Entanglement enhancement in a modulated optomechanical system via squeezed vacuum field

doi:10.1088/1674-1056/ae2d37

中国物理B ›› 2026, Vol. 35 ›› Issue (4): 40311-040311.doi: 10.1088/1674-1056/ae2d37

Entanglement enhancement in a modulated optomechanical system via squeezed vacuum field

Huan-Huan Cheng(程欢欢), Chen-Rui Yang(杨晨锐), Gao-Feng Jiao(焦高锋), Cheng-Hua Bai(白成华), and Shao-Xiong Wu(武少雄)†

School of Semiconductor and Physics, North University of China, Taiyuan 030051, China

收稿日期:2025-10-27 修回日期:2025-12-11 接受日期:2025-12-16 发布日期:2026-04-07
通讯作者: Shao-Xiong Wu E-mail:sxwu@nuc.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 12204440 and 12404418), the China Postdoctoral Science Foundation (Grant No. 2025M773357), and the Fundamental Research Program of Shanxi Province, China (Grant No. 202303021212171).

Entanglement enhancement in a modulated optomechanical system via squeezed vacuum field

Huan-Huan Cheng(程欢欢), Chen-Rui Yang(杨晨锐), Gao-Feng Jiao(焦高锋), Cheng-Hua Bai(白成华), and Shao-Xiong Wu(武少雄)†

School of Semiconductor and Physics, North University of China, Taiyuan 030051, China

Received:2025-10-27 Revised:2025-12-11 Accepted:2025-12-16 Published:2026-04-07
Contact: Shao-Xiong Wu E-mail:sxwu@nuc.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant Nos. 12204440 and 12404418), the China Postdoctoral Science Foundation (Grant No. 2025M773357), and the Fundamental Research Program of Shanxi Province, China (Grant No. 202303021212171).

摘要/Abstract

摘要： We present a double-cavity optomechanical system with a mechanical oscillator, which is jointly driven by an amplitude-modulated laser field and a weak squeezed vacuum field, aiming to explore quantum entanglement effects under the unresolved-sideband regime. Within our proposed scheme, it is possible not only to surpass the limit of maximum steady-state entanglement ln2 for bipartite entanglement, achieving strong entanglement, but also to significantly enhance tripartite entanglement and improve the system's robustness against thermal noise. Meanwhile, the introduction of the squeezed vacuum field plays a crucial role in entanglement control, enabling not only a several-fold enhancement of entanglement but also continuous and precise manipulation of its strength within specific ranges. The suggested method demonstrates exceptional flexibility and adaptability under a wide range of operating conditions, offering a new pathway for theoretical and experimental investigations of strong bipartite entanglement and tripartite entanglement.

关键词: optomechanical system, quantum entanglement, pump modulation, squeezed vacuum field

Abstract: We present a double-cavity optomechanical system with a mechanical oscillator, which is jointly driven by an amplitude-modulated laser field and a weak squeezed vacuum field, aiming to explore quantum entanglement effects under the unresolved-sideband regime. Within our proposed scheme, it is possible not only to surpass the limit of maximum steady-state entanglement ln2 for bipartite entanglement, achieving strong entanglement, but also to significantly enhance tripartite entanglement and improve the system's robustness against thermal noise. Meanwhile, the introduction of the squeezed vacuum field plays a crucial role in entanglement control, enabling not only a several-fold enhancement of entanglement but also continuous and precise manipulation of its strength within specific ranges. The suggested method demonstrates exceptional flexibility and adaptability under a wide range of operating conditions, offering a new pathway for theoretical and experimental investigations of strong bipartite entanglement and tripartite entanglement.

Key words: optomechanical system, quantum entanglement, pump modulation, squeezed vacuum field

中图分类号: (Entanglement and quantum nonlocality)

03.65.Ud

03.67.Mn (Entanglement measures, witnesses, and other characterizations) 42.50.-p (Quantum optics)

Huan-Huan Cheng(程欢欢), Chen-Rui Yang(杨晨锐), Gao-Feng Jiao(焦高锋), Cheng-Hua Bai(白成华), and Shao-Xiong Wu(武少雄). Entanglement enhancement in a modulated optomechanical system via squeezed vacuum field[J]. 中国物理B, 2026, 35(4): 40311-040311.

参考文献

[1] Kippenberg T J and Vahala K J 2008 Science 321 1172
[2] Favero I and Karrai K 2009 Nat. Photonics 3 201
[3] Aspelmeyer M, Kippenberg T J and Marquardt F 2014 Rev. Mod. Phys. 86 1391
[4] Imamoglu A, Schmidt H, Woods G and Deutsch M 1997 Phys. Rev. Lett. 79 1467
[5] Xia K, Nori F and Xiao M 2018 Phys. Rev. Lett. 121 203602
[6] Dong Y, Zheng X, Wang D and Zhao P 2025 Chin. Phys. B 34 044203
[7] Man X X, Sun J, Zhang W Z, Luo L and Jin G 2024 Chin. Phys. B 33 120303
[8] Ashkin A 1980 Science 210 1081
[9] Bai C H, Wang D Y, Zhang S, Liu S and Wang H F 2019 Ann. Phys. 531 1800271
[10] Einstein A, Podolsky B and Rosen N 1935 Phys. Rev. 47 777
[11] Schrödinger E 1935 Math. Proc. Cambridge Philos. Soc. 31 555
[12] Dong L H,Wu X J, Bai C H andWu S X 2025 Chin. Phys. B 34 020304
[13] Vitali D, Gigan S, Ferreira A, Böhm H R, Tombesi P, Guerreiro A, Vedral V, Zeilinger A and AspelmeyerM2007 Phys. Rev. Lett. 98 030405
[14] Chen P, Luo D W and Yu T 2025 Phys. Rev. Research 7 013161
[15] Wu S X, Bai C H, Li G, Yu C S and Zhang T 2024 Opt. Express 32 260
[16] Yang W Q, Leng X, Cheng J and Zhang W Z 2024 Chin. Phys. B 33 060313
[17] Liu M Y, Gong Y, Chen J, Wang Y W and Xiong W 2025 Chin. Phys. B 34 057202
[18] Zhou B Y, Pan N, Yu L and Li G X 2024 Phys. Rev. A 110 032401
[19] Yang J, Zhao C, Wang D W, Peng R and Zhou L 2024 Phys. Rev. Appl. 21 044056
[20] Wu S X, Bai C H, Li G, Yu C S and Zhang T 2023 J. Opt. Soc. Am. B 40 2885
[21] Li R, Long Y and Zhang X 2025 Chin. Phys. B 34 020307
[22] Asjad M, Agarwal G S, KimMS, Tombesi P, Giuseppe G Di and Vitali D 2014 Phys. Rev. A 89 023849
[23] Tong J L, Hao Y, Wu S X, Bai C H and Bai S 2025 Adv. Quantum Technol. 8 2400654
[24] Agarwal G S and Huang S 2016 Phys. Rev. A 93 043844
[25] Wu X J, Cheng H H, Wu Q, Bai C H and Wu S X 2024 Opt. Express 32 35663
[26] Chen S S, Xie Y L, Zhang J J, Zhang N N, Guo Y R, Yang H and Ma Y 2025 Chin. Phys. B 34 014201
[27] Birnbaum K M, Boca A, Miller R, Boozer A D, Northup T E and Kimble H J 2005 Nature 436 87
[28] Luo Y, Zhang X, Xiao Y, Xu J, Li H, Yang Y and Xia X 2025 Chin. Phys. B 34 014203
[29] Gao X C, Wu X J, Bai C H, Wu S X and Yu C S 2023 Opt. Express 31 36796
[30] Rabl P 2011 Phys. Rev. Lett. 107 063601
[31] Huang R, Miranowicz A, Liao J Q, Nori F and Jing H 2018 Phys. Rev. Lett. 121 153601
[32] Wu S X, Gao X C, Cheng H H and Bai C H 2025 Phys. Rev. A 111 043714
[33] Metelmann A and Clerk A A 2015 Phys. Rev. X 5 021025
[34] Qian Y B, Zhang Z Y, Tang L, Lai D G and Hou B P 2024 Phys. Rev. A 109 043103
[35] Vinokur V M, Baturina T I, Fistul M V, Mironov A Y, Baklanov M R and Strunk C 2008 Nature 452 613
[36] Zhirov O V and Shepelyansky D L 2006 Eur. Phys. J. D 38 375
[37] Liao C G, Chen R X, Xie H, He M Y and Lin X M 2019 Phys. Rev. A 99 033818
[38] Vaidya G M, Jäger S B and Shankar A 2025 Phys. Rev. A 111 012410
[39] Lai D G, Qin W, Hou B P, Miranowicz A and Nori F 2021 Phys. Rev. A 104 043521
[40] Qiu J, Jin L J, Peng Z Y, Chesi S andWang Y D 2022 Phys. Rev. A 105 033514
[41] Shao W, Li J and Wang L L 2023 Phys. Rev. A 107 063505
[42] Clarke J, Neveu P, Khosla K E, Verhagen E and VannerMR 2023 Phys. Rev. Lett. 131 053601
[43] Li J, Zhu S Y and Agarwal G S 2018 Phys. Rev. Lett. 121 203601
[44] Guo Y, Zhao J, Cao L, Li Y and Lu H Y 2025 Chin. Phys. B 34 024203
[45] Yang J, Lu T X, Peng M, Liu J, Jiao Y F and Jing H 2024 Opt. Express 32 785
[46] Hei X L, Li P B, Pan X F and Nori F 2023 Phys. Rev. Lett. 130 073602
[47] Zheng Q, Cao Y and Yan P 2025 Chin. Phys. B 34 107514
[48] Chen J, Fan X G, Xiong W, Wang D and Ye L 2024 Phys. Rev. A 109 043512
[49] Din G, Abbas M and Zhang P 2024 Eur. Phys. J. Plus 139 591
[50] Ghosh J, Mondal S, Varshney S K and Debnath K 2024 Phys. Rev. A 109 023512
[51] Yang Z, Xiong B, Zhao C and Zhou L 2025 Opt. Express 33 5123
[52] Dilawaiz, Qamar S and Irfan M 2024 Phys. Rev. A 109 043708
[53] Hussain B, Qamar S and Irfan M 2022 Phys. Rev. A 105 063704
[54] Wang Y, Wu J L, Jiao Y F, Lu T X, Zhang H L, Jiang L Y, Kuang L M and Jing H 2025 Phys. Rev. A 111 013709
[55] Feng J S, Tan L, Gu H Q and Liu W M 2017 Phys. Rev. A 96 063818
[56] Liu Z Q, Liu J, Tan L and Liu W M 2024 Phys. Rev. A 110 023707
[57] Zhang W J, Zhang Y, Guo Q, Liu A P, Li G and Zhang T 2021 Phys. Rev. A 104 053506
[58] Chakraborty S and Sarma A K 2018 Phys. Rev. A 97 022336
[59] Mari A and Eisert J 2009 Phys. Rev. Lett. 103 213603
[60] Liu Y C, Xiao Y F, Jiang X F, Li B B, Li Y and Gong Q 2012 Phys. Rev. A 85 013843
[61] Sedlmeir F, Foreman M R, Vogl U, Zeltner R, Schunk G, Strekalov D V, Marquardt C, Leuchs G and Schwefel H G 2017 Phys. Rev. Appl. 7 024029
[62] Trainor L S, Sedlmeir F, Peuntinger C and Schwefel H G 2018 Phys. Rev. Appl. 9 024007
[63] Singh V, Shevchuk O, Blanter Y M and Steele G A 2016 Phys. Rev. B 93 245407
[64] Hochreiter A, Bredol P, David F, Demiralp B, Weber H B and Weig E M 2025 Phys. Rev. Appl. 24 034005
[65] Kono S, Masuyama Y, Ishikawa T, Tabuchi Y, Yamazaki R, Usami K, Koshino K and Nakamura Y 2017 Phys. Rev. Lett. 119 023602
[66] Bienfait A, Campagne-Ibarcq P, Kiilerich A H, Zhou X, Probst S, Pla J J, Schenkel T, Vion D, Esteve D, Morton J J L, Moelmer K and Bertet P 2017 Phys. Rev. X 7 041011
[67] Vidal G and Werner R F 2002 Phys. Rev. A 65 032314
[68] Plenio M B 2005 Phys. Rev. Lett. 95 090503
[69] Adesso G and Illuminati F 2006 New J. Phys. 8 15
[70] Adesso G and Illuminati F 2007 J. Phys. A: Math. Theor. 40 7821

Entanglement enhancement in a modulated optomechanical system via squeezed vacuum field

Entanglement enhancement in a modulated optomechanical system via squeezed vacuum field

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Junqing Li(李俊青), Shuo Dong(董硕), and Jianhua Wei(魏建华). Geometric control of concurrence and quantum gate operations in triangular triple quantum dots[J]. 中国物理B, 2026, 35(2): 20302-020302.
[2]	Yingjia Yang(杨应佳), Liwei Liu(刘利伟), Lianchun Yu(俞连春), Weizheng Kong(孔伟正), Haiyan Jiao(焦海燕), Xiaoyan Deng(邓小燕), and Xiaoyong Li(李小勇). Chaos of cavity optomechanical system with Coulomb coupling[J]. 中国物理B, 2025, 34(8): 80503-080503.
[3]	Qinghong Liao(廖庆洪), Songyun Ouyang(欧阳嵩沄), Shaoping Cheng(程绍平), and Yiping Cheng(程依萍). Coherent feedback ground-state cooling of mechanical resonators assisted by a quantum well[J]. 中国物理B, 2025, 34(4): 44202-044202.
[4]	Bai Liu(刘白), Jun Zhang(张俊), Shupin Qiu(邱书品), and Mingwu Zhang(张明武). A pure quantum secret sharing scheme based on GHZ basis measurement and quantum entanglement exchange[J]. 中国物理B, 2025, 34(3): 30304-030304.
[5]	Ling-Hui Dong(董凌晖), Xiao-Jie Wu(武晓捷), Cheng-Hua Bai(白成华), and Shao-Xiong Wu(武少雄). Enhancing entanglement and steering in a hybrid atom-optomechanical system via Duffing nonlinearity[J]. 中国物理B, 2025, 34(2): 20304-020304.
[6]	Fang-Fang Du(杜芳芳), Zhi-Guo Fan(范志国), Xue-Mei Ren(任雪梅), Ming Ma(马明), and Wen-Yao Liu(刘文耀). Established conversions for hybrid entangled states assisted by error-predicted parity-discriminated devices[J]. 中国物理B, 2025, 34(1): 10303-010303.
[7]	Shan-Shan Chen(陈珊珊), Yi-Long Xie(谢亦龙), Jing-Jing Zhang(张京京), Na-Na Zhang(张娜娜), Yong-Rui Guo(郭永瑞), Huan Yang(杨桓), and Yong Ma(马勇). Enhanced mechanical squeezing in an optomechanical system via backward stimulated Brillouin scattering[J]. 中国物理B, 2025, 34(1): 14201-014201.
[8]	Jian-Zhuang Wu(武建壮), Ying Xi(奚滢), Bo-Ya Li(李博雅), Lian-E Lu(芦连娥), and Yong-Hong Ma(马永红). Generation of macroscopic entanglement in ensemble systems based on silicon vacancy centers[J]. 中国物理B, 2024, 33(9): 90308-090308.
[9]	Zhi-Peng Yang(杨智鹏), Yu-Ran Zhang(张煜然), Fu-Li Li(李福利), and Heng Fan(范桁). Delayed-measurement one-way quantum computing on cloud quantum computer[J]. 中国物理B, 2024, 33(9): 90304-090304.
[10]	Guoyao Li(李国耀) and Zhangqi Yin(尹璋琦). Entangling two levitated charged nanospheres through Coulomb interaction[J]. 中国物理B, 2024, 33(7): 74205-074205.
[11]	Geng-Biao Wei(韦庚彪), Liu Ye(叶柳), and Dong Wang(王栋). Detecting the quantum phase transition from the perspective of quantum information in the Aubry-André model[J]. 中国物理B, 2024, 33(7): 70301-070301.
[12]	Wen-Quan Yang(杨文全), Xuan Leng(冷轩), Jiong Cheng(程泂), and Wen-Zhao Zhang(张闻钊). Nonlinearly induced entanglement in dissipatively coupled optomechanical system[J]. 中国物理B, 2024, 33(6): 60313-060313.
[13]	Jin-Song Huang(黄劲松), Hong-Wu Huang(黄红武), Yan-Ling Li(李艳玲), and Zhong-Hui Xu(徐中辉). Single-photon scattering and quantum entanglement of two giant atoms with azimuthal angle differences in a waveguide system[J]. 中国物理B, 2024, 33(5): 50506-050506.
[14]	Xin-Xin Man(满鑫鑫), Jing Sun(孙静), Wen-Zhao Zhang(张闻钊), Lijuan Luo(罗丽娟), and Guangri Jin(金光日). Nonlinear enhanced mass sensor based on optomechanical system[J]. 中国物理B, 2024, 33(12): 120303-120303.
[15]	Shan-Shan Chen(陈珊珊), Jing-Jing Zhang(张京京), Jia-Neng Li(李嘉能), Na-Na Zhang(张娜娜), Yong-Rui Guo(郭永瑞), and Huan Yang(杨桓). Nonreciprocal mechanical entanglement in a spinning optomechanical system[J]. 中国物理B, 2024, 33(11): 110305-110305.