Generation of microwave-phonon and magnon-optics entangled states

XU Minghui; LIU Xiaomin; SHI Jiajia; ZHANG Chong; ZHANG Jing; YANG Rongguo; GAO Jiangrui

doi:10.7498/aps.74.20241664

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:

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).

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References

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Cited By

图 1 (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

Figure 1. (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.

DownLoad: Full-Size Img PowerPoint

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

Figure 2. 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.

DownLoad: Full-Size Img PowerPoint

图 3 微波-声子, 光-磁以及微波-光纠缠随压缩参数r的变化

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 5 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}}} $

Figure 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}}} $.

DownLoad: Full-Size Img PowerPoint

图 6 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

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

DownLoad: Full-Size Img PowerPoint

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[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
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[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
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[12]	Du P L, Wang Y, Liu K, Yang R G, Zhang J 2023 Opt. Express 31 479420
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[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
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[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
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[31]	Fan Z Y, Shen R C, Wang Y P, Li J, You J Q 2022 Phys. Rev. A 105 033507 Google Scholar
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[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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