微波-声子与光-磁纠缠态的产生

徐明慧; 刘晓敏; 史佳佳; 张冲; 张静; 杨荣国; 郜江瑞

doi:10.7498/aps.74.20241664

摘要

量子纠缠是量子计算和量子通信网络的核心资源. 本文提出了一种在腔光磁力系统中同时获得微波-声子和光-磁纠缠的理论模型. 该模型基于磁振子的混合量子系统, 注入由超导电光装置产生的光-微波纠缠光束作为内腔场, 并且用蓝失谐微波场激发磁振子模式产生磁振子-声子纠缠. 通过光力分束器及微波-磁子状态交换相互作用转移纠缠, 最终可以获得微波-声子和光-磁纠缠. 理论上从系统哈密顿量和量子郎之万方程出发, 得到漂移矩阵 A , 由漂移矩阵的负本征值保证文章计算的纠缠处于稳定状态. 再利用对数负性分析研究了系统中量子纠缠的特性与相关参数的依赖关系. 研究表明, 该系统可同时获得微波-声子以及光-磁之间稳态纠缠, 并且在系统中直接注入纠缠的微波与光可以显著地提升纠缠对温度的鲁棒性. 该研究将在量子网络和混合量子系统的量子信息处理方面奠定基础.

关键词:

量子纠缠 /
光磁力 /
双模压缩

Abstract

Quantum entanglement is a key resource for performing quantum computing and building quantum communication networks. By injecting a microwave-optical dual-mode entanglement field into the system, as well as pumping the optical and microwave cavities, and by appropriately choosing the detuning relationship between the pumping field and the modes, it is shown in this work that microwave-phonon entanglement E_aband magnon-optics entanglement E_cm can be generated simultaneously in the cavity opto-magnomechanic system, and the entanglement can be in a steady state. Specifically, the model is based on a hybrid quantum system of magnons, where a microwave-light entanglement generated by an optically pulsed superconducting electro-optical device through spontaneous parametric down-conversion process is injected as the intracavity field, and a blue-detuned microwave field is used to excite the magnon modes to produce magnon-phonon entanglement. Through the interaction between an optomechanical beam splitter and microwave-magnon state-swap, steady microwave-phonon entanglement E_ab and magnon-optics entanglement E_cm are successfully realized. The entanglement E_ab and E_cm in the system are analyzed using the logarithmic negativity. The effects of several parameters of the system, such as environment temperature, coupling strength and dissipation rate, on the degree of entanglement are investigated. In particular, the entanglement E_ab and E_cm generated in this system can exist both simultaneously and individually. Especially when g_am = 0, the entanglement E_ab and E_cm still exist. Moreover, directly injecting entangled microwave-light into the system can significantly enhance the robustness of the entanglement against temperature, which will have broad application prospects in quantum information processing in quantum networks and hybrid quantum systems. Notably, the entanglement E_ab and E_cm exist even at a temperature of 1.3 K. Our research has potential value for applications in the fields of quantum information processing and quantum networks.

Keywords:

PACS:

42.50.-p	(Quantum optics)
42.65.-k	(Nonlinear optics)
03.67.Bg	(Entanglement production and manipulation)

作者及机构信息

1.
山西大学物理电子工程学院, 太原　030006

2.
山西大学, 光量子技术与器件全国重点实验室, 太原　030006

3.
山西大学光电研究所, 太原　030006

通信作者: 杨荣国, yrg@sxu.edu.cn

基金项目: 国家重点研发计划(批准号: 2021YFC2201802)、国家自然科学基金(批准号: 11874248, 11874249)和雷达信号处理全国重点实验室基金(批准号: JKW202401)资助的课题.

Authors and contacts

1.
College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China

2.
State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University, Taiyuan 030006, China

3.
Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China

Corresponding author: YANG Rongguo, yrg@sxu.edu.cn

Funds: Project supported by the National Research and Develoment Program of China (Grant No. 2021YFC2201802), the National Natural Science Foundation of China (Grant Nos. 11874248, 11874249), and the Foundation of National Key Laboratory of Radar Signal Processing, China (Grant No. JKW202401).

文章全文

参考文献

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[13]	Aspelmeyer M, Kippenberg T J, Marquardt F 2014 Rev. Mod. Phys. 86 1391 Google Scholar
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[15]	罗均文, 吴德伟, 苗强, 魏天丽 2020 物理学报 69 054203 Google Scholar Luo J W, Wu D W, Miao Q, Wei T L 2020 Acta Phys. Sin. 69 054203 Google Scholar
[16]	Palomaki T A, Teufel J D, Simmonds R W, Lehnert K W 2013 Science 342 710 Google Scholar
[17]	Riedinger R, Wallucks A, Marinkovi´c I, Löschnauer C, Aspelmeyer M, Hong S, Gröblacher S 2018 Nature 556 473 Google Scholar
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[19]	Zhang X F, Zou C L, Jiang L, Tang H X 2016 Sci. Adv. 2 e1501286 Google Scholar
[20]	Shen R C, Li J, Fan Z Y, Wang Y P, You J Q 2022 Phys. Rev. Lett. 129 123601 Google Scholar
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[38]	Li J, Zhu S Y, Agarwal G S 2018 Phys. Rev. Lett. 121 203601 Google Scholar
[39]	Lachance-Quirion D, Tabuchi Y, Gloppe A, Usami K, Nakamura Y 2019 Appl. Phys. Express 12 070101 Google Scholar
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(a), (b) OMM系统示意图. YIG晶体中的磁振子模式m耦合到微波腔模a并且通过磁致伸缩引起振动声子b耦合到光学腔模c. 图(b)中蓝色(红色)线表示参量下转换(分束器)相互作用; (c)模型采用的模式频率和带宽. 当光学腔模与驱动激光场的反斯托克斯边带(蓝色)在频率为( ${\omega _{\text{l}}} + {\omega _{\text{b}}}$ )处共振, 并且磁子模和微波腔模同时与微波驱动场的斯托克斯边带(红色)在频率为( ${\omega _0} - {\omega _{\text{b}}}$ )处共振, 可以建立微波-声子以及光-磁子之间的稳态纠缠E_ab和E_cm

(a), (b) OMM system scheme. A magnon mode m in a YIG crystal couples to a microwave cavity mode a and to an optical cavity mode c via the mechanical vibration b induced by the magnetostriction. The blue (red) line in Figure (b) denotes the effective parametric down-conversion (beam-splitter) interaction; (c) mode frequency and bandwidth used adopted in the protocol. When the optical cavity is resonant with the (blue) anti-Stokes sideband of the driving laser at frequency ( ${\omega _0} - {\omega _{\text{b}}}$ ), and the magnon and microwave cavity modes are resonant with the (red) Stokes sideband of the microwave drive field at frequency ( ${\omega _{\text{l}}} + {\omega _{\text{b}}}$ ), microwave-mechanics entanglement E_ab and magnon-optics entanglement E_cm can be generated at steady state.

下载: 全尺寸图片幻灯片

图 2 稳态纠缠随磁子模式和微波腔模式有效失谐量变化密度图　(a)微波-声子纠缠E_ab; (b)光-磁纠缠E_cm

Density plot of steady-state entanglement versus effective detunings ${\varDelta _{\text{a}}}$ and ${\tilde \varDelta _{\text{m}}}$ : (a) Microwave-mechanics entanglement E_ab; (b) magnon-optics entanglement E_cm.

下载: 全尺寸图片幻灯片

图 3 微波-声子, 光-磁以及微波-光纠缠随压缩参数r的变化

Fig. 3. Stationary microwave-mechanics entanglement E_ab, magnon-optics entanglement E_cmand microwave-optics entanglement E_ac versus squeezing parameter r.

下载: 全尺寸图片幻灯片

图 4 光-磁和微波-声子之间纠缠随有效耦合强度变化　(a)有效光力耦合强度G_c; (b)有效磁力耦合强度G_m; (c)微波-磁子耦合强度g_am

Fig. 4. Stationary magnon-optics entanglement E_cm and microwave-mechanics entanglement E_ab versus effective coupling strength: (a) The effective optomechanical coupling strength G_c; (b) the effective magno-mechanical coupling strength G_m; (c) the microwave-magnon coupling rate g_am.

下载: 全尺寸图片幻灯片

微波-声子以及光-磁之间纠缠随不同模式耗散率变化　(a) 微波腔模耗散率 ${\kappa _{\text{a}}}$ ; (b) 磁振子模耗散率 ${\kappa _{\text{m}}}$ ; (c) 光学腔模耗散率 ${\kappa _{\text{c}}}$

Fig. 5. Stationary microwave-mechanics entanglement E_ab and magnon-optics entanglement E_cm versus dissipation rates: (a) Microwave cavity mode dissipation rate ${\kappa _{\text{a}}}$ ; (b) magnon mode dissipation rate ${\kappa _{\text{m}}}$ ; (c) optical cavity mode dissipation rate ${\kappa _{\text{c}}}$ .

下载: 全尺寸图片幻灯片

微波-声子以及光-磁之间纠缠　(a) 随温度T变化; (b) 随机械振子耗散率 ${\gamma _{\text{b}}}$ 变化

Fig. 6. Stationary microwave-mechanics entanglement E_ab and magnon-optics entanglement E_cm versus: (a) Temperature T; (b) mechanical damping rate ${\gamma _{\text{b}}}$ .

下载: 全尺寸图片幻灯片

[1]	Tang J F, Hou Z B, Shang J W , Zhu H J, Xiang G Y, Li C F, Guo G C 2020 Phys. Rev. Lett. 124 060502 Google Scholar
[2]	Konrad T, De Melo F, Tiersch M, Kasztelan C, Aragão A, 2008 Buchleitner A Nat. Phys. 4 99 Google Scholar
[3]	Aspelmeyer M, Böhm H R, Gyatso T, Jennewein T, Kaltenbaek R, Lindenthal M, Molina-Terriza G, Poppe A, Taraba M, Ursin R, Walther P, Zeilinger A 2003 Science 301 621 Google Scholar
[4]	杨荣国, 张超霞, 李妮, 张静, 郜江瑞 2019 物理学报 68 094205 Google Scholar Yang R G, Zhang C X, Li N, Zhang J, Gao J R 2019 Acta Phys. Sin. 68 094205 Google Scholar
[5]	Liang Y Y, Yang R G, Zhang J, Zhang T C 2023 Opt. Express 31 11775 Google Scholar
[6]	Zhang K, Wang W, Liu S H, Pan X Z, Du J J, Lou Y B, Yu S, Lü S C, Treps N, Fabre C, Jing J T 2020 Phys. Rev. Lett. 124 090501 Google Scholar
[7]	郝景晨, 杜培林, 孙恒信, 刘奎, 张静, 杨荣国, 郜江瑞 2024 物理学报 73 074203 Google Scholar Hao J C, Du P L, Sun H X, Liu K, Zhang J, Yang R G, Gao J R 2024 Acta Phys. Sin. 73 074203 Google Scholar
[8]	闫智辉, 贾晓军, 谢常德, 彭堃墀 2012 物理学报 61 014206 Google Scholar Yan Z H, Jia X J, Xie C D, Peng K C 2012 Acta Phys. Sin. 61 014206 Google Scholar
[9]	Liu K, Cui S Z, Yang R G, Zhang J X, Gao J R 2012 Chin. Phys. Lett. 29 060304 Google Scholar
[10]	刘奎, 马龙, 苏必达, 李佳明, 孙恒信, 郜江瑞 2020 物理学报 69 124203 Google Scholar Liu K, Ma L, Su B D, Li J M, Sun H X, Gao J R 2020 Acta Phys. Sin. 69 124203 Google Scholar
[11]	Yang R G, Zhang J, Klich I, González-Arciniegas C, Pfister O 2020 Phys. Rev. A 101 043832 Google Scholar
[12]	Du P L, Wang Y, Liu K, Yang R G, Zhang J 2023 Opt. Express 31 479420
[13]	Aspelmeyer M, Kippenberg T J, Marquardt F 2014 Rev. Mod. Phys. 86 1391 Google Scholar
[14]	Liu X M, Yang R G, Zhang J, Zhang T C 2023 Opt. Express 31 30005 Google Scholar
[15]	罗均文, 吴德伟, 苗强, 魏天丽 2020 物理学报 69 054203 Google Scholar Luo J W, Wu D W, Miao Q, Wei T L 2020 Acta Phys. Sin. 69 054203 Google Scholar
[16]	Palomaki T A, Teufel J D, Simmonds R W, Lehnert K W 2013 Science 342 710 Google Scholar
[17]	Riedinger R, Wallucks A, Marinkovi´c I, Löschnauer C, Aspelmeyer M, Hong S, Gröblacher S 2018 Nature 556 473 Google Scholar
[18]	Wollman E E, Lei C U, Weinstein A J, Suh J, Kronwald A, Marquardt F, Clerk A A, Schwab K C 2015 Science 349 952 Google Scholar
[19]	Zhang X F, Zou C L, Jiang L, Tang H X 2016 Sci. Adv. 2 e1501286 Google Scholar
[20]	Shen R C, Li J, Fan Z Y, Wang Y P, You J Q 2022 Phys. Rev. Lett. 129 123601 Google Scholar
[21]	Huebl H, Zollitsch C W, Lotze J, Hocke F, Greifenstein M, Marx A, Gross R, Goennenwein S T B 2013 Phys. Rev. Lett. 111 127003 Google Scholar
[22]	Tabuchi Y, Ishino S, Ishikawa T, Yamazaki R, Usami K, Nakamura Y 2014 Phys. Rev. Lett. 113 083603 Google Scholar
[23]	Bai L, Harder M, Chen Y P, Fan X, Xiao J Q, Hu C M 2015 Phys. Rev. Lett. 114 227201 Google Scholar
[24]	Osada A, Hisatomi R, Noguchi A, Tabuchi Y, Yamazaki R, Usami K, Sadgrove M, Yalla R, Nomura M, Nakamura Y 2016 Phys. Rev. Lett. 116 223601 Google Scholar
[25]	Zhang X F, Zhu N, Zou C L, Tang H X 2016 Phys. Rev. Lett. 117 123605 Google Scholar
[26]	Osada A, Gloppe A, Hisatomi R, Noguchi A, Yamazaki R, Nomura M, Nakamura Y, Usami K 2018 Phys. Rev. Lett. 120 133602 Google Scholar
[27]	Zhu N, Zhang X, Han X, Zou C L, Zhong C, Wang C H, Jiang L, Tang H X 2020 Optica 7 1291 Google Scholar
[28]	Haigh J A, Nunnenkamp A, Ramsay A J 2021 Phys. Rev. Lett. 127 143601 Google Scholar
[29]	Yang Z B, Liu X D, Yin X Y, Ming Y, Liu H Y, Yang R C 2021 Phys. Rev. Appl. 15 024042 Google Scholar
[30]	Yin X Y, Yang Z B, Huang Y M, Wan Q M, Yang R C, Liu H Y 2023 Ann. Phys. 535 2200603 Google Scholar
[31]	Fan Z Y, Shen R C, Wang Y P, Li J, You J Q 2022 Phys. Rev. A 105 033507 Google Scholar
[32]	Fan Z Y, Qian H, Li J 2023 Quantum Sci. Technol. 8 015014 Google Scholar
[33]	Fan Z Y, Qiu L, Gröblacher S, Li J 2023 Laser Photonics Rev. 17 2200866 Google Scholar
[34]	Rueda A, Hease W, Barzanjeh S, Fink J M 2019 npj Quantum Inf. 5 108 Google Scholar
[35]	Hease W, Rueda A, Sahu R, Wulf M, Arnold G, Schwefel H G L, Fink J M 2020 PRX Quantum 1 020315 Google Scholar
[36]	Andersen U L, Gehring T, Marquardt C, Leuchs G 2016 Phys. Scr. 91 053001 Google Scholar
[37]	Sahu R, Qiu L, Hease W, Arnold G, Minoguchi Y, Rabl P, Fink J M 2023 Science 380 718 Google Scholar
[38]	Li J, Zhu S Y, Agarwal G S 2018 Phys. Rev. Lett. 121 203601 Google Scholar
[39]	Lachance-Quirion D, Tabuchi Y, Gloppe A, Usami K, Nakamura Y 2019 Appl. Phys. Express 12 070101 Google Scholar
[40]	Heyroth F, Hauser C, Trempler P, Geyer P, Syrowatka F, Dreyer R, Ebbinghaus S G, Woltersdorf G, Schmidt G 2019 Phys. Rev. Appl. 12 054031 Google Scholar
[41]	Vidal G, Werner R F 2002 Phys. Rev. A 65 032314 Google Scholar
[42]	Plenio M B 2005 Phys. Rev. Lett. 95 090503 Google Scholar
[43]	Tan H T, Deng W W, Li G X 2017 Phys. Rev. A 95 053842 Google Scholar
[44]	Luo Y X, Cong L J, Zheng Z G, Liu H Y, Ming Y, Yang R C 2023 Opt. Express 31 34764 Google Scholar

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