High-fidelity storage and on-demand retrieval of quantum states via a microwave waveguide

Zhu Dao-Quan; Xiang Yu; Sun Feng-Xiao; He Qiong-Yi

doi:10.7498/aps.71.20220477

Abstract

On-demand quantum memory is an important step towards practical applications in various quantum information tasks such as long-distance entanglement distribution, quantum computation, and quantum networks. In this work, based on stimulated Raman adiabatic passage (STIRAP) protocol, we introduce a controllable delay between the reading pulse and writing pulse so that the quantum state can be stored in the superconducting waveguide and finally retrieved on demand with high fidelity. Through systematic numerical simulations, we find that if the duration of the writing pulse is set to be in a certain range, the readout unit is capable of retrieving the quantum state stored in the waveguide with high fidelity at any moment after a critical time. Moreover, we also investigate the robustness of our protocol, and find that the fidelity is robust against both the average number of thermal photons in the waveguide and the duration of the reading pulse. The numerical results also show that the pulse area in our protocol is only about one third of that in the original STIRAP protocol. Our protocol provides a practical way to combine the advantages of both on-demand quantum memory and the STIRAP protocol.

Keywords:

Authors and contacts

1.
State Key Laboratory of Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, China
2.
Nano-optoelectronics Frontier Center of Ministry of Education, Peking University, Beijing 100871, China

Corresponding author: Sun Feng-Xiao, sunfengxiao@pku.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12147148) and the Natural Science Foundation of Beijing, China (Grant No.Z190005).

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References

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Cited By

图 1 量子态存储与异地读取方案图. $ {E_{\text{C}}} $, $ {E_{\text{L}}} $分别代表两端读写腔的电容充电能和电感能量. $ {E_{{\text{C, B}}}} $和$ {E_{{\text{L, B}}}} $为波导中每个单元的电容充电能和电感能量

Figure 1. Setup for quantum state storage and remote retrieval. $ {E_{\text{C}}} $, $ {E_{\text{L}}} $ are the capacitive and inductive energies of both writing and reading cavities, respectively. $ {E_{{\text{C, B}}}} $ and $ {E_{{\text{L, B}}}} $ are the capacitive and inductive energies for the unit cell within the waveguide.

DownLoad: Full-Size Img PowerPoint

图 2 读出量子态与写入量子态之间的保真度随着读写脉冲持续时间$ T $、读出脉冲延迟$ \Delta T $的变化关系图. 这里的读出脉冲与写入脉冲最大强度均为$ A = 0.1\omega $. 图中所有的时间、频率都以读写腔的频率$ \omega $为参考进行无量纲化. 当脉冲写入时间满足$ 100/\omega \lesssim T \lesssim 200/\omega $时, 读出脉冲可以在临界时间$ {T_{\text{C}}} $之后的任意时刻对量子态进行高保真读取

Figure 2. The fidelity of the scheme as a function of the duration of the pulse $ T $ and the delay of the reading pulse $ \Delta T $. The amplitudes of both the writing and reading pulse are$ A = 0.1\omega $. Each frequency and time scale in this figure are normalized by the bare frequency $ \omega $ of the writing/reading cavities. One can notice that once the duration of the writing pulse satisfies the condition $ 100/\omega \lesssim T \lesssim 200/\omega $, high-fidelity quantum state retrieval is possible after the critical time $ {T_{\text{C}}} $.

DownLoad: Full-Size Img PowerPoint

图 3 量子态的存储与读取结果展示 (a)和(b)分别为写入量子态与读出量子态的Wigner准概率分布; (c)所需写入脉冲与读出脉冲的波形以及量子态的读取保真度. 参数取值分别为: $ T = 150/\omega $, $ \Delta T = 400/\omega $, $ A = 0.1\omega $

Figure 3. Numerical results for the storage and the retrieval of a quantum state in a waveguide: (a) and (b) are Wigner distributions of the initial state and the final state, respectively; (c) shows the pulses of our protocol used for storing and retrieving the quantum state. The related parameters are $ T = 150/\omega $, $ \Delta T = 400/\omega $, $ A = 0.1\omega $.

DownLoad: Full-Size Img PowerPoint

图 4 量子态保真度的鲁棒性. 将写入腔的初态制备在1个压缩态$ \left| {\left. {\psi (0)} \right\rangle = } \right.\left| {\left. {\alpha , r} \right\rangle } \right. $, 其中$ \alpha = \sqrt 2 $, $ r = 0.5 $. (a)和(b)分别展示了保真度对微波腔中平均热光子数, 以及对读出脉冲持续时间的鲁棒性. 参数取值分别为: 写入脉冲持续时间$ T = 150/\omega $, 读出脉冲延迟$ \Delta T = 400/\omega $, 脉冲的最大幅值$ A = 0.1\omega $

Figure 4. Robustness of the fidelity for the retrieval of the quantum state. The initial state in the writing cavity is prepared to be a squeezed coherent state $ \left| {\left. {\psi (0)} \right\rangle = } \right.\left| {\left. {\alpha , r} \right\rangle } \right. $ with $ \alpha = \sqrt 2 $ and $ r = 0.5 $. (a) and (b) show the robustness of the fidelity against the average number of thermal photons inside the waveguide and the duration of the reading pulse, respectively. Here we fix the duration of the writing pulse $ T = 150/\omega $, the delay of the reading pulse $ \Delta T = 400/\omega $ and the maximum amplitude for both pulses $ A = 0.1\omega $.

DownLoad: Full-Size Img PowerPoint

[1]	Duan L M, Lukin M D, Cirac J I, Zoller P 2001 Nature 414 413 Google Scholar
[2]	Sun C P, Li Y, Liu X F 2003 Phys. Rev. Lett. 91 147903 Google Scholar
[3]	Lvovsky A I, Sanders B C, Tittel W 2009 Nat. Photon. 3 706 Google Scholar
[4]	Hua Y L, Zhou Z Q, Li C F, Guo G C 2018 Chin. Phys. B 27 020303 Google Scholar
[5]	窦建鹏, 李航, 庞晓玲, 张超妮, 杨天怀, 金贤敏 2019 物理学报 68 030307 Google Scholar Dou J P, Li H, Pang X L, Zhang C N, Yang T H, Jin X 2019 Acta Phys. Sin. 68 030307 Google Scholar
[6]	Gisin N, Thew R 2007 Nat. Photon. 1 165 Google Scholar
[7]	Zhang W, Ding D S, Sheng Y B, Zhou L, Shi B S, Guo G C 2017 Phys. Rev. Lett. 118 220501 Google Scholar
[8]	Humphreys P C, Kolthammer W S, Nunn J, Barbieri M, Datta A, Walmsley I A 2014 Phys. Rev. Lett. 113 130502 Google Scholar
[9]	周宗权 2022 物理学报 71 070301 Google Scholar Zhou Z Q 2022 Acta Phys. Sin. 71 070301 Google Scholar
[10]	Gouzien É, Sangouard N 2021 Phys. Rev. Lett. 127 140503 Google Scholar
[11]	Saglamyurek E, Sinclair N, Jin J, Slater J A, Oblak D, Bussieres F, George M, Ricken R, Sohler W, Tittel W 2011 Nature 469 512 Google Scholar
[12]	Zhao B, Chen Y A, Bao X H, Strassel T, Chuu C S, Jin X M, Schmiedmayer J, Yuan Z S, Chen S, Pan J W 2009 Nat. Phys. 5 95 Google Scholar
[13]	Simon C 2017 Nat. Photon. 11 678 Google Scholar
[14]	Nickerson N H, Fitzsimons J F, Benjamin S C 2014 Phys. Rev. X 4 041041 Google Scholar
[15]	Brecht T, Pfaff W, Wang C, Chu Y, Frunzio L, Devoret M H, Schoelkopf R J 2016 npj Quantum Inf. 2 16002 Google Scholar
[16]	Magnard P, Storz S, Kurpiers P, Schär J, Marxer F, Lütolf J, Walter T, Besse J C, Gabureac M, Reuer K, Akin A, Royer B, Blais A, Wallraff A 2020 Phys. Rev. Lett. 125 260502 Google Scholar
[17]	Xiang Z L, Zhang M Z, Jiang L, Rabl P 2017 Phys. Rev. X 7 011035 Google Scholar
[18]	Vermersch B, Guimond P O, Pichler H, Zoller P 2017 Phys. Rev. Lett. 118 133601 Google Scholar
[19]	Axline C J, Burkhart L D, Pfaff W, Zhang M Z, Chou K, Campagne-Ibarcq P, Reinhold P, Frunzio L, Girvin S, Jiang L, Devoret M H, Schoelkopf R J 2018 Nat. Phys. 14 705 Google Scholar
[20]	Jing B, Wang X J, Yu Y, Sun P F, Jiang Y, Yang S J, Jiang W H, Luo X Y, Zhang J, Jiang X, Bao X H, Pan J W 2019 Nat. Photon. 13 210 Google Scholar
[21]	Afzelius M, Simon C, De Riedmatten H, Gisin N 2009 Phys. Rev. A 79 052329 Google Scholar
[22]	Jobez P, Laplane C, Timoney N, Gisin N, Ferrier A, Goldner P, Afzelius M 2015 Phys. Rev. Lett. 114 230502 Google Scholar
[23]	Gündoğan M, Ledingham P M, Kutluer K, Mazzera M, De Riedmatten H 2015 Phys. Rev. Lett. 114 230501 Google Scholar
[24]	Zhong T, Kindem J M, Bartholomew J G, Rochman J, Craiciu I, Miyazono E, Bettinelli M, Cavalli E, Verma V, Nam S W, Marsili F, Shaw M D, Beyer A D, Faraon A 2017 Science 357 1392 Google Scholar
[25]	Yang T S, Zhou Z Q, Hua Y L, Liu X, Li Z F, Li P Y, Ma Y, Liu C, Liang P J, Li X, Xiao Y C, Hu J, Li C F, Guo G C 2018 Nat. Commun. 9 3407 Google Scholar
[26]	Bao Z H, Wang Z L, Wu Y K, Li Y, Ma C, Song Y P, Zhang H Y, Duan L M 2021 Phys. Rev. Lett. 127 010503 Google Scholar
[27]	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
[28]	Pang X L, Yang A L, Dou J P, Li H, Zhang C N, Poem E, Saunders D J, Tang H, Nunn J, Walmsley I A, Jin X M 2020 Sci. Adv. 6 eaax1425 Google Scholar
[29]	Rakonjac J V, Lago-Rivera D, Seri A, Mazzera M, Grandi S, De Riedmatten H 2021 Phys. Rev. Lett. 127 210502 Google Scholar
[30]	Specht H P, Nölleke C, Reiserer A, Uphoff M, Figueroa E, Ritter S, Rempe G 2011 Nature 473 190 Google Scholar
[31]	Ding D S, Zhang W, Zhou Z Y, Shi S, Pan J S, Xiang G Y, Wang X S, Jiang Y K, Shi B S, Guo G C 2014 Phys. Rev. A 90 042301 Google Scholar
[32]	Wang Y F, Li J F, Zhang S C, Su K Y, Zhou Y R, Liao K Y, Du S W, Yan H, Zhu S L 2019 Nat. Photon. 13 346 Google Scholar
[33]	Guo J X, Feng X T, Yang P Y, Yu Z F, Chen L Q, Yuan C H, Zhang W P 2019 Nat. Commun. 10 148 Google Scholar
[34]	Chen B, Qiu C, Chen S, Guo J, Chen L Q, Ou Z Y, Zhang W P 2015 Phys. Rev. Lett. 115 043602 Google Scholar
[35]	Rui J, Jiang Y, Yang S J, Zhao B, Bao X H, Pan J W 2015 Phys. Rev. Lett. 115 133002 Google Scholar
[36]	邓瑞婕, 闫智辉, 贾晓军 2017 物理学报 66 074201 Google Scholar Deng R J, Yan Z H, Jia X J 2017 Acta Phys. Sin. 66 074201 Google Scholar
[37]	Jia X J, Yan Z H, Duan Z Y, Su X L, Wang H, Xie C D, Peng K C 2012 Phys. Rev. Lett. 109 253604 Google Scholar
[38]	Yan Z H, Wu L, Jia X J, Liu Y H, Deng R J, Li S J, Wang H, Xie C D, Peng K C 2017 Nat. Commun. 8 718 Google Scholar
[39]	Chen S, Chen Y A, Zhao B, Yuan Z S, Schmiedmayer J, Pan J W 2007 Phys. Rev. Lett. 99 180505 Google Scholar
[40]	Bouillard M, Boucher G, Ortas J F, Pointard B, Tualle-Brouri R 2019 Phys. Rev. Lett. 122 210501 Google Scholar
[41]	Yoshikawa J, Makino K, Kurata S, Van Loock P, Furusawa A 2013 Phys. Rev. X 3 041028 Google Scholar
[42]	Hashimoto Y, Toyama T, Yoshikawa J, Makino K, Okamoto F, Sakakibara R, Takeda S, Van Loock P, Furusawa A 2019 Phys. Rev. Lett. 123 113603 Google Scholar
[43]	Sillanpää, M A, Park J I, Simmonds R W 2007 Nature 449 438 Google Scholar
[44]	Pfaff W, Axline C J, Burkhart L D, Vool U, Reinhold P, Frunzio L, Jiang L, Devoret M H, Schoelkopf R J 2017 Nat. Phys. 13 882 Google Scholar
[45]	Zhong M J, 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
[46]	Tang J S, Zhou Z Q, Wang Y T, Li Y L, Liu X, Hua Y L, Zou Y, Wang S, He D L, Chen G, Sun Y N, Yu Y, Li M F, Zha G W, Ni H Q, Niu Z C, Li C F, Guo G C 2015 Nat. Commun. 6 8652 Google Scholar
[47]	Lee K C, Sprague M R, Sussman B J, Nunn J, Langford N K, Jin X M, Champion T, Michelberger P, Reim K F, England D, Jaksch D, Walmsley I A 2011 Science 334 1253 Google Scholar
[48]	Bradley C E, Randall J, Abobeih M H, Berrevoets R C, Degen M J, Bakker M A, Markham M, Twitchen D J, Taminiau T H 2019 Phys. Rev. X 9 031045 Google Scholar
[49]	Sun S, Kim H, Luo Z C, Solomon G S, Waks E 2018 Science 361 57 Google Scholar
[50]	England D G, Fisher K A G, MacLean J W, Bustard P J, Lausten R, Resch K J, Sussman B J 2015 Phys. Rev. Lett. 114 053602 Google Scholar
[51]	Kutluer K, Distante E, Casabone B, Duranti S, Mazzera M, De Riedmatten H 2019 Phys. Rev. Lett. 123 030501 Google Scholar
[52]	Heller L, Farrera P, Heinze G, De Riedmatten H 2020 Phys. Rev. Lett. 124 210504 Google Scholar
[53]	Bao X H, Reingruber A, Dietrich P, Rui J, Dück A, Strassel T, Li L, Liu N L, Zhao B, Pan J W 2012 Nat. Phys. 8 517 Google Scholar
[54]	Vitanov N V, Rangelov A A, Shore B W, Bergmann K 2017 Rev. Mod. Phys. 89 015006 Google Scholar
[55]	Fedoseev V, Luna F, Hedgepeth I, Löffler W, Bouwmeester D 2021 Phys. Rev. Lett. 126 113601 Google Scholar
[56]	Kandel Y P, Qiao H F, Fallahi S, Gardner G C, Manfra M J, Nichol J M 2019 Nature 573 553 Google Scholar
[57]	Vool U, Devoret M 2017 Int. J. Circuit Theory Appl. 45 897 Google Scholar
[58]	Blais A, Grimsmo A L, Girvin S M, Wallraff A 2021 Rev. Mod. Phys. 93 025005 Google Scholar
[59]	Jeong H, Ralph T, Bowen W 2007 J. Opt. Soc. Am. B 24 355 Google Scholar
[60]	Reagor M, Paika H, Catelanib G, Sun L Y, Axline C, Holland E, Pop I M, Maslukc N A, Brecht T, Frunzio L, Devoret M H, Glazman L, Schoelkopfd R J 2013 Appl. Phys. Lett. 102 192604 Google Scholar

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Vol. 71, Issue 13 - 2022-07-05

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