Quantum memory and manipulation based on erbium doped crystals

Zhou Pai; Li Xia-Xia; Xing Xue-Yan; Chen Yu-Hui; Zhang Xiang-Dong

doi:10.7498/aps.71.20211803

Abstract

Quantum information is a rapidly emerging field aiming at combining two of the greatest advances in science and technology of the twentieth century, that is, quantum mechanics and information science. To reliably generate, store, process, and transmit quantum information, diverse systems have been studied. While for specific tasks some of these systems are more suitable than others, no single system can meet all envisioned demands. Erbium doped crystal has optical transition at 1.5 μm and possesses long optical coherence time and spin coherence time, and thus is one of the best candidates in building several essential blocks for quantum information applications. In this review, we summarize the applications of erbium doped crystals in quantum memories, quantum transducers, quantum sources, and quantum manipulations based on erbium-erbium interactions. Finally, the outlooks for near term prospects of the mentioned topics are also given.

Keywords:

Authors and contacts

Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China

Corresponding author: Chen Yu-Hui, stephen.chen@bit.edu.cn ; Zhang Xiang-Dong, zhangxd@bit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 91850205), the Start-up Fund of Beijing Institute of Technology, China, and the Science and Technology Innovation Project of Beijing Institute of Technology, China.

FullText HTML : translate this paragraph

References

[1]	DiVincenzo D P 1995 Science 270 255 Google Scholar
[2]	Wang Y 2012 Stat. Sci. 27 373 Google Scholar
[3]	Aspuru-Guzik A, Walther P 2012 Nat. Phys. 8 285 Google Scholar
[4]	Sangouard N, Simon C, De Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33 Google Scholar
[5]	Grezes C, Julsgaard B, Kubo Y, Ma W L, Stern M, Bienfait A, Nakamura K, Isoya J, Onoda S, Ohshima T, Jacques V, Vion D, Esteve D, Liu R B, Molmer K, Bertet P 2015 Phys. Rev. A 92 020301 Google Scholar
[6]	Thiel C, Böttger T, Cone R 2011 J. Lumin. 131 353 Google Scholar
[7]	Awschalom D D, Hanson R, Wrachtrup J, Zhou B B 2018 Nat. Photonics 12 516 Google Scholar
[8]	Clarke J, Wilhelm F K 2008 Nature 453 1031 Google Scholar
[9]	Reithmaier J P, Sek G, Löffler A, Hofmann C, Kuhn S, Reitzenstein S, Keldysh L V, Kulakovskii V D, Reinecke T L, Forchel A 2004 Nature 432 197 Google Scholar
[10]	Heshami K, England D G, Humphreys P C, Bustard P J, Acosta V M, Nunn J, Sussman B J 2016 J. Mod. Opt. 63 2005 Google Scholar
[11]	Schoelkopf R J, Girvin S M 2008 Nature 451 664 Google Scholar
[12]	Xiang Z L, Ashhab S, You J, Nori F 2013 Rev. Mod. Phys. 85 623 Google Scholar
[13]	Kurizki G, Bertet P, Kubo Y, Mølmer K, Petrosyan D, Rabl P, Schmiedmayer J 2015 Proc. Natl. Acad. Sci. U. S. A. 112 3866 Google Scholar
[14]	Liu G, Jacquier B 2005 Spectroscopic Properties of Rare Earths in Optical Materials (Berlin, Heidelberg: Springer)
[15]	Bussières F, Sangouard N, Afzelius M, de Riedmatten H, Simon C, Tittel W 2013 J. Mod. Opt. 60 1519 Google Scholar
[16]	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
[17]	Sun Y, Thiel C, Cone R, Equall R, Hutcheson R 2002 J. Lumin. 98 281 Google Scholar
[18]	张雪莹, 袁晨智, 魏世海, 席琪, 敬波, 王浟, 宋海智, 邓光伟, 周强 2019 低温 41 315 Google Scholar Zhang X Y, Yuan C Z, Wei S H, Xi Q, Jing B, Wang Y, Song H Z, Deng G W, Zhou Q 2019 Low Temp. Phys. Lett. 41 315 Google Scholar
[19]	Böttger T, Thiel C W, Cone R L, Sun Y 2009 Phys. Rev. B 79 115104 Google Scholar
[20]	Rančić M, Hedges M P, Ahlefeldt R L, M J Sellars 2018 Nat. Phys. 14 50 Google Scholar
[21]	Fraval E, Sellars M J, Longdell J J 2004 Phys. Rev. Lett. 92 077601 Google Scholar
[22]	Ma Y, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 2381 Google Scholar
[23]	Ortu A, Tiranov A, Welinski S, Fröwis F, Gisin N, Ferrier A, Goldner P, Afzelius M 2018 Nat. Mater. 17 671 Google Scholar
[24]	Hashimoto D, Shimizu K 2016 J. Lumin. 171 183 Google Scholar
[25]	Chen Y H, Fernandez-Gonzalvo X, Longdell J J 2016 Phys. Rev. B 94 075117 Google Scholar
[26]	Chen Y H, Fernandez-Gonzalvo X, Horvath S P, Rakonjac J V, Longdell J J 2018 Phys. Rev. B 97 024419 Google Scholar
[27]	Guillot-Noël O, Goldner P, Du Y L, Baldit E, Monnier P, Bencheikh K 2006 Phys. Rev. B 74 214409 Google Scholar
[28]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[29]	Gong M, Wang S, Zha C, Chen M C, Huang H L, Wu Y, Zhu Q, Zhao Y, Li S, Guo S, Keitel C H 2021 Science 372 948 Google Scholar
[30]	Probst S, Rotzinger H, Ustinov A V, Bushev P A 2015 Phy. Rev. B 92 014421 Google Scholar
[31]	Rakonjac J V, Chen Y H, Horvath S P, Longdell J J 2020 Phys. Rev. B 101 184430 Google Scholar
[32]	Cacciapuoti A S, Caleffi M, Tafuri M, Tafuri F, Cataliotti F S, Gherardini S, Bianchi G, Keitel C H 2018 IEEE Network 34 137 Google Scholar
[33]	Simon C 2017 Nat. Photonics 11 678 Google Scholar
[34]	Zhong T, Goldner P 2019 Nanophotonics 8 2003 Google Scholar
[35]	Baumann I, Brinkmann R, Dinand M, Sohler W, Beckers L, Buchal C, Fleuster M, Holzbrecher H, Paulus H, Müller K H, Gog T, Materlik G, Witte O, Stolz H, Von Der Osten W 1996 Appl. Phys. A 64 33 Google Scholar
[36]	Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussìres F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512 Google Scholar
[37]	Askarani M F, Puigibert M G, Lutz T, Verma V B, Shaw M D, Nam S W, Sinclair N, Oblak D, Tittel W 2019 Phys. Rev. Appl. 11 054056 Google Scholar
[38]	Liu C, Zhou Z Q, Zhu T X, Zheng L, Jin M, Liu X, Li P Y, Huang J Y, Ma Y, Tu T, Yang T S, Li C F, Guo G C 2020 Optica 7 192 Google Scholar
[39]	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
[40]	Zhong T, Kindem J M, Bartholomew J G, Rochman J, Craiciu I, Miyazono E, Bettinelli M, Cavalli E, Verma V, Nam S W 2017 Science 357 1392 Google Scholar
[41]	Craiciu I, Lei M, Rochman J, Kindem J M, Bartholomew J G, Miyazono E, Zhong E, Sinclair N, Faraon A 2019 Phys. Rev. Appl. 12 024062 Google Scholar
[42]	Craiciu I, Lei M, Rochman J, Bartholomew J G, Faraon A 2021 Optica 8 114 Google Scholar
[43]	Dajczgewand J, Le Gouët J L, Louchet-Chauvet A, Chanelière T 2014 Opt. Lett. 39 2711 Google Scholar
[44]	Dutta S, Goldschmidt E A, Barik S, Saha U, Waks E 2020 Nano Lett. 20 741 Google Scholar
[45]	Lin J, Bo F, Cheng Y, Xu J 2020 Photonics Res. 8 1910 Google Scholar
[46]	Zhu D, Shao L, Yu M, Cheng R, Desiatov B, Xin C J, Hu Y, Holzgrafe J, Ghosh S, Shams-Ansari A, Puma E, Sinclair N, Reimer C, Zhang M, Lončar M, 2021 Adv. Opt. Photonics 13 242 Google Scholar
[47]	Liu Y A, Yan X S, Wu J W, Zhu B, Chen Y P, Chen X F 2021 Sci. China Phys. Mech. Astron. 64 234262 Google Scholar
[48]	Luo Q, Hao Z Z, Yang C, Zhang R, Zheng D H, Liu H D, Bo F, Kong Y F, Zhang G Q, Xu J J 2021 Sci. China Phys. Mech. Astron. 64 234263 Google Scholar
[49]	Xiao Z, Wu K, Cai M, Li T, Chen J 2021 Opt. Lett. 46 4128 Google Scholar
[50]	Sher M S M 2021 Opt. Eng. 60 047101 Google Scholar
[51]	Wang S, Yang L, Cheng R, Xu Y, Shen M, Cone R L, Thiel C W, Tang H X 2020 Appl. Phys. Lett. 116 151103 Google Scholar
[52]	Yang L, Wang S, Shen M, Xu Y, Xie J, Tang H X 2021 Opt. Express 29 15497 Google Scholar
[53]	Omi H, Tawara T, Tateishi M 2012 AIP Adv. 2 012141 Google Scholar
[54]	Adachi S, Kawakami Y, Kaji R, Tawara T, Omi H 2018 Appl. Sci. 8 874 Google Scholar
[55]	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
[56]	Jin J, Saglamyurek E, Grimau Puigibert M L, Verma V, Marsili F, Nam S W, Oblak D, Tittel W 2015 Phys. Rev. Lett. 115 140501 Google Scholar
[57]	Grimau Puigibert M L, Askarani M F, Davidson J H, Verma V B, Shaw M D, Nam S W, Lutz T, Amaral G C, Oblak D, Tittel W 2020 Phys. Rev. Research 2 013039 Google Scholar
[58]	Saglamyurek E, Puigibert M G, Zhou Q, Giner L, Marsili F, Verma V B, Nam S W, Oesterling L, Nippa D, Oblak D, Tittel W 2016 Nat. Commun. 7 11202 Google Scholar
[59]	Xi Q, Wei S, Yuan C, Zhang X, Wang Y, Song H, Deng G, Jing B, Oblak D, Zhou Q 2020 Sci. China Inf. Sci. 63 180505 Google Scholar
[60]	Wei S H, Jing B, Zhang X Y, Wang H Q, Li H, You L X, Wang Z, Wang Y, Deng G W, Song H Z, Oblak D, Guo G C, Zhou Q 2021 CLEO: QELS_Fundamental Science San Jose, USA, May 9–14, 2021 paper FM4M.2
[61]	Lambert N J, Rueda A, Sedlmeir F, Schwefel H G 2020 Adv. Quantum Technol. 3 1900077 Google Scholar
[62]	Morsch O https://ethz.ch/en/news-and-events/eth-news/news /2020/03/longest-microwave-quantum-link.html [2020-05-03]
[63]	Williamson L A, Chen Y H, Longdell J J 2014 Phys. Rev. Lett. 113 203601 Google Scholar
[64]	Han X, Fu W, Zou C L, Jiang L, Tang H X, 2021 Optica 8 1050 Google Scholar
[65]	Andrews R W, Peterson R W, Purdy T P, Cicak K, Simmonds R W, Regal C A, Lehnert K W 2014 Nat. Phys. 10 321 Google Scholar
[66]	Higginbotham A P, Burns P S, Urmey M D, Peterson R W, Kampel N S, Brubaker B M, Smith G, Lehnert K W, Regal C A 2018 Nat. Phys. 14 1038 Google Scholar
[67]	Fernandez-Gonzalvo X, Horvath S P, Chen Y H, Longdell J J 2019 Phys. Rev. A 102 063718 Google Scholar
[68]	Fernandez-Gonzalvo X, Chen Y H, Yin C, Rogge S, Longdell J J 2015 Phys. Rev. A 92 062313 Google Scholar
[69]	Barnett P S, Longdell J J 2020 Phys. Rev. A 102 063718 Google Scholar
[70]	King G G, Barnett P S, Bartholomew J G, Faraon A, Longdell J J 2021 Phys. Rev. B 103 214305 Google Scholar
[71]	Ohta R, Herpin Bastidas V M, Tawara T, Yamaguchi H, Okamoto H 2021 Phys. Rev. Lett. 126 47404 Google Scholar
[72]	Aharonovich I, Englund D, Toth M 2016 Nat. Photonics 10 631 Google Scholar
[73]	段兆晨, 李金朋, 何玉明 2018 低温 40 1 Duan Z, Li J, He Y 2018 Low Temp. Rev. Lett. 40 1
[74]	Meyer-Scott E, Silberhorn C, Migdall A 2020 Rev. Sci. Instrum. 91 041101 Google Scholar
[75]	Cao X, Zopf M, Ding F 2019 J. Semicond. 40 071901 Google Scholar
[76]	Buckley S, Rivoire K, Vučković J 2012 Rep. Prog. Phys. 75 126503 Google Scholar
[77]	Cade N I, Gotoh H, Kamada H, Nakano H, Anantathanasarn S, Nötzel R 2006 Appl. Phys. Lett. 89 181113 Google Scholar
[78]	Dibos A M, Raha M, Phenicie C M, Thompson J D 2018 Phys. Rev. Lett. 120 243601 Google Scholar
[79]	Lukin M D, Fleischhauer M, Cote R, Duan L M, Jaksch D, Cirac J I, Zoller P 2001 Phys. Rev. Lett. 87 037901 Google Scholar
[80]	Ohlsson N, Mohan R K, Kroll S 2002 Opt. Commun. 201 71 Google Scholar
[81]	Longdell J J, Sellars M J, Manson N B 2004 Phys. Rev. Lett. 93 130503 Google Scholar
[82]	Bertaina S, Gambarelli S, Tkachuk A, Kurkin I N, Malkin B, Stepanov A, Barbara B 2007 Nat. Nanotechnol. 2 39 Google Scholar
[83]	Chen S, Raha M, Phenicie C M, Ourari S, Thompson J D 2020 Science 370 592 Google Scholar
[84]	Carmichael H J, Walls D F 1977 Phys. Rev. B 10 1977 Google Scholar
[85]	Bowden C M, Sung C C 1979 Phys. Rev. A 19 2392 Google Scholar
[86]	Zental G 1977 Solid State Commun. 23 401 Google Scholar
[87]	Hehlen M P, Güdel H U, Shu Q, Rai J, Rai S, Rand S C 1994 Phys. Rev. Lett. 73 1103 Google Scholar
[88]	Carr C, Ritter R, Wade C G, Adams C S, Weatherill K J 2013 Phys. Rev. Lett. 111 113901 Google Scholar
[89]	Chen Y H, Horvath S P, Longdell J J, Zhang K J 2021 Phys. Rev. Lett. 126 110601 Google Scholar
[90]	Lee T E, Häffner H, Cross M C 2012 Phys. Rev. Lett. 108 023602 Google Scholar
[91]	Williamson L A, Borgh M O, Ruostekoski J 2020 Phys. Rev. Lett. 125 073602 Google Scholar
[92]	Ripka F, Kübler H, Löw R, Pfau T 2018 Science 362 446 Google Scholar

Cited By

图 1 若干代表性量子体系的特征参数^[13]. 不同材料在图中的位置是根据该体系本身的相干时间(x轴)和工作频率(y轴)排列的. 例如, 核自旋和电子自旋在低温下具有较长的相干时间; 超导量子比特、量子机械系统和微波光子腔与传统电磁波有很强的耦合作用; 同时通信波段的光子在信息的长距离传输方面具有无可比拟的优势

Figure 1. Blocks of hybrid quantum systems^[13]. Some typical systems with different functionalities are placed in the diagram according to their coherence time (x axis) and their excitation frequencies (y axis). For example, nuclear spins and electron spins feature with their long coherence time; superconducting qubits, quantum mechanical systems and microwave cavities can be strongly coupled to electromagnetic fields in radio or microwave frequencies; and photons at telecom wavelengths are unparalleled in sending information over long distance.

DownLoad: Full-Size Img PowerPoint

图 2 晶体材料中磁噪声导致的退相干效应　(a)晶体中的离子本身都具有电子自旋磁矩或者核自旋磁矩. 温度不为零时, 这些磁矩会发生无规则的抖动, 从而改变我们观测的某个离子的局域磁场, 使得它的跃迁频率发生变化$ \Delta \omega $. (b)电子自旋的塞曼效应. 对于自旋$ S = 1/2 $的电子系统, 在外加磁场的情况下, 能级会发生劈裂, 自旋能级之间的跃迁频率ω也是随外加磁场而变化的. 由塞曼效应导致的能级劈裂是线性的. (c)铒离子的超精细能级相互作用. 对于¹⁶⁷Er离子来说, 其电子自旋哈密顿量除了包含塞曼效应项, 还存在电子自旋和核自旋的超精细相互作用项${\boldsymbol{I}}\cdot {\boldsymbol{A}} \cdot {\boldsymbol{S}}$. ¹⁶⁷Er完整的自旋哈密顿量应为$H = \mu_{\rm e} {\boldsymbol{B}}\cdot {\boldsymbol{g}} \cdot {\boldsymbol{S}} +{\boldsymbol{I}}\cdot $$ {\boldsymbol{A}} \cdot {\boldsymbol{S}}+{\boldsymbol{I}}\cdot {\boldsymbol{Q}} \cdot {\boldsymbol{I}}+\mu_{\rm n} {\boldsymbol{B}} \cdot {\boldsymbol{I}}$, 其中${\boldsymbol{g}}$是电子的塞曼矩阵, ${\boldsymbol{Q}}$是电四极矩阵, $g_{\rm n} = -0.1618$是核g因子. 在存在超精细相互作用时, 离子能级结构对外界磁场变化的响应会变成非线性的, 使得在某些特殊的外加磁场下跃迁频率对磁场变化的一阶导数为零, $ \partial{ \omega} / \partial{B} = 0 $

Figure 2. Magnetic decoherence in crystals. (a) Ions that form a crystal possess electron spins or nuclear spins, which are cartooned as small magnets here. With environment temperature above zero, these magnets vibrate around their lattice positions. As a result, a vibrating magnetic field is added to the local field of a targeted ion and its transition frequency is changed by an amount of $ \Delta \omega $. (b) Zeeman effect of electron spins. For electrons with spin $ S = 1/2 $, applying a magnetic field splits the energy levels. The transition frequency ω is linear to the applied magnetic field. (c) Illustration of the hyperfine structure of erbium ions. For ¹⁶⁷Er ions that possess both electron spins and nuclear spins, the spin Hamiltonian is $H = \mu_{\rm e} {\boldsymbol{B}}\cdot {\boldsymbol{g}} \cdot {\boldsymbol{S}} +{\boldsymbol{I}}\cdot $$ {\boldsymbol{A}} \cdot {\boldsymbol{S}}+{\boldsymbol{I}}\cdot {\boldsymbol{Q}} \cdot {\boldsymbol{I}}+\mu_{\rm n} {\boldsymbol{B}} \cdot {\boldsymbol{I}}$, where $\mu_{\rm e}$ is the Bohr magneton, B is the applied magnetic field, g is the Zeeman g-matrix, A is the hyperfine matrix, Q is the electric quadrupole matrix, $\mu_{\rm n}$ is the nuclear magneton, and $g_{\rm n} = -0.1618$ is the nuclear g factor. Due to the hyperfine interactions, the transition frequency ω is no longer a linear function of the applied magnetic field, which leads to $ \partial{ \omega } / \partial{B} = 0 $ at some specific magnetic field.

DownLoad: Full-Size Img PowerPoint

图 3 ¹⁶⁷Er:YSO 晶体的基态能级在外加磁场下的变化情况　(a) ¹⁶⁷Er:YSO的16个超精细能级随外加磁场的变化情况, 其中b和c标记了图(b)和(c)对应的区域; (b)箭头b对应区域的能级变化情况; (c)箭头c对应区域的能级变化情况

Figure 3. Hyperfine structure of ¹⁶⁷Er:YSO as a function of applied magnetic field. (a) The ground state of ¹⁶⁷Er:YSO consists of 16 hyperfine energy levels, all of which show nonlinear behaviour around $ B = 0 $. Letter b and c indicate the regime of panel (b) and (c). (b) Zoomed picture of energy level as indicated by b in panel (a). (c) Zoomed picture of energy level as indicated by c in panel (c).

DownLoad: Full-Size Img PowerPoint

图 4 基于掺铒晶体可集成量子存储器的主要技术方案　(a) 在铌酸锂晶体材料上通过离子扩散制备波导结构的量子存储器^[37]; (b) 利用聚焦离子束刻蚀技术在 YVO 晶体上制备一维光子晶体结构的存储器^[41]; (c)采用激光直写技术在 YSO 晶体上制备波导结构的存储器^[38]; (d) 在 YSO 晶体上制备硅基光子学结构的存储器^[42]

Figure 4. On-chip erbium quantum memories: (a) Quantum memory based on erbium- and titanium-indiffused lithium-niobate waveguide^[37]; (b) nanophotonic quantum memory by using focued-ion-beam to fabricate a one-dimensional photonic cavity in a YVO crystal^[41]; (c) waveguide memory fabricated by femtosecond-laser micromachining on the surface of a YSO crystal^[38]; (d) quantum memory comprised of an amorphous silicon (αSi) waveguide on a YSO crystal^[42].

DownLoad: Full-Size Img PowerPoint

图 5 基于掺铒晶体量子频率转换　(a) 一种实现微波光子到1.5 μm光子的量子转换器. 掺铒晶体提供实现频率转换所必需的电光非线性, 然后分别用光学腔和微波腔来增强在各自波段的光和物质相互作用. 这样一种技术方案原则上可以在低噪声的条件下实现量子效率为100%的频率转换^[63]. (b) 基于掺铒晶体的量子频率转换实验, 实现量子效率为$ 10^{-5} $的频率转换^[68]

Figure 5. Quantum transducer based on erbium doped crystal. (a) Apparatus for quantum conversion between microwave photons and 1.5 μm optical photons. Both a microwave cavity and an optical cavity are used to enhance the light-matter interactions in their corresponding frequency regimes. Together with the large non-linearity provided by erbium ions, a low-noise and 100%-efficiency conversion can be expected ^[63]. (b) Quantum conversion from microwave photons to optical photons^[68]. The quantum efficiency is $ 10^{-5} $

DownLoad: Full-Size Img PowerPoint

图 6 基于掺铒晶体的单光子辐射　(a) 空间分辨和光谱分辨相结合的技术方法. 上图, 一般的聚焦光束会和多个铒离子发生相互作用, 不同颜色的铒离子在1.5 μm附近具有不同的辐射波长. 左下图, 利用微纳光学结构可以将光场有效地束缚在微纳尺度, 大大减小和光场发生相互作用的铒离子. 右下图, 在一个微纳光学腔中和光场发生相互作用的铒离子数目仍然很多, 不同发光波长的铒离子构成了该材料的非均匀线宽, 通过利用窄线宽的激光(小于单个铒离子的均匀线宽), 便可以选择性的单独激发红色的铒离子(其他颜色的铒离子由于频率失谐而没有被激发), 从而实现单个铒离子的探测. (b) 上图, 在Er:YSO掺杂晶体上制备硅的光子晶体腔; 下图, 铒离子的单光子辐射, 不同铒离子的辐射频率略有不同^[78]

Figure 6. Single photon sources based on erbium doped crystal. (a) Single ion detection by combining spatial and spectral resolutions. Upper panel, illustration of a large amount of ions inside a crystal interact with a focused laser beam. Dots with different color indicate that erbium ions have slightly different transition frequency around 1.5 μm. Bottom left, using nanophotonic structure to further confine the optical mode can largely reduce the number of interacting ions; bottom right, if at the same time introducing a narrow-frequency window to pick specific ions in the inhomogeneous line, one can isolate single erbium ions, e.g., using a narrow-frequency laser that is resonant with the red ions to saturate the homogeneous line while leaving ions with other colors non-excited. (b) Top, illustration of a silicon waveguide patterned with photonic crystal cavities on the top of a Er:YSO crystal. Bottom, photo-emission spectra of single erbium ions that have slightly different frequency around 1.5 μm^[78]

DownLoad: Full-Size Img PowerPoint

图 7 基于铒离子间相互作用的量子调控　(a) 利用空间分辨和光谱分辨技术, 在Er:YSO晶体上实现了对6个铒离子的相干操控^[83]; (b) 由于铒离子间的相互作用而导致的本征光学不稳相^[89].

Figure 7. Quantum manipulation based on erbium-erbium interactions: (a) Combining spatial resolution of nanophotonics and spectral resolution of narrow-frequency laser, six erbium ions can be addressed and controlled independently^[83]; (b) intrinsic optical instability due to ion-ion interactions^[89].

DownLoad: Full-Size Img PowerPoint

map

[1]	DiVincenzo D P 1995 Science 270 255 Google Scholar
[2]	Wang Y 2012 Stat. Sci. 27 373 Google Scholar
[3]	Aspuru-Guzik A, Walther P 2012 Nat. Phys. 8 285 Google Scholar
[4]	Sangouard N, Simon C, De Riedmatten H, Gisin N 2011 Rev. Mod. Phys. 83 33 Google Scholar
[5]	Grezes C, Julsgaard B, Kubo Y, Ma W L, Stern M, Bienfait A, Nakamura K, Isoya J, Onoda S, Ohshima T, Jacques V, Vion D, Esteve D, Liu R B, Molmer K, Bertet P 2015 Phys. Rev. A 92 020301 Google Scholar
[6]	Thiel C, Böttger T, Cone R 2011 J. Lumin. 131 353 Google Scholar
[7]	Awschalom D D, Hanson R, Wrachtrup J, Zhou B B 2018 Nat. Photonics 12 516 Google Scholar
[8]	Clarke J, Wilhelm F K 2008 Nature 453 1031 Google Scholar
[9]	Reithmaier J P, Sek G, Löffler A, Hofmann C, Kuhn S, Reitzenstein S, Keldysh L V, Kulakovskii V D, Reinecke T L, Forchel A 2004 Nature 432 197 Google Scholar
[10]	Heshami K, England D G, Humphreys P C, Bustard P J, Acosta V M, Nunn J, Sussman B J 2016 J. Mod. Opt. 63 2005 Google Scholar
[11]	Schoelkopf R J, Girvin S M 2008 Nature 451 664 Google Scholar
[12]	Xiang Z L, Ashhab S, You J, Nori F 2013 Rev. Mod. Phys. 85 623 Google Scholar
[13]	Kurizki G, Bertet P, Kubo Y, Mølmer K, Petrosyan D, Rabl P, Schmiedmayer J 2015 Proc. Natl. Acad. Sci. U. S. A. 112 3866 Google Scholar
[14]	Liu G, Jacquier B 2005 Spectroscopic Properties of Rare Earths in Optical Materials (Berlin, Heidelberg: Springer)
[15]	Bussières F, Sangouard N, Afzelius M, de Riedmatten H, Simon C, Tittel W 2013 J. Mod. Opt. 60 1519 Google Scholar
[16]	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
[17]	Sun Y, Thiel C, Cone R, Equall R, Hutcheson R 2002 J. Lumin. 98 281 Google Scholar
[18]	张雪莹, 袁晨智, 魏世海, 席琪, 敬波, 王浟, 宋海智, 邓光伟, 周强 2019 低温 41 315 Google Scholar Zhang X Y, Yuan C Z, Wei S H, Xi Q, Jing B, Wang Y, Song H Z, Deng G W, Zhou Q 2019 Low Temp. Phys. Lett. 41 315 Google Scholar
[19]	Böttger T, Thiel C W, Cone R L, Sun Y 2009 Phys. Rev. B 79 115104 Google Scholar
[20]	Rančić M, Hedges M P, Ahlefeldt R L, M J Sellars 2018 Nat. Phys. 14 50 Google Scholar
[21]	Fraval E, Sellars M J, Longdell J J 2004 Phys. Rev. Lett. 92 077601 Google Scholar
[22]	Ma Y, Ma Y Z, Zhou Z Q, Li C F, Guo G C 2021 Nat. Commun. 12 2381 Google Scholar
[23]	Ortu A, Tiranov A, Welinski S, Fröwis F, Gisin N, Ferrier A, Goldner P, Afzelius M 2018 Nat. Mater. 17 671 Google Scholar
[24]	Hashimoto D, Shimizu K 2016 J. Lumin. 171 183 Google Scholar
[25]	Chen Y H, Fernandez-Gonzalvo X, Longdell J J 2016 Phys. Rev. B 94 075117 Google Scholar
[26]	Chen Y H, Fernandez-Gonzalvo X, Horvath S P, Rakonjac J V, Longdell J J 2018 Phys. Rev. B 97 024419 Google Scholar
[27]	Guillot-Noël O, Goldner P, Du Y L, Baldit E, Monnier P, Bencheikh K 2006 Phys. Rev. B 74 214409 Google Scholar
[28]	Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505 Google Scholar
[29]	Gong M, Wang S, Zha C, Chen M C, Huang H L, Wu Y, Zhu Q, Zhao Y, Li S, Guo S, Keitel C H 2021 Science 372 948 Google Scholar
[30]	Probst S, Rotzinger H, Ustinov A V, Bushev P A 2015 Phy. Rev. B 92 014421 Google Scholar
[31]	Rakonjac J V, Chen Y H, Horvath S P, Longdell J J 2020 Phys. Rev. B 101 184430 Google Scholar
[32]	Cacciapuoti A S, Caleffi M, Tafuri M, Tafuri F, Cataliotti F S, Gherardini S, Bianchi G, Keitel C H 2018 IEEE Network 34 137 Google Scholar
[33]	Simon C 2017 Nat. Photonics 11 678 Google Scholar
[34]	Zhong T, Goldner P 2019 Nanophotonics 8 2003 Google Scholar
[35]	Baumann I, Brinkmann R, Dinand M, Sohler W, Beckers L, Buchal C, Fleuster M, Holzbrecher H, Paulus H, Müller K H, Gog T, Materlik G, Witte O, Stolz H, Von Der Osten W 1996 Appl. Phys. A 64 33 Google Scholar
[36]	Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussìres F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512 Google Scholar
[37]	Askarani M F, Puigibert M G, Lutz T, Verma V B, Shaw M D, Nam S W, Sinclair N, Oblak D, Tittel W 2019 Phys. Rev. Appl. 11 054056 Google Scholar
[38]	Liu C, Zhou Z Q, Zhu T X, Zheng L, Jin M, Liu X, Li P Y, Huang J Y, Ma Y, Tu T, Yang T S, Li C F, Guo G C 2020 Optica 7 192 Google Scholar
[39]	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
[40]	Zhong T, Kindem J M, Bartholomew J G, Rochman J, Craiciu I, Miyazono E, Bettinelli M, Cavalli E, Verma V, Nam S W 2017 Science 357 1392 Google Scholar
[41]	Craiciu I, Lei M, Rochman J, Kindem J M, Bartholomew J G, Miyazono E, Zhong E, Sinclair N, Faraon A 2019 Phys. Rev. Appl. 12 024062 Google Scholar
[42]	Craiciu I, Lei M, Rochman J, Bartholomew J G, Faraon A 2021 Optica 8 114 Google Scholar
[43]	Dajczgewand J, Le Gouët J L, Louchet-Chauvet A, Chanelière T 2014 Opt. Lett. 39 2711 Google Scholar
[44]	Dutta S, Goldschmidt E A, Barik S, Saha U, Waks E 2020 Nano Lett. 20 741 Google Scholar
[45]	Lin J, Bo F, Cheng Y, Xu J 2020 Photonics Res. 8 1910 Google Scholar
[46]	Zhu D, Shao L, Yu M, Cheng R, Desiatov B, Xin C J, Hu Y, Holzgrafe J, Ghosh S, Shams-Ansari A, Puma E, Sinclair N, Reimer C, Zhang M, Lončar M, 2021 Adv. Opt. Photonics 13 242 Google Scholar
[47]	Liu Y A, Yan X S, Wu J W, Zhu B, Chen Y P, Chen X F 2021 Sci. China Phys. Mech. Astron. 64 234262 Google Scholar
[48]	Luo Q, Hao Z Z, Yang C, Zhang R, Zheng D H, Liu H D, Bo F, Kong Y F, Zhang G Q, Xu J J 2021 Sci. China Phys. Mech. Astron. 64 234263 Google Scholar
[49]	Xiao Z, Wu K, Cai M, Li T, Chen J 2021 Opt. Lett. 46 4128 Google Scholar
[50]	Sher M S M 2021 Opt. Eng. 60 047101 Google Scholar
[51]	Wang S, Yang L, Cheng R, Xu Y, Shen M, Cone R L, Thiel C W, Tang H X 2020 Appl. Phys. Lett. 116 151103 Google Scholar
[52]	Yang L, Wang S, Shen M, Xu Y, Xie J, Tang H X 2021 Opt. Express 29 15497 Google Scholar
[53]	Omi H, Tawara T, Tateishi M 2012 AIP Adv. 2 012141 Google Scholar
[54]	Adachi S, Kawakami Y, Kaji R, Tawara T, Omi H 2018 Appl. Sci. 8 874 Google Scholar
[55]	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
[56]	Jin J, Saglamyurek E, Grimau Puigibert M L, Verma V, Marsili F, Nam S W, Oblak D, Tittel W 2015 Phys. Rev. Lett. 115 140501 Google Scholar
[57]	Grimau Puigibert M L, Askarani M F, Davidson J H, Verma V B, Shaw M D, Nam S W, Lutz T, Amaral G C, Oblak D, Tittel W 2020 Phys. Rev. Research 2 013039 Google Scholar
[58]	Saglamyurek E, Puigibert M G, Zhou Q, Giner L, Marsili F, Verma V B, Nam S W, Oesterling L, Nippa D, Oblak D, Tittel W 2016 Nat. Commun. 7 11202 Google Scholar
[59]	Xi Q, Wei S, Yuan C, Zhang X, Wang Y, Song H, Deng G, Jing B, Oblak D, Zhou Q 2020 Sci. China Inf. Sci. 63 180505 Google Scholar
[60]	Wei S H, Jing B, Zhang X Y, Wang H Q, Li H, You L X, Wang Z, Wang Y, Deng G W, Song H Z, Oblak D, Guo G C, Zhou Q 2021 CLEO: QELS_Fundamental Science San Jose, USA, May 9–14, 2021 paper FM4M.2
[61]	Lambert N J, Rueda A, Sedlmeir F, Schwefel H G 2020 Adv. Quantum Technol. 3 1900077 Google Scholar
[62]	Morsch O https://ethz.ch/en/news-and-events/eth-news/news /2020/03/longest-microwave-quantum-link.html [2020-05-03]
[63]	Williamson L A, Chen Y H, Longdell J J 2014 Phys. Rev. Lett. 113 203601 Google Scholar
[64]	Han X, Fu W, Zou C L, Jiang L, Tang H X, 2021 Optica 8 1050 Google Scholar
[65]	Andrews R W, Peterson R W, Purdy T P, Cicak K, Simmonds R W, Regal C A, Lehnert K W 2014 Nat. Phys. 10 321 Google Scholar
[66]	Higginbotham A P, Burns P S, Urmey M D, Peterson R W, Kampel N S, Brubaker B M, Smith G, Lehnert K W, Regal C A 2018 Nat. Phys. 14 1038 Google Scholar
[67]	Fernandez-Gonzalvo X, Horvath S P, Chen Y H, Longdell J J 2019 Phys. Rev. A 102 063718 Google Scholar
[68]	Fernandez-Gonzalvo X, Chen Y H, Yin C, Rogge S, Longdell J J 2015 Phys. Rev. A 92 062313 Google Scholar
[69]	Barnett P S, Longdell J J 2020 Phys. Rev. A 102 063718 Google Scholar
[70]	King G G, Barnett P S, Bartholomew J G, Faraon A, Longdell J J 2021 Phys. Rev. B 103 214305 Google Scholar
[71]	Ohta R, Herpin Bastidas V M, Tawara T, Yamaguchi H, Okamoto H 2021 Phys. Rev. Lett. 126 47404 Google Scholar
[72]	Aharonovich I, Englund D, Toth M 2016 Nat. Photonics 10 631 Google Scholar
[73]	段兆晨, 李金朋, 何玉明 2018 低温 40 1 Duan Z, Li J, He Y 2018 Low Temp. Rev. Lett. 40 1
[74]	Meyer-Scott E, Silberhorn C, Migdall A 2020 Rev. Sci. Instrum. 91 041101 Google Scholar
[75]	Cao X, Zopf M, Ding F 2019 J. Semicond. 40 071901 Google Scholar
[76]	Buckley S, Rivoire K, Vučković J 2012 Rep. Prog. Phys. 75 126503 Google Scholar
[77]	Cade N I, Gotoh H, Kamada H, Nakano H, Anantathanasarn S, Nötzel R 2006 Appl. Phys. Lett. 89 181113 Google Scholar
[78]	Dibos A M, Raha M, Phenicie C M, Thompson J D 2018 Phys. Rev. Lett. 120 243601 Google Scholar
[79]	Lukin M D, Fleischhauer M, Cote R, Duan L M, Jaksch D, Cirac J I, Zoller P 2001 Phys. Rev. Lett. 87 037901 Google Scholar
[80]	Ohlsson N, Mohan R K, Kroll S 2002 Opt. Commun. 201 71 Google Scholar
[81]	Longdell J J, Sellars M J, Manson N B 2004 Phys. Rev. Lett. 93 130503 Google Scholar
[82]	Bertaina S, Gambarelli S, Tkachuk A, Kurkin I N, Malkin B, Stepanov A, Barbara B 2007 Nat. Nanotechnol. 2 39 Google Scholar
[83]	Chen S, Raha M, Phenicie C M, Ourari S, Thompson J D 2020 Science 370 592 Google Scholar
[84]	Carmichael H J, Walls D F 1977 Phys. Rev. B 10 1977 Google Scholar
[85]	Bowden C M, Sung C C 1979 Phys. Rev. A 19 2392 Google Scholar
[86]	Zental G 1977 Solid State Commun. 23 401 Google Scholar
[87]	Hehlen M P, Güdel H U, Shu Q, Rai J, Rai S, Rand S C 1994 Phys. Rev. Lett. 73 1103 Google Scholar
[88]	Carr C, Ritter R, Wade C G, Adams C S, Weatherill K J 2013 Phys. Rev. Lett. 111 113901 Google Scholar
[89]	Chen Y H, Horvath S P, Longdell J J, Zhang K J 2021 Phys. Rev. Lett. 126 110601 Google Scholar
[90]	Lee T E, Häffner H, Cross M C 2012 Phys. Rev. Lett. 108 023602 Google Scholar
[91]	Williamson L A, Borgh M O, Ruostekoski J 2020 Phys. Rev. Lett. 125 073602 Google Scholar
[92]	Ripka F, Kübler H, Löw R, Pfau T 2018 Science 362 446 Google Scholar

[1]	Xiao Yi-Xin, Zhu Tian-Xiang, Liang Peng-Jun, Wang Yi-Yang, Zhou Zong-Quan, Li Chuan-Feng. Optical and hyperfine spectroscopic investigations on europium ions doped in yttrium orthosilicate waveguides fabricated by focused ion beam milling. Acta Physica Sinica, 2024, 73(22): 220303. doi: 10.7498/aps.73.20241070
[2]	Liang Peng-Jun, Zhu Tian-Xiang, Xiao Yi-Xin, Wang Yi-Yang, Han Yong-Jian, Zhou Zong-Quan, Li Chuan-Feng. Concentration-dependent optical and spin inhomogeneous linewidth of europium-doped yttrium orthosilicate crystals. Acta Physica Sinica, 2024, 73(10): 100301. doi: 10.7498/aps.73.20240116
[3]	Wang Yun-Fei, Zhou Ying, Wang Ying, Yan Hui, Zhu Shi-Liang. Performance and application analysis of quantum memory. Acta Physica Sinica, 2023, 72(20): 206701. doi: 10.7498/aps.72.20231203
[4]	Li Li-Juan, Ming Fei, Song Xue-Ke, Ye Liu, Wang Dong. Review on entropic uncertainty relations. Acta Physica Sinica, 2022, 71(7): 070302. doi: 10.7498/aps.71.20212197
[5]	Zhou Zong-Quan. “Quantum memory” quantum computers and noiseless phton echoes. Acta Physica Sinica, 2022, 71(7): 070305. doi: 10.7498/aps.71.20212245
[6]	Xing Xue-Yan, Li Xia-Xia, Chen Yu-Hui, Zhang Xiang-Dong. Optical echo memory based on photonic crystal cavities. Acta Physica Sinica, 2022, 71(11): 114201. doi: 10.7498/aps.71.20220083
[7]	. Quantum memory and manipulation based on erbium doped crystals. Acta Physica Sinica, 2021, (): . doi: 10.7498/aps.70.20211803
[8]	Li Zong-Feng, Liu Duan-Cheng, Zhou Zong-Quan, Li Chuan-Feng. Atomic frequency comb optical memory in EuCl₃·6H₂O crystal. Acta Physica Sinica, 2021, 70(16): 160302. doi: 10.7498/aps.70.20210648
[9]	Shi Bao-Sen, Ding Dong-Sheng, Zhang Wei, Li En-Ze. Raman protocol-based quantum memories. Acta Physica Sinica, 2019, 68(3): 034203. doi: 10.7498/aps.68.20182215
[10]	Dou Jian-Peng, Li Hang, Pang Xiao-Ling, Zhang Chao-Ni, Yang Tian-Huai, Jin Xian-Min. Research progress of quantum memory. Acta Physica Sinica, 2019, 68(3): 030307. doi: 10.7498/aps.68.20190039
[11]	Yang Tian-Shu, Zhou Zong-Quan, Li Chuan-Feng, Guo Guang-Can. Multimode solid-state quantum memory. Acta Physica Sinica, 2019, 68(3): 030303. doi: 10.7498/aps.68.20182207
[12]	Wang Ye, Zhang Jing-Ning, Kim Kihwan. Single-ion qubit with coherence time exceeding 10 minutes. Acta Physica Sinica, 2019, 68(3): 030306. doi: 10.7498/aps.68.20181729
[13]	An Zi-Ye, Wang Xu-Jie, Yuan Zhen-Sheng, Bao Xiao-Hui, Pan Jian-Wei. Coherent manipulation of single collective excitations in a cold atomic ensemble. Acta Physica Sinica, 2018, 67(22): 224203. doi: 10.7498/aps.67.20181183
[14]	Deng Rui-Jie, Yan Zhi-Hui, Jia Xiao-Jun. Analysis of electromagnetically induced transparency based on quantum memory of squeezed state of light. Acta Physica Sinica, 2017, 66(7): 074201. doi: 10.7498/aps.66.074201
[15]	Sun Ying, Zhao Shang-Hong, Dong Chen. Long distance measurement device independent quantum key distribution with quantum memories. Acta Physica Sinica, 2015, 64(14): 140304. doi: 10.7498/aps.64.140304
[16]	Li Jiang-Fan, Shan Shu-Min, Yang Jian-Kun, Jiang Zong-Fu. An explicit analytical solution of the Schr?dinger equation for a detuned quantum frequency conversion system. Acta Physica Sinica, 2007, 56(10): 5597-5601. doi: 10.7498/aps.56.5597
[17]	FENG SHAO-XIN, LI BAO-HUI, JIN QING-HUA, GUO ZHEN-YA, DING DA-TONG. DETERMINATION OF EMPIRICAL PARAMETERS OF INTER-IONIC POTENTIALS FOR LITHIUM NIOB ATE. Acta Physica Sinica, 2000, 49(12): 2433-2436. doi: 10.7498/aps.49.2433
[18]	Liu Tang-Kun, Wang Ji-Suo, Liu Xiao-Jun, Zhan Ming-Sheng. . Acta Physica Sinica, 2000, 49(4): 708-712. doi: 10.7498/aps.49.708
[19]	WANG JIN-GUO, ZHANG ZHI-GUO, XU JI-REN, FU PAN-MING, YAN XIU-LI, WU XING, JIANG YAN-DAO. STUDY ON UPCONVERSION FLUORESCENCE OF Er3+-DOPED YTTRIUM VANADATE. Acta Physica Sinica, 1998, 47(5): 747-755. doi: 10.7498/aps.47.747
[20]	XU ZHI ZHONG. THE EFFECTS OF INTERVALLEY INTERACTIONS ON THE ELECTRONIC STRUCTURES IN QUANTUM WELLS Ge0.3Si0.7/Si/Ge0.3Si0.7 GROWN ON Ge0.3Si0.7(001). Acta Physica Sinica, 1997, 46(4): 775-782. doi: 10.7498/aps.46.775

Catalog

Vol. 71, Issue 6 - 2022-03-20

Metrics

Abstract views: 5992
PDF Downloads: 225
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