Eur. Phys. J. D 58 1 Google Scholar
[24]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413 Google Scholar
[25]	Hiraishi M, IJspeert M, Tawara T, Adachi S, Kaji R, Omi H, Gotoh H 2019 Opt. Lett. 44 4933 Google Scholar
[26]	Welinski S, Woodburn P T, Lauk N, Cone R L, Simon C, Goldner P, Thiel C W 2019 Phys. Rev. Lett. 122 247401 Google Scholar
[27]	Probst S, Rotzinger H, Wünsch S, Jung P, Jerger M, M Siegel, Ustinov A V, Bushev P A 2013 Phys. Rev. Lett. 110 157001 Google Scholar
[28]	Fernandez-Gonzalvo X, Chen Y H, Yin C, Rogge S, Longdell J J 2015 Phys. Rev. A 92 062313 Google Scholar
[29]	Kornher T, Xiao D W, Xia K, Sardi F, Zhao N, Kolesov R, Wrachtrup J 2020 Phys. Rev. Lett. 124 170402 Google Scholar
[30]	Kinos A, Hunger D, Kolesov R, Mølmer K, de Riedmatten H, Goldner P, Tallaire A, Morvan L, Berger P, Welinski S, Karrai K, Rippe L, Kröll S, Walther A 2021 arXiv: 2103.15743 [Quantum Physics]
[31]	Kinos A, Rippe L, Kröll S, Walther A 2021 Phys. Rev. A 104 052624 Google Scholar
[32]	Kinos A, Rippe L, Serrano D, Walther A, Kröll S 2022 Phys. Rev. A 105 032603 Google Scholar
[33]	Wang P, Luan C Y, Qiao M, Um M, Zhang J, Wang Y, Yuan X, Gu M, Zhang J, Kim K 2021 Nat. Commun. 12 233 Google Scholar
[34]	de Riedmatten H, Afzelius M, Staudt M U, Simon C, Gisin N 2008 Nature 456 773 Google Scholar
[35]	Ma Y, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 2381 Google Scholar
[36]	Heinze G, Hubrich C, Halfmann T 2013 Phys. Rev. Lett. 111 033601 Google Scholar
[37]	Clausen C, Usmani I, Bussières F, Sangouard N, Afzelius M, de Riedmatten H, Gisin N 2011 Nature 469 508 Google Scholar
[38]	Liu X, Hu J, Li Z F, Li X, Li P Y, Liang P J, Zhou Z Q, Li C F, Guo G C 2021 Nature 594 41 Google Scholar
[39]	Rakonjac J V, Lago-Rivera D, Seri A, Mazzera M, Grandi S, de Riedmatten H 2021 Phys. Rev. Lett. 127 210502 Google Scholar
[40]	Usmani I, Clausen C, Bussières F, Sangouard N, Afzelius M, Gisin N 2012 Nat. Photonics 6 234 Google Scholar
[41]	Rakonjac J V, Corrielli G, Lago-Rivera D, Seri A, Mazzera M, Grandi S, Osellame R, de Riedmatten H 2022 Sci. Adv. 8 eabn3919 Google Scholar
[42]	Lago-Rivera D, Grandi S, Rakonjac J V, Seri A, de Riedmatten H 2021 Nature 594 37 Google Scholar
[43]	Tiranov A, Strassmann P C, Lavoie J, Brunner N, Huber M, Verma V B, Nam S W, Mirin R P, Lita A E, Marsili F, Afzelius M, Bussières F, Gisin N 2016 Phys. Rev. Lett. 117 240506 Google Scholar
[44]	Kutluer K, Distante E, Casabone B, Duranti S, Mazzera M, Riedmatten H 2019 Phys. Rev. Lett. 123 030501 Google Scholar
[45]	Zhou Z Q, Hua Y L, Liu X, Chen G, Xu J S, Han Y J, Li C F, Guo G C 2015 Phys. Rev. Lett. 115 070502 Google Scholar
[46]	Ferguson K R, Beavan S E, Longdell J J, Sellars M J 2016 Phys. Rev. Lett. 117 020501 Google Scholar
[47]	Beavan S E, Hedges M P, Sellars M J 2012 Phys. Rev. Lett. 109 093603 Google Scholar
[48]	Sabooni M, Li Q, Kröll S, Rippe L 2013 Phys. Rev. Lett. 110 133604 Google Scholar
[49]	Jobez P, Usmani I, Timoney N, Laplane C, Gisin N, Afzelius M 2014 New J. Phys. 16 083005 Google Scholar
[50]	Schraft D, Hain M, Lorenz N, Halfmann T 2016 Phys. Rev. Lett. 116 073602 Google Scholar
[51]	Davidson J H, Lefebvre P, Zhang J, Oblak D, Tittel W 2020 Phys. Rev. A 101 042333 Google Scholar
[52]	Bussieres F, Clausen C, Tiranov A, Korzh B, Verma V B, Nam S W, Marsili F, Ferrier A, Goldner P, Herrmann H, Silberhorn C, Sohler W, Afzelius M, Gisin N 2014 Nat. Photonics 8 775 Google Scholar
[53]	Usmani I, Afzelius M, de Riedmatten H, Gisin N 2010 Nat. Commun. 1 12 Google Scholar
[54]	Rippe L, Julsgaard B, Walther A, Ying Y, Kröll S 2008 Phys. Rev. A 77 022307 Google Scholar
[55]	Kolesov R, Xia K, Reuter R, Stöhr R, Zappe A, Meijer J, Hemmer P R, Wrachtrup J 2012 Nat. Commun. 3 1029 Google Scholar
[56]	Perrot A, Goldner P, Giaume D, Lovrić M, Andriamiadamanana C, Gonçalves R R, Ferrier A 2013 Phys. Rev. Lett. 111 203601 Google Scholar
[57]	Scarafagio M, Tallaire A, Tielrooij K J, Cano D, Grishin A, Chavanne M H, Koppens F, Ringuedé A, Cassir M, Serrano D, Goldner P, Ferrier A 2019 J. Phys. Chem. C 123 13354 Google Scholar
[58]	McAuslan D L, Longdell J J, Sellars M J 2009 Phys. Rev. A 80 062307 Google Scholar
[59]	Becher C, Gao W, Kar S, Marciniak C D, Monz T, Bartholomew J G, Goldner P, Loh H, Marcellina E, Goh K E J, Koh T S, Weber B, Mu Z, Tsai J Y, Yan Q, Huber-Loyola T, Höfling S, Gyger S, Steinhauer S, Zwiller V 2023 Mater. Quantum Technol. 3 012501 Google Scholar
[60]	Levenson M D L, Yen W, 1987 Lasers, Spectroscopy and New Ideas (Vol. 1) (Berlin: Springer-Verla) pp205–206
[61]	Stoneham A M 1969 Rev. Mod. Phys. 41 82 Google Scholar
[62]	Kunkel N, Bartholomew J, Welinski S, Ferrier A, Ikesue A, Goldner P 2016 Phys. Rev. B 94 184301 Google Scholar
[63]	Böttger T, Thiel C W, Sun Y, Cone R L 2006 Phys. Rev. B 73 075101 Google Scholar
[64]	Goldner P, Ferrier A, Guillot-Noöl O 2015 Rare Earth-doped Crystals for Quantum Information Processing (Vol. 1) (Amsterdam: Elsevier) pp1–78
[65]	Hahn E L 1950 Phys. Rev. B 80 580 Google Scholar
[66]	Kurnit N A, Abella I D, Hartmann S R 1964 Phys. Rev. Lett. 13 567 Google Scholar
[67]	Scully M O, Zubairy M S 1997 Quantum Optics (Vol. 1) (Cambridge: University Press) pp156–158
[68]	Abragam A 1983 The Principles of Nuclear Magnetism (Vol. 1) (Oxford: Oxford University Press) pp19–36
[69]	Brewer R G, Shoemaker R L 1972 Phys. Rev. A 6 2001 Google Scholar
[70]	Zhong T, Goldner P 2019 Nanophotonics 8 2003 Google Scholar
[71]	Kunkel N, Goldner P 2018 Z. Anorg. Allg. Chem. 644 66 Google Scholar
[72]	Dibos A M, Raha M, Phenicie C M, Thompson J D 2018 Phys. Rev. Lett. 120 243601 Google Scholar
[73]	Williamson L A, Chen Y H, Longdell J J 2014 Phys. Rev. Lett. 113 203601 Google Scholar
[74]	Zhong T, Kindem J M, Bartholomew J G, Rochman J, Craiciu I, Miyazono E, Bettinelli M, Cavalli E, Soni V, Nam S W, Marsili F, Shaw M D, Beyer A D, Faraon A 2017 Science 357 1392 Google Scholar
[75]	Ahlefeldt R L, Pearce M J, Hush M R, Sellars M J 2020 Phys. Rev. A 101 012309 Google Scholar
[76]	Grimm M, Beckert A, Aeppli G, Müller M 2021 PRX Quantum 2 010312 Google Scholar
[77]	Gouzien E, Sangouard N 2021 Phys. Rev. Lett. 127 140503 Google Scholar
[78]	Meltzer R S, Hong K S 2000 Phys. Rev. B 61 3396 Google Scholar
[79]	Utikal T, Eichhammer E, Petersen L, Renn A, Götzinger S, Sandoghdar V 2014 Nat. Commun. 5 3627 Google Scholar
[80]	Eichhammer E, Utikal T, Götzinger S, Sandoghdar V 2015 New J. Phys. 17 083018 Google Scholar
[81]	Liu S, Serrano D, Fossati A, Tallaire A, Ferrier A, Goldner P 2018 RSC Advances 8 37098 Google Scholar
[82]	Liu S, Fossati A, Serrano D, Tallaire A, Ferrier A, Goldner P 2020 ACS Nano 14 9953 Google Scholar
[83]	Casabone B, Benedikter J, Hümmer T, Oehl F, de Oliveira Lima K, Haensch T W, Ferrier A, Goldner P, de Riedmatten H, David H 2018 New J. Phys. 20 095006 Google Scholar
[84]	Casabone B, Deshmukh C, Liu S, Serrano D, Ferrier A, Hümmer T, Goldner P, Hunger D, de Riedmatten H 2021 Nat. Commun. 12 3570 Google Scholar
[85]	Zhong T, Kindem J M, Miyazono E, Faraon A 2015 Nat. Commun. 6 8206 Google Scholar
[86]	Zhong T, Kindem J M, Rochman J, Faraon A 2017 Nat. Commun. 8 14107 Google Scholar
[87]	Craiciu I, Lei M, Rochman J, Kindem J M, Bartholomew J G, Miyazono E, Zhong T, Sinclair N, Faraon A 2019 Phys. Rev. Appl. 12 024062 Google Scholar
[88]	Raha M, Chen S, Phenicie C P, Ourari S, Dibos A M, Thompson J D 2020 Nat. Commun. 11 1605 Google Scholar
[89]	Chen S, Raha M, Phenicie C M, Ourari S, Thompson J D 2020 Science 370 592 Google Scholar
[90]	Rice P R, Carmichael H J 1988 IEEE J. Quantum Electron 24 1351 Google Scholar
[91]	de Oliveira Lima K, Rocha Gonçalves R G, Giaume D, Ferrier A, Goldner P 2015 J. Lumin. 168 276 Google Scholar
[92]	Bartholomew J G, de Oliveira Lima K, Ferrier A, Goldner P 2017 Nano Lett. 17 778 Google Scholar
[93]	Alqedra M K, Deshmukh C, Liu S , Serrano D, Horvath S P, Rafie-Zinedine S, Abdelatief A, Rippe L, Kröll S, Casabone B, Ferrier A, Tallaire A, Goldner P, de Riedmatten H, Walther A 2023 arXiv: 2303.02054 [Quantum Physics]
[94]	Ferrier A, Thiel C W, Tumino B, Ramirez M O, Bausá L E, Cone R L, Ikesue A, Goldner P 2013 Phys. Rev. B 87 041102 Google Scholar
[95]	Serrano D, J Karlsson, Fossati A, Ferrier A, Goldner P 2018 Nat. Commun. 9 2127 Google Scholar
[96]	Serrano D, Deshmukh C, Liu S, Tallaire A, Ferrier A, Riedmatten H, Goldner P 2019 Phys. Rev. B 100 144304 Google Scholar
[97]	Fossati A, Liu S, Karlsson J, Ikesue A, Tallaire A, Ferrier A, Serrano D, Goldner P 2020 Nano Lett. 20 7087 Google Scholar
[98]	Ferrier A, Harada N, Scarafagio M, Briand E, Ganem J, Vickridge I, Seyeux A, Marcus P, Serrano D, Goldner P, Tallaire A 2020 J. Phys. Chem. C 124 19725 Google Scholar
[99]	Flinn G P, Jang K W, Ganem J J, Jones M L, Meltzer R S, Macfarlane R M 1994 J. Lumin. 58 374 Google Scholar
[100]	Harada N, Ferrier A, Serrano D, Persechino M, Briand E, Bachelet R, Vickridge I, Ganem J J, Goldner P, Tallaire A 2020 J. Appl. Phys. 128 055304 Google Scholar
[101]	Singh M K, Prakash A, Wolfowicz G, Wen J, Huang Y, Rajh T, Awschalom D D, Zhong T, Guha S 2020 APL Materials 8 031111 Google Scholar
[102]	Harada N, Tallaire A, Serrano D, Seyeux A, Marcus P, Portier X, C Labbé, Goldner P, Ferrier A 2022 Mater. Adv. 3 300 Google Scholar
[103]	Wicker C, Huang Y, Qiao H, Singh M, Prakash A, Dibos A, Guha S, Zhong T 2020 2020 IEEE Photonics Conference (IPC), Virtual Conference, September 28–October 1, 2020 p1
[104]	Cano D, Ferrier A, Soundarapandian K, Reserbat-Plantey A, Scarafagio M, Tallaire A, Seyeux A, Marcus P, de Riedmatten H, Goldner P, Koppens F H L, Tielrooij K J 2020 Nat. Commun. 11 4094 Google Scholar
[105]	Probst S, Tkalcec A, Rotzinger H, Rieger D, Le Floch J M, Goryachev M, Tobar M E, Ustinov A V, Bushev P A 2014 Phys. Rev. B 90 100404 Google Scholar
[106]	Ulanowski A, Merkel B, Reiserer A 2022 Sci. Adv. 8 eabo4538 Google Scholar
[107]	Lau H K, Qiao H, Clerk A A, Zhong T 2022 arXiv: 2208.00886 [Quantum Physics]
[108]	Lauritzen B, Hastings-Simon S R, Riedmatten H de, Afzelius M, Gisin N 2008 Phys. Rev. A 78 043402 Google Scholar
[109]	Miyazono E, Zhong T, Craiciu I, Kindem J, Faraon A 2016 Appl. Phys. Lett. 108 011111 Google Scholar
[110]	Merkel B, Ulanowski A, Reiserer A 2020 Phys. Rev. X 10 041025 Google Scholar
[111]	Ruskuc A, Wu C J, Rochman J, Choi J, Faraon A 2022 Nature 602 408 Google Scholar
[112]	Zhong T, Kindem J M, Bartholomew J G, Rochman J, Craiciu I, Verma V, Nam S W, Marsili F D, Shaw M D, Beyer A, Faraon A 2018 Phys. Rev. Lett. 121 183603 Google Scholar
[113]	Bartholomew J G, Rochman J, Xie T, Kindem J M, Ruskuc A, Craiciu I, Lei M, Faraon A 2020 Nat. Commun. 11 3266 Google Scholar
[114]	Calmano T, Siebenmorgen J, Hellmig O, Petermann K, Huber G 2010 Appl. Phys. B 100 131 Google Scholar
[115]	Corrielli G, Seri A, Mazzera M, Osellame R, Riedmatten H de 2016 Phys. Rev. Appl. 5 054013 Google Scholar
[116]	Liu C, Zhu T X, Su M X, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2020 Phys. Rev. Lett. 125 260504 Google Scholar
[117]	Weis R S, Gaylord T K 1985 Appl. Phys. A 37 191 Google Scholar
[118]	Sinclair N, Saglamyurek E, Mallahzadeh H, Slater J A, George M, Ricken R, Hedges M P, Oblak D, Simon C, Sohler W, Tittel W 2014 Phys. Rev. Lett. 113 053603 Google Scholar
[119]	Curtz N, Thew R, Simon C, Gisin N, Zbinden H 2010 Opt Express 18 22099 Google Scholar
[120]	Li M, Ling J, He Y, Javid U A, Xue S, Lin Q 2020 Nat. Commun. 11 4123 Google Scholar
[121]	Guarino A, Poberaj G, Rezzonico D, Degl’Innocenti R, Günter P 2007 Nat. Photonics 1 407 Google Scholar
[122]	Sinclair N, Saglamyurek E, George M, Ricken R, la Mela C, Sohler W, Tittel W 2010 J. Lumin. 130 1586 Google Scholar
[123]	Sinclair N, Oblak D, Thiel C W, Cone R L, Tittel W 2017 Phys. Rev. Lett. 118 110504 Google Scholar
[124]	Vredenberg A M, Hunt N E J, Schubert E F, Jacobson D C, Poate J M, Zydzik G J 1993 Phys. Rev. Lett. 71 517 Google Scholar
[125]	Yin C, Rancic M, de Boo G G, Stavrias N, McCallum J C, Sellars M J, Rogge S 2013 Nature 497 91 Google Scholar
[126]	Lansbergen G P, Rahman R, Wellard C J, Woo I, Caro J, Collaert N, Biesemans S, Klimeck G, Hollenberg L C L, Rogge S 2008 Nat. Phys. 4 656 Google Scholar
[127]	Wicker C, Huang Y, Qiao H, Zhong T 2021 Conference on Lasers and Electro-Optics San Jose, California, United States, May 9–14, 2021 pFTh1 P.6
[128]	Bharuth-Ram K, Vetter U, Hofsäss H, Ronning C, and Dietrich M 2002 Nucl. Instrum. Meth. B 190 835 Google Scholar
[129]	Magyar A, Hu W, Shanley T, Flatté M E, Hu E, Aharonovich I 2014 Nat. Commun. 5 3523 Google Scholar
[130]	Xia K, Sardi F, Sauerzapf C, Kornher T, Becker H W, Kis Z, Kovacs L, Dertli D, Foglszinger J, Kolesov R, Wrachtrup J 2022 Optica 9 445 Google Scholar
[131]	Macfarlane R M, Shelby R M 1981 Opti. Commun. 39 169
[132]	Karlsson J, Kunkel N, Ikesue A, Ferrier A, Goldner P 2017 J. Phys.: Condens. Matter 29 125501 Google Scholar
[133]	Fukumori R, Huang Y, Yang J, Zhang H, Zhong T 2020 Phys. Rev. B 101 214202 Google Scholar
[134]	Gupta S, Wu X, Zhang H, Yang J, Zhong T 2022 arXiv: 2207.02708 [Quantum Physics]
[135]	Serrano D, Kuppusamy S K, Heinrich B, Fuhr O, Hunger D, Ruben M, Goldner P 2022 Nature 603 241 Google Scholar

施引文献

图 1 量子网络技术与固态稀土量子系统研究平台^[59]　 (a)要实现鲁棒性和可扩展的量子网络, 每个小规模局域网络中的量子网络节点均需要装备一整套的高性能量子软硬件设备, 包括用于产生纠缠的量子单光子源、用于网络同步的量子存储器和中继站、用于连接不同量子物理系统(如光波和微波)的量子转换器(适配器), 以及用于处理量子信息和执行纠错操作的量子计算机等; (b)固态稀土离子系统具有丰富且高度相干的4f-4f光学跃迁和自旋跃迁, 是发展上述量子网络中各种关键量子硬件设备的主要物理系统之一; (c) 稀土离子掺杂晶体发展的多条路径, 将目前固态稀土量子系统的研究工作转化为大规模复杂量子网络中可操控部署的技术, 依赖于对材料局限性更深入的理解以及微纳尺度稀土晶体材料制备和合成等方面新的突破

Fig. 1. Enabling technologies for quantum networks and rare earth doped crystal platforms^[59]: (a) To realize robust and scalable quantum networks, each network node in small-scale local networks will need to incorporate a suite of quantum technologies. Essential devices include sources of entanglement, quantum memories for network synchronization and repeater stations, converters and transducers to act as adapters for quantum technologies operating in different physical regimes (e.g. microwave and optical), and quantum computers to process information and perform error correction operations. (b) Rare-earth ion crystals possess abundant and highly coherent 4f-4f optical transitions and spin transitions, thus are among the leading material systems to realize the varied devices that are critical to quantum network operation. (c) Multiple avenues for rare earth doped crystal development. Translating current work into deployable technologies in large, complex networks will be accelerated by a deeper understanding of material limitations and new breakthroughs in nanoscale rare earth based material synthesis and fabrication

下载: 全尺寸图片幻灯片

图 2 稀土离子掺杂晶体的非均匀线宽($\varGamma_{\mathrm{inh}}$)和均匀线宽($\varGamma_{\mathrm{h}}$)示意图. 晶格中的单个稀土离子只对非常窄的频率范围内的光有共振吸收($\varGamma_{\mathrm{h}}$), 但由于局域环境的不同, 不同位置处稀土离子吸收的频率略有不同, 整体表现为展宽更大的非均匀线宽($\varGamma_{\mathrm{inh}}$)

Fig. 2. Inhomogeneous broadening ($\varGamma_{\mathrm{inh}}$) and homogeneous broadening ($\varGamma_{\mathrm{h}}$) of rare earth doped crystals. Single rare earth ion in the lattice has a sharp absorption peak ($\varGamma_{\mathrm{h}}$). Due to the different local environment, rare earth ions at different locations have different absorption frequency. The inhomogeneous absorption profile of an ensemble of ions is the sum of the homogeneous profile of the different individual ions ($\varGamma_{\mathrm{inh}}$)

下载: 全尺寸图片幻灯片

图 3 光谱烧孔原理示意图　(a)三种超精细基态能级被均匀占据, 频率为$\omega_{\mathrm{0}}$的激光将中间态离子泵浦到激发态, 被激发的离子可以衰减到任何一种超精细基态, 但重新回到中间态的离子会再次被激光激发, 使得离子都被转移到另外两种超精细基态; (b) 在非均匀展宽上的烧“孔”

Fig. 3. Schematic representation of holeburning technique: (a) All three hyperfine ground states are equally populated until a laser with frequency $\omega_{\mathrm{0}}$ pumps the ions in the middle state to a optically excited state. The excited ions can decay to any of the hyperfine ground states, but only those that decay to the middle state will be repumped by the laser. All ions are transferred to the other two hyperfine ground states. (b) A spectral “hole” is burned in the inhomogeneous profile

下载: 全尺寸图片幻灯片

图 4 (a)双脉冲回波和(b)三脉冲回波分别对应的脉冲序列及对应的离子态在布洛赫球上的演化

Fig. 4. Evolution of ion states on the Bloch sphere and corresponding pulse sequence for (a) two pulse echo and (b) three pulse echo respectively

下载: 全尺寸图片幻灯片

图 5 (a)化学刻蚀前后$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体的光学回波信号衰减曲线. 内附图为对应的纳米粉体的TEM形貌^[81]; (b)$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体在初次800 ℃煅烧(上左), 二次1200 ℃煅烧(上右)并微波等离子体处理后(下)的TEM形貌^[82]; (c) $\mathrm{Eu}^{3+}$离子$\mathrm{^5 D_{0}}$-$^7\mathrm{F}_{0}$跃迁在不同制备条件下的光学相干时间T₂和非均匀线宽$\varGamma_{\mathrm{inh}}$. 样品在0处的光学跃迁频率为(516.0979 ± 0.0002) THz ((580.8830 ± 0.0001) nm)^[82]

Fig. 5. (a) Photon echo decays for initial and etched nanoparticles. The insets are corresponding TEM images^[81]. (b) TEM structural and morphological evolution of the nanoparticles for annealing at 800 ℃ (top-left), a second annealing at 1200 ℃ with microwave excitation power (top-right, lower), respectively^[82]. (c) Coherence time $T_{2}$ and inhomogeneous linewidth $\varGamma_{\mathrm{inh}}$ of $\mathrm{Eu}^{3+}$ ion $^5\mathrm{D}_{0}$-$^7\mathrm{F}_{0}$ transition under different preparation conditions. The optical transition frequency at 0 is (516.0979 ± 0.0002) THz ((580.8830 ± 0.0001) nm)^[82]

下载: 全尺寸图片幻灯片

图 6 $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体的均匀线宽随温度的变化. 黑色、灰色和浅灰色区域分别表示双声子拉曼效应(TPR)、局域无序二能级系统(TSL)以及与温度无关的光谱展宽的贡献. 在主图和插图中, 阴影区域都代表了与温度无关的展宽(最浅)、TLS相互作用展宽和TPR相互作用展宽(最暗)^[92]

Fig. 6. Temperature dependence of the homogeneous line width of $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ nanoparticles. The black, gray and light-gray regions represent the contribution of two-phonon Raman (TPR) interactions, local disordered two-level system (TSL) interactions and the temperature independent broadening, respectively. In both the main figure and inset the shaded areas represent the temperature independent broadening (lightest), TLS interaction broadening and TPR interaction broadening (darkest)^[92]

下载: 全尺寸图片幻灯片

图 7 (a)基于$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体的SEMM量子存储装置示意图^[97]; (b)存储脉冲序列及输出脉冲幅值随存储时间的函数关系^[97]; (c) $\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$纳米粉体与可调谐F-P光学微腔的耦合示意图^[84]; (d) $\mathrm{Er}^{3+}$离子经历的Purcell增强效应, 其中约50%的离子经历大于15的Purcell效应, 至少10%的离子经历大于72的Purcell增强, 腔长度通过施加移动光纤的电压偏移V来控制^[84]

Fig. 7. (a) Scheme of SEMM memory based on $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ nanoparticles^[97]; (b) storage pulse sequence and output pulse amplitude as a function of the total storage time^[97]; (c) scheme of the tunable fiber-based microcavity with $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ nanoparticles^[84]; (d) estimated probability of given ions decay with Purcell factor, which 50% of the ions experience a Purcell factor larger than 15 and 10% larger than 72. The cavity length is controlled by applying a voltage offset V that moves the fiber^[84]

下载: 全尺寸图片幻灯片

图 8 (a)退火工艺对$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$薄膜组分的影响示意图; (b)薄膜组分设计和结构优化(未掺杂底部缓冲层和顶部覆盖层对$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$进行封装); (c)不同后处理工艺对薄膜非均匀线宽和峰位的影响, 其中N.A.表示未退火处理, STA表示慢速退火处理, RTA表示快速退火处理; (d)制备得到的未后处理较厚$\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$薄膜(样品D)的最窄非均匀线宽; (e)经过1100℃-Ar气氛和600℃-${\rm{O}}_{\mathrm{2}}$气氛两步退火后样品D的光谱烧孔测试, 得到3 K温度下孔的宽度为10 MHz, 即$\mathrm{Eu}^{3+}$的均匀线宽窄至5 MHz^[102]

Fig. 8. (a) Effect of annealing for a single $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ thin film. (b) Composition design and structure optimization of thin film (Encapsulation of $\mathrm{Eu}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$ by undoped buffer and cap layers). (c) Inhomogeneous linewidth and position for different post-treatments. N.A. stands for not annealed (in green/empty symbol); STA, slow thermal annealing (in blue/filled symbol); RTA, rapid thermal annealing (in orange, half-filled symbols). (d) Inhomogeneous linewidth of the as grown thick film (sample D) revealing the lowest broadening; (e) SHB measurements of a 2 mm-thick multilayer sample (labelled D) with 2-step annealing. The hole width of 10 MHz at 3 K, i.e. the homogeneous broadening narrowed to 5 MHz^[102]

下载: 全尺寸图片幻灯片

图 9 (a) $\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$-Si光子晶体腔结构示意图以及离子腔耦合协作性和纠缠保真度随腔质量因子的变化^[103]; (b)$\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$-石墨烯杂化系统的动态调制示意图^[104]

Fig. 9. (a) Schematic of $\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$-Si photonic crystal cavity and the ion-cavity coupling cooperativity and entanglement fidelity as a function of cavity quality factor^[103]; (b) concept of dynamic modulation of hybrid $\mathrm{Er}^{3+}:\mathrm{Y}_{2}\mathrm{O}_{3}$-graphene system^[104]

下载: 全尺寸图片幻灯片

图 10 基于腔增强的稀土离子单晶微纳系统　(a)稀土离子光子晶体腔^[85]; (b)一维硅光子晶体腔^[72]; (c) F-P腔^[106]; (d)微环腔或回音壁模式(WGM)腔^[107]

Fig. 10. Cavity enhanced nanoscale rare earth doped systems: (a) Rare earth ions based photonic crystal cavity^[85]; (b) one-dimensional silicon photonic crystal cavity^[72]; (c) F-P cavity^[106]; (d) microring or whispering gallery modes (WGM) cavity^[107]

下载: 全尺寸图片幻灯片

图 11 (a)腔保护的概念说明: 对于具有洛伦兹线性的系综(上), 由于非均匀展宽的Δ, 极化不受保护并发生退相, 即线宽展宽. 而具有高斯线性的系综(下)可以被集体超辐射激发并保护, 不受退相影响. 图中箭头表示每个离子偶极子矢量^[86]. (b)观察到一个不随等待时间$T_{\mathrm{w}}$变化的有效线宽$\varGamma_{\mathrm{eff}}$^[110]. 插图为三脉冲光子回波序列. (c)基于$\mathrm{Er}^{3+}:\mathrm{YSO}$光子晶体腔的片上多模量子存储, (I)存储10个时间多模式2μs; (II)通过双梳过程获得的可见度, 插图为在最大建设性干扰(虚线黑线)和最大破坏性干扰(实红色线)情况下的4个输出脉冲(中间两个重叠)^[87]. (d)激发脉冲后, 单个腔耦合$\mathrm{Er}^{3+}$离子(蓝色)与没有腔增强的荧光寿命比较(橙色)^[72]. (e)在纳米光子腔中进行光学耦合的$^{171}\mathrm{Yb}$量子位元的多体核自旋寄存器示意图^[111]

Fig. 11. (a) Conceptual illustration of cavity protection for an ensemble coupled to a cavity mode: For a Lorentzian ensemble (upper), the polaritons are not protected and undergo dephasing (linewidth broadening) due to inhomogeneous broadening Δ. A Gaussian ensemble (lower) can be fully protected with the collective superradiant excitation free of such dephasing. Arrows represent the phasor of each atomic dipole^[86]. (b) A constant effective linewidth $\varGamma_{\mathrm{eff}}$ independent of the waiting time $T_{\mathrm{w}}$ has been observed^[110]. Inset: Three-pulse photon echo sequence. (c) On-chip multimode and coherent storage in the $\mathrm{Er}^{3+}:\mathrm{YSO}$ nanophotonic cavity. (I) Storage of ten temporal modes for 10 μs; (II) visbility curve acquired in a double-comb experiment, and inset is four output pulses (middle two overlapping) in the case of maximally constructive (dashed black line) and maximally destructive (solid red line) interferenc^[87]. (d) Fluorescent lifetime comparison between a single cavity-coupled $\mathrm{Er}^{3+}$ ion (blue) and a bulk ensemble without cavity enhancement (orange)^[72]. (e) Schematic of a many-body nuclear spin register for optically coupled $^{171}\mathrm{Yb}$ qubits in a nanophotonic cavity^[111]

下载: 全尺寸图片幻灯片

[1]	Xu F, Ma X, Zhang Q, Lo H K, Pan J W 2020 Rev. Mod. Phys. 92 025002 Google Scholar
[2]	Sangouard N, Simon C, de Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33 Google Scholar
[3]	Kimble H J 2008 Nature 453 1023 Google Scholar
[4]	Kok P, Munro W J, Nemoto K, Ralph T C, Dowling J P, Milburn G J 2007 Rev. Mod. Phys. 79 797 Google Scholar
[5]	Wehner S, Elkouss D, Hanson R 2018 Science 362 eaam9288 Google Scholar
[6]	Paesani S, Borghi M, Signorini S, Mainos A, Pavesi L, Laing A 2020 Nat. Commun. 11 2502 Google Scholar
[7]	Hedges M P, Longdell J J, Li Y, Sellars M J 2010 Nature 465 1052 Google Scholar
[8]	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
[9]	Saglamyurek E, Jin J, Verma V B, Shaw M D, Marsili F, Nam S W, Oblak D, Tittel W 2015 Nat. Photonics 9 83 Google Scholar
[10]	Guo M C, Liu S P, Sun W Y, Ren M M, Wang F D, Zhong M J 2023 Front. Phys. 18 21303
[11]	Dutt M V G, Childress L, Jiang L, Togan E, Maze J, Jelezko F, Zibrov A, Hemmer P R, Lukin M D 2007 Science 316 1312 Google Scholar
[12]	Taminiau T H, Cramer J, van der Sar T, Dobrovitski V V, Hanson R 2014 Nat. Nanotechnol. 9 171 Google Scholar
[13]	O’Brien C, Lauk N, Blum S, Morigi G, Fleischhauer M 2014 Phys. Rev. Lett. 113 063603 Google Scholar
[14]	Degen C L, Reinhard F, Cappellaro P 2017 Rev. Mod. Phys. 89 035002 Google Scholar
[15]	Wolfowicz G, Heremans F J, Anderson C P, Kanai S, Seo H, Gali A, Galli G, Awschalom D D 2021 Nat. Rev. Mater. 6 906 Google Scholar
[16]	Thiel C W, Böttger T, Cone R L 2011 J. Lumin. 131 353 Google Scholar
[17]	Hull R, Parisi J, Osgood R M, Warlimont H, Liu G, Jacquier B 2005 Spectroscopic Properties of Rare Earth in Optical Materials (Vol. 1) (Berlin: Springer-Verla) pp204–213
[18]	Macfarlane R M 2002 J. Lumin. 100 1 Google Scholar
[19]	Könz F, Sun Y, Thiel C W, Cone R L, Equall R W, Hutcheson R L, Macfarlane R M 2003 Phys. Rev. B 68 085109 Google Scholar
[20]	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
[21]	Tittel W, Afzelius M, Chaneliére T, Cone R L, Kröll S A, Moiseev S, Sellars M 2010 Laser Photonics Rev. 4 244 Google Scholar
[22]	Ortu A, Holzäpfel A, Etesse J, Afzelius M 2022 npj Quantum Inf. 8 29 Google Scholar
[23]	Simon C, Afzelius M, Appel J, de la Giroday A B, Dewhurst S J, Gisin N, Hu C Y, Jelezko F, Kröll S, Müller J H, Nunn J, Polzik E S, Rarity J G, de Riedmatten H, Rosenfeld W, Shields A J, Sköld N, Stevenson R M, Thew R, Walmsley I A, Weber M C, Weinfurter H, Wrachtrup J, Young R J 2010 Eur. Phys. J. D 58 1 Google Scholar
[24]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413 Google Scholar
[25]	Hiraishi M, IJspeert M, Tawara T, Adachi S, Kaji R, Omi H, Gotoh H 2019 Opt. Lett. 44 4933 Google Scholar
[26]	Welinski S, Woodburn P T, Lauk N, Cone R L, Simon C, Goldner P, Thiel C W 2019 Phys. Rev. Lett. 122 247401 Google Scholar
[27]	Probst S, Rotzinger H, Wünsch S, Jung P, Jerger M, M Siegel, Ustinov A V, Bushev P A 2013 Phys. Rev. Lett. 110 157001 Google Scholar
[28]	Fernandez-Gonzalvo X, Chen Y H, Yin C, Rogge S, Longdell J J 2015 Phys. Rev. A 92 062313 Google Scholar
[29]	Kornher T, Xiao D W, Xia K, Sardi F, Zhao N, Kolesov R, Wrachtrup J 2020 Phys. Rev. Lett. 124 170402 Google Scholar
[30]	Kinos A, Hunger D, Kolesov R, Mølmer K, de Riedmatten H, Goldner P, Tallaire A, Morvan L, Berger P, Welinski S, Karrai K, Rippe L, Kröll S, Walther A 2021 arXiv: 2103.15743 [Quantum Physics]
[31]	Kinos A, Rippe L, Kröll S, Walther A 2021 Phys. Rev. A 104 052624 Google Scholar
[32]	Kinos A, Rippe L, Serrano D, Walther A, Kröll S 2022 Phys. Rev. A 105 032603 Google Scholar
[33]	Wang P, Luan C Y, Qiao M, Um M, Zhang J, Wang Y, Yuan X, Gu M, Zhang J, Kim K 2021 Nat. Commun. 12 233 Google Scholar
[34]	de Riedmatten H, Afzelius M, Staudt M U, Simon C, Gisin N 2008 Nature 456 773 Google Scholar
[35]	Ma Y, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 2381 Google Scholar
[36]	Heinze G, Hubrich C, Halfmann T 2013 Phys. Rev. Lett. 111 033601 Google Scholar
[37]	Clausen C, Usmani I, Bussières F, Sangouard N, Afzelius M, de Riedmatten H, Gisin N 2011 Nature 469 508 Google Scholar
[38]	Liu X, Hu J, Li Z F, Li X, Li P Y, Liang P J, Zhou Z Q, Li C F, Guo G C 2021 Nature 594 41 Google Scholar
[39]	Rakonjac J V, Lago-Rivera D, Seri A, Mazzera M, Grandi S, de Riedmatten H 2021 Phys. Rev. Lett. 127 210502 Google Scholar
[40]	Usmani I, Clausen C, Bussières F, Sangouard N, Afzelius M, Gisin N 2012 Nat. Photonics 6 234 Google Scholar
[41]	Rakonjac J V, Corrielli G, Lago-Rivera D, Seri A, Mazzera M, Grandi S, Osellame R, de Riedmatten H 2022 Sci. Adv. 8 eabn3919 Google Scholar
[42]	Lago-Rivera D, Grandi S, Rakonjac J V, Seri A, de Riedmatten H 2021 Nature 594 37 Google Scholar
[43]	Tiranov A, Strassmann P C, Lavoie J, Brunner N, Huber M, Verma V B, Nam S W, Mirin R P, Lita A E, Marsili F, Afzelius M, Bussières F, Gisin N 2016 Phys. Rev. Lett. 117 240506 Google Scholar
[44]	Kutluer K, Distante E, Casabone B, Duranti S, Mazzera M, Riedmatten H 2019 Phys. Rev. Lett. 123 030501 Google Scholar
[45]	Zhou Z Q, Hua Y L, Liu X, Chen G, Xu J S, Han Y J, Li C F, Guo G C 2015 Phys. Rev. Lett. 115 070502 Google Scholar
[46]	Ferguson K R, Beavan S E, Longdell J J, Sellars M J 2016 Phys. Rev. Lett. 117 020501 Google Scholar
[47]	Beavan S E, Hedges M P, Sellars M J 2012 Phys. Rev. Lett. 109 093603 Google Scholar
[48]	Sabooni M, Li Q, Kröll S, Rippe L 2013 Phys. Rev. Lett. 110 133604 Google Scholar
[49]	Jobez P, Usmani I, Timoney N, Laplane C, Gisin N, Afzelius M 2014 New J. Phys. 16 083005 Google Scholar
[50]	Schraft D, Hain M, Lorenz N, Halfmann T 2016 Phys. Rev. Lett. 116 073602 Google Scholar
[51]	Davidson J H, Lefebvre P, Zhang J, Oblak D, Tittel W 2020 Phys. Rev. A 101 042333 Google Scholar
[52]	Bussieres F, Clausen C, Tiranov A, Korzh B, Verma V B, Nam S W, Marsili F, Ferrier A, Goldner P, Herrmann H, Silberhorn C, Sohler W, Afzelius M, Gisin N 2014 Nat. Photonics 8 775 Google Scholar
[53]	Usmani I, Afzelius M, de Riedmatten H, Gisin N 2010 Nat. Commun. 1 12 Google Scholar
[54]	Rippe L, Julsgaard B, Walther A, Ying Y, Kröll S 2008 Phys. Rev. A 77 022307 Google Scholar
[55]	Kolesov R, Xia K, Reuter R, Stöhr R, Zappe A, Meijer J, Hemmer P R, Wrachtrup J 2012 Nat. Commun. 3 1029 Google Scholar
[56]	Perrot A, Goldner P, Giaume D, Lovrić M, Andriamiadamanana C, Gonçalves R R, Ferrier A 2013 Phys. Rev. Lett. 111 203601 Google Scholar
[57]	Scarafagio M, Tallaire A, Tielrooij K J, Cano D, Grishin A, Chavanne M H, Koppens F, Ringuedé A, Cassir M, Serrano D, Goldner P, Ferrier A 2019 J. Phys. Chem. C 123 13354 Google Scholar
[58]	McAuslan D L, Longdell J J, Sellars M J 2009 Phys. Rev. A 80 062307 Google Scholar
[59]	Becher C, Gao W, Kar S, Marciniak C D, Monz T, Bartholomew J G, Goldner P, Loh H, Marcellina E, Goh K E J, Koh T S, Weber B, Mu Z, Tsai J Y, Yan Q, Huber-Loyola T, Höfling S, Gyger S, Steinhauer S, Zwiller V 2023 Mater. Quantum Technol. 3 012501 Google Scholar
[60]	Levenson M D L, Yen W, 1987 Lasers, Spectroscopy and New Ideas (Vol. 1) (Berlin: Springer-Verla) pp205–206
[61]	Stoneham A M 1969 Rev. Mod. Phys. 41 82 Google Scholar
[62]	Kunkel N, Bartholomew J, Welinski S, Ferrier A, Ikesue A, Goldner P 2016 Phys. Rev. B 94 184301 Google Scholar
[63]	Böttger T, Thiel C W, Sun Y, Cone R L 2006 Phys. Rev. B 73 075101 Google Scholar
[64]	Goldner P, Ferrier A, Guillot-Noöl O 2015 Rare Earth-doped Crystals for Quantum Information Processing (Vol. 1) (Amsterdam: Elsevier) pp1–78
[65]	Hahn E L 1950 Phys. Rev. B 80 580 Google Scholar
[66]	Kurnit N A, Abella I D, Hartmann S R 1964 Phys. Rev. Lett. 13 567 Google Scholar
[67]	Scully M O, Zubairy M S 1997 Quantum Optics (Vol. 1) (Cambridge: University Press) pp156–158
[68]	Abragam A 1983 The Principles of Nuclear Magnetism (Vol. 1) (Oxford: Oxford University Press) pp19–36
[69]	Brewer R G, Shoemaker R L 1972 Phys. Rev. A 6 2001 Google Scholar
[70]	Zhong T, Goldner P 2019 Nanophotonics 8 2003 Google Scholar
[71]	Kunkel N, Goldner P 2018 Z. Anorg. Allg. Chem. 644 66 Google Scholar
[72]	Dibos A M, Raha M, Phenicie C M, Thompson J D 2018 Phys. Rev. Lett. 120 243601 Google Scholar
[73]	Williamson L A, Chen Y H, Longdell J J 2014 Phys. Rev. Lett. 113 203601 Google Scholar
[74]	Zhong T, Kindem J M, Bartholomew J G, Rochman J, Craiciu I, Miyazono E, Bettinelli M, Cavalli E, Soni V, Nam S W, Marsili F, Shaw M D, Beyer A D, Faraon A 2017 Science 357 1392 Google Scholar
[75]	Ahlefeldt R L, Pearce M J, Hush M R, Sellars M J 2020 Phys. Rev. A 101 012309 Google Scholar
[76]	Grimm M, Beckert A, Aeppli G, Müller M 2021 PRX Quantum 2 010312 Google Scholar
[77]	Gouzien E, Sangouard N 2021 Phys. Rev. Lett. 127 140503 Google Scholar
[78]	Meltzer R S, Hong K S 2000 Phys. Rev. B 61 3396 Google Scholar
[79]	Utikal T, Eichhammer E, Petersen L, Renn A, Götzinger S, Sandoghdar V 2014 Nat. Commun. 5 3627 Google Scholar
[80]	Eichhammer E, Utikal T, Götzinger S, Sandoghdar V 2015 New J. Phys. 17 083018 Google Scholar
[81]	Liu S, Serrano D, Fossati A, Tallaire A, Ferrier A, Goldner P 2018 RSC Advances 8 37098 Google Scholar
[82]	Liu S, Fossati A, Serrano D, Tallaire A, Ferrier A, Goldner P 2020 ACS Nano 14 9953 Google Scholar
[83]	Casabone B, Benedikter J, Hümmer T, Oehl F, de Oliveira Lima K, Haensch T W, Ferrier A, Goldner P, de Riedmatten H, David H 2018 New J. Phys. 20 095006 Google Scholar
[84]	Casabone B, Deshmukh C, Liu S, Serrano D, Ferrier A, Hümmer T, Goldner P, Hunger D, de Riedmatten H 2021 Nat. Commun. 12 3570 Google Scholar
[85]	Zhong T, Kindem J M, Miyazono E, Faraon A 2015 Nat. Commun. 6 8206 Google Scholar
[86]	Zhong T, Kindem J M, Rochman J, Faraon A 2017 Nat. Commun. 8 14107 Google Scholar
[87]	Craiciu I, Lei M, Rochman J, Kindem J M, Bartholomew J G, Miyazono E, Zhong T, Sinclair N, Faraon A 2019 Phys. Rev. Appl. 12 024062 Google Scholar
[88]	Raha M, Chen S, Phenicie C P, Ourari S, Dibos A M, Thompson J D 2020 Nat. Commun. 11 1605 Google Scholar
[89]	Chen S, Raha M, Phenicie C M, Ourari S, Thompson J D 2020 Science 370 592 Google Scholar
[90]	Rice P R, Carmichael H J 1988 IEEE J. Quantum Electron 24 1351 Google Scholar
[91]	de Oliveira Lima K, Rocha Gonçalves R G, Giaume D, Ferrier A, Goldner P 2015 J. Lumin. 168 276 Google Scholar
[92]	Bartholomew J G, de Oliveira Lima K, Ferrier A, Goldner P 2017 Nano Lett. 17 778 Google Scholar
[93]	Alqedra M K, Deshmukh C, Liu S , Serrano D, Horvath S P, Rafie-Zinedine S, Abdelatief A, Rippe L, Kröll S, Casabone B, Ferrier A, Tallaire A, Goldner P, de Riedmatten H, Walther A 2023 arXiv: 2303.02054 [Quantum Physics]
[94]	Ferrier A, Thiel C W, Tumino B, Ramirez M O, Bausá L E, Cone R L, Ikesue A, Goldner P 2013 Phys. Rev. B 87 041102 Google Scholar
[95]	Serrano D, J Karlsson, Fossati A, Ferrier A, Goldner P 2018 Nat. Commun. 9 2127 Google Scholar
[96]	Serrano D, Deshmukh C, Liu S, Tallaire A, Ferrier A, Riedmatten H, Goldner P 2019 Phys. Rev. B 100 144304 Google Scholar
[97]	Fossati A, Liu S, Karlsson J, Ikesue A, Tallaire A, Ferrier A, Serrano D, Goldner P 2020 Nano Lett. 20 7087 Google Scholar
[98]	Ferrier A, Harada N, Scarafagio M, Briand E, Ganem J, Vickridge I, Seyeux A, Marcus P, Serrano D, Goldner P, Tallaire A 2020 J. Phys. Chem. C 124 19725 Google Scholar
[99]	Flinn G P, Jang K W, Ganem J J, Jones M L, Meltzer R S, Macfarlane R M 1994 J. Lumin. 58 374 Google Scholar
[100]	Harada N, Ferrier A, Serrano D, Persechino M, Briand E, Bachelet R, Vickridge I, Ganem J J, Goldner P, Tallaire A 2020 J. Appl. Phys. 128 055304 Google Scholar
[101]	Singh M K, Prakash A, Wolfowicz G, Wen J, Huang Y, Rajh T, Awschalom D D, Zhong T, Guha S 2020 APL Materials 8 031111 Google Scholar
[102]	Harada N, Tallaire A, Serrano D, Seyeux A, Marcus P, Portier X, C Labbé, Goldner P, Ferrier A 2022 Mater. Adv. 3 300 Google Scholar
[103]	Wicker C, Huang Y, Qiao H, Singh M, Prakash A, Dibos A, Guha S, Zhong T 2020 2020 IEEE Photonics Conference (IPC), Virtual Conference, September 28–October 1, 2020 p1
[104]	Cano D, Ferrier A, Soundarapandian K, Reserbat-Plantey A, Scarafagio M, Tallaire A, Seyeux A, Marcus P, de Riedmatten H, Goldner P, Koppens F H L, Tielrooij K J 2020 Nat. Commun. 11 4094 Google Scholar
[105]	Probst S, Tkalcec A, Rotzinger H, Rieger D, Le Floch J M, Goryachev M, Tobar M E, Ustinov A V, Bushev P A 2014 Phys. Rev. B 90 100404 Google Scholar
[106]	Ulanowski A, Merkel B, Reiserer A 2022 Sci. Adv. 8 eabo4538 Google Scholar
[107]	Lau H K, Qiao H, Clerk A A, Zhong T 2022 arXiv: 2208.00886 [Quantum Physics]
[108]	Lauritzen B, Hastings-Simon S R, Riedmatten H de, Afzelius M, Gisin N 2008 Phys. Rev. A 78 043402 Google Scholar
[109]	Miyazono E, Zhong T, Craiciu I, Kindem J, Faraon A 2016 Appl. Phys. Lett. 108 011111 Google Scholar
[110]	Merkel B, Ulanowski A, Reiserer A 2020 Phys. Rev. X 10 041025 Google Scholar
[111]	Ruskuc A, Wu C J, Rochman J, Choi J, Faraon A 2022 Nature 602 408 Google Scholar
[112]	Zhong T, Kindem J M, Bartholomew J G, Rochman J, Craiciu I, Verma V, Nam S W, Marsili F D, Shaw M D, Beyer A, Faraon A 2018 Phys. Rev. Lett. 121 183603 Google Scholar
[113]	Bartholomew J G, Rochman J, Xie T, Kindem J M, Ruskuc A, Craiciu I, Lei M, Faraon A 2020 Nat. Commun. 11 3266 Google Scholar
[114]	Calmano T, Siebenmorgen J, Hellmig O, Petermann K, Huber G 2010 Appl. Phys. B 100 131 Google Scholar
[115]	Corrielli G, Seri A, Mazzera M, Osellame R, Riedmatten H de 2016 Phys. Rev. Appl. 5 054013 Google Scholar
[116]	Liu C, Zhu T X, Su M X, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2020 Phys. Rev. Lett. 125 260504 Google Scholar
[117]	Weis R S, Gaylord T K 1985 Appl. Phys. A 37 191 Google Scholar
[118]	Sinclair N, Saglamyurek E, Mallahzadeh H, Slater J A, George M, Ricken R, Hedges M P, Oblak D, Simon C, Sohler W, Tittel W 2014 Phys. Rev. Lett. 113 053603 Google Scholar
[119]	Curtz N, Thew R, Simon C, Gisin N, Zbinden H 2010 Opt Express 18 22099 Google Scholar
[120]	Li M, Ling J, He Y, Javid U A, Xue S, Lin Q 2020 Nat. Commun. 11 4123 Google Scholar
[121]	Guarino A, Poberaj G, Rezzonico D, Degl’Innocenti R, Günter P 2007 Nat. Photonics 1 407 Google Scholar
[122]	Sinclair N, Saglamyurek E, George M, Ricken R, la Mela C, Sohler W, Tittel W 2010 J. Lumin. 130 1586 Google Scholar
[123]	Sinclair N, Oblak D, Thiel C W, Cone R L, Tittel W 2017 Phys. Rev. Lett. 118 110504 Google Scholar
[124]	Vredenberg A M, Hunt N E J, Schubert E F, Jacobson D C, Poate J M, Zydzik G J 1993 Phys. Rev. Lett. 71 517 Google Scholar
[125]	Yin C, Rancic M, de Boo G G, Stavrias N, McCallum J C, Sellars M J, Rogge S 2013 Nature 497 91 Google Scholar
[126]	Lansbergen G P, Rahman R, Wellard C J, Woo I, Caro J, Collaert N, Biesemans S, Klimeck G, Hollenberg L C L, Rogge S 2008 Nat. Phys. 4 656 Google Scholar
[127]	Wicker C, Huang Y, Qiao H, Zhong T 2021 Conference on Lasers and Electro-Optics San Jose, California, United States, May 9–14, 2021 pFTh1 P.6
[128]	Bharuth-Ram K, Vetter U, Hofsäss H, Ronning C, and Dietrich M 2002 Nucl. Instrum. Meth. B 190 835 Google Scholar
[129]	Magyar A, Hu W, Shanley T, Flatté M E, Hu E, Aharonovich I 2014 Nat. Commun. 5 3523 Google Scholar
[130]	Xia K, Sardi F, Sauerzapf C, Kornher T, Becker H W, Kis Z, Kovacs L, Dertli D, Foglszinger J, Kolesov R, Wrachtrup J 2022 Optica 9 445 Google Scholar
[131]	Macfarlane R M, Shelby R M 1981 Opti. Commun. 39 169
[132]	Karlsson J, Kunkel N, Ikesue A, Ferrier A, Goldner P 2017 J. Phys.: Condens. Matter 29 125501 Google Scholar
[133]	Fukumori R, Huang Y, Yang J, Zhang H, Zhong T 2020 Phys. Rev. B 101 214202 Google Scholar
[134]	Gupta S, Wu X, Zhang H, Yang J, Zhong T 2022 arXiv: 2207.02708 [Quantum Physics]
[135]	Serrano D, Kuppusamy S K, Heinrich B, Fuhr O, Hunger D, Ruben M, Goldner P 2022 Nature 603 241 Google Scholar

[1]	王一诺, 宋昭阳, 马玉林, 华南, 马鸿洋. 基于DNA编码与交替量子随机行走的彩色图像加密算法. 物理学报, 2021, 70(23): 230302. doi: 10.7498/aps.70.20211255
[2]	李保民, 胡明亮, 范桁. 量子相干. 物理学报, 2019, 68(3): 030304. doi: 10.7498/aps.68.20181779
[3]	史保森, 丁冬生, 张伟, 李恩泽. 基于拉曼协议的量子存储. 物理学报, 2019, 68(3): 034203. doi: 10.7498/aps.68.20182215
[4]	窦建鹏, 李航, 庞晓玲, 张超妮, 杨天怀, 金贤敏. 量子存储研究进展. 物理学报, 2019, 68(3): 030307. doi: 10.7498/aps.68.20190039
[5]	姚洪斌, 蒋相站, 曹长虹, 李文亮. HD⁺分子的强场光解离动力学及其量子调控的理论研究. 物理学报, 2019, 68(17): 178201. doi: 10.7498/aps.68.20190400
[6]	王文彬, 朱银燕, 殷立峰, 沈健. 复杂氧化物中电子相分离的量子调控. 物理学报, 2018, 67(22): 227502. doi: 10.7498/aps.67.20182007
[7]	李明, 陈阳, 郭光灿, 任希锋. 表面等离激元量子信息应用研究进展. 物理学报, 2017, 66(14): 144202. doi: 10.7498/aps.66.144202
[8]	杨增强, 张力达. 红外激光载波包络相位对氦原子的极紫外光(XUV)吸收谱的量子调控研究. 物理学报, 2015, 64(13): 133203. doi: 10.7498/aps.64.133203
[9]	姚洪斌, 李文亮, 张季, 彭敏. K2分子在强激光场下的量子调控：缀饰态选择性分布. 物理学报, 2014, 63(17): 178201. doi: 10.7498/aps.63.178201
[10]	李卓, 邢莉娟. 差错基、量子码与群代数. 物理学报, 2013, 62(13): 130306. doi: 10.7498/aps.62.130306
[11]	王云江, 白宝明, 彭进业, 王新梅. 针对X-Z型Pauli信道的量子稀疏图码的反馈式和积译码算法. 物理学报, 2011, 60(3): 030306. doi: 10.7498/aps.60.030306
[12]	邢莉娟, 李卓, 张武军. 加强的量子汉明限. 物理学报, 2011, 60(5): 050304. doi: 10.7498/aps.60.050304
[13]	王云江, 白宝明, 王新梅. 量子稀疏图码的反馈式迭代译码. 物理学报, 2010, 59(11): 7591-7595. doi: 10.7498/aps.59.7591
[14]	尹辑文, 肖景林, 于毅夫, 王子武. 库仑势对抛物量子点量子比特消相干的影响. 物理学报, 2008, 57(5): 2695-2698. doi: 10.7498/aps.57.2695
[15]	邢莉娟, 李卓, 白宝明, 王新梅. 量子卷积码的编译码方法. 物理学报, 2008, 57(8): 4695-4699. doi: 10.7498/aps.57.4695
[16]	李卓, 邢莉娟. 量子Generalized Reed-Solomon码. 物理学报, 2008, 57(1): 28-30. doi: 10.7498/aps.57.28
[17]	李卓, 邢莉娟. 一类基于级联结构的量子好码. 物理学报, 2007, 56(10): 5602-5606. doi: 10.7498/aps.56.5602
[18]	张权, 张尔扬. 非对称二状态量子密钥分配协议最优参量研究. 物理学报, 2002, 51(8): 1684-1689. doi: 10.7498/aps.51.1684
[19]	张权, 唐朝京, 张森强. B92量子密钥分配协议的变形及其无条件安全性证明. 物理学报, 2002, 51(7): 1439-1447. doi: 10.7498/aps.51.1439
[20]	张权, 唐朝京, 高峰. 量子Turbo码. 物理学报, 2002, 51(1): 15-20. doi: 10.7498/aps.51.15

计量

文章访问数: 5907
PDF下载量: 156
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板

微纳尺度稀土掺杂晶体的量子相干性能及其应用研究进展