Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators

doi:10.1088/1674-1056/ac67c3

中国物理B ›› 2022, Vol. 31 ›› Issue (9): 90301-090301.doi: 10.1088/1674-1056/ac67c3

• • 下一篇

Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators

Kai-Qian Huang(黄恺芊)¹, Wei-Lin Li(李蔚琳)¹, Wen-Lei Zhao(赵文垒)^2,†, and Zhi Li(李志)^1,3,4,‡

1 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China;
2 School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China;
3 Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China;
4 Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China

收稿日期:2022-02-17 修回日期:2022-04-06 接受日期:2022-04-18 出版日期:2022-08-19 发布日期:2022-08-19
通讯作者: Wen-Lei Zhao, Zhi Li E-mail:wlzhao@jxust.edu.cn;lizphys@m.scnu.edu.cn
基金资助:
W. Zhao was supported by the National Natural Science Foundation of China (Grant No. 12065009) and Science and Technology Planning Project of Ganzhou City (Grant No. 202101095077). K. Q. Huang and Z. Li were supported by the National Natural Science Foundation of China (Grant Nos. 11704132, 11874017, and U1830111), the Natural Science Foundation of Guangdong Province, China (Grant No. 2021A1515012350), and the KPST of Guangzhou (Grant No. 201804020055).

Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators

Kai-Qian Huang(黄恺芊)¹, Wei-Lin Li(李蔚琳)¹, Wen-Lei Zhao(赵文垒)^2,†, and Zhi Li(李志)^1,3,4,‡

1 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China;
2 School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China;
3 Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China;
4 Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China

Received:2022-02-17 Revised:2022-04-06 Accepted:2022-04-18 Online:2022-08-19 Published:2022-08-19
Contact: Wen-Lei Zhao, Zhi Li E-mail:wlzhao@jxust.edu.cn;lizphys@m.scnu.edu.cn
Supported by:
W. Zhao was supported by the National Natural Science Foundation of China (Grant No. 12065009) and Science and Technology Planning Project of Ganzhou City (Grant No. 202101095077). K. Q. Huang and Z. Li were supported by the National Natural Science Foundation of China (Grant Nos. 11704132, 11874017, and U1830111), the Natural Science Foundation of Guangdong Province, China (Grant No. 2021A1515012350), and the KPST of Guangzhou (Grant No. 201804020055).

摘要/Abstract

摘要： We investigate the quantum entanglement in a non-Hermitian kicking system. In the Hermitian case, the out-of-time ordered correlators (OTOCs) exhibit the unbounded power-law increase with time. Correspondingly, the linear entropy, which is a common measurement of entanglement, rapidly increases from zero to almost unity, indicating the formation of quantum entanglement. For strong enough non-Hermitian driving, both the OTOCs and linear entropy rapidly saturate as time evolves. Interestingly, with the increase of non-Hermitian kicking strength, the long-time averaged value of both OTOCs and linear entropy has the same transition point where they exhibit the sharp decrease from a plateau, demonstrating the disentanglment. We reveal the mechanism of disentanglement with the extension of Floquet theory to non-Hermitian systems.

关键词: out-of-time ordered correlators, quantum entanglement, non-Hermiticity

Abstract: We investigate the quantum entanglement in a non-Hermitian kicking system. In the Hermitian case, the out-of-time ordered correlators (OTOCs) exhibit the unbounded power-law increase with time. Correspondingly, the linear entropy, which is a common measurement of entanglement, rapidly increases from zero to almost unity, indicating the formation of quantum entanglement. For strong enough non-Hermitian driving, both the OTOCs and linear entropy rapidly saturate as time evolves. Interestingly, with the increase of non-Hermitian kicking strength, the long-time averaged value of both OTOCs and linear entropy has the same transition point where they exhibit the sharp decrease from a plateau, demonstrating the disentanglment. We reveal the mechanism of disentanglement with the extension of Floquet theory to non-Hermitian systems.

Key words: out-of-time ordered correlators, quantum entanglement, non-Hermiticity

中图分类号: (Quantum mechanics)

03.65.-w

Kai-Qian Huang(黄恺芊), Wei-Lin Li(李蔚琳), Wen-Lei Zhao(赵文垒), and Zhi Li(李志). Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators[J]. 中国物理B, 2022, 31(9): 90301-090301.

参考文献

[1] Maldacena J, Shenker S H and Stanford D 2016 J. High Energy Phys. 106 1
[2] Jahnke V, Kim K Y and Yoon J 2019 J. High Energy Phys. 37 1
[3] Prakash R and Lakshminarayan A 2020 Phys. Rev. B 101 121108
[4] Rozenbaum E B, Ganeshan S and Galitski V 2019 Phys. Rev. B 100 035112
[5] Rozenbaum E B, Bunimovich L A and Galitski V 2020 Phys. Rev. Lett. 125 014101
[6] Wang J Z, Benenti G, Casati G and Wang W G 2020 Phys. Rev. Res. 2 043178
[7] Aleiner I L, Faoro L and Ioffe L B 2016 Ann. Phys. 375 378
[8] Li J, Fan R, Wang H, Ye B, Zeng B, Zhai H, Peng X and Du J 2017 Phys. Rev. X 7 031011
[9] Lewis-Swan R J, Safavi-Naini A, Bollinger J J and Rey A M 2019 Nat. Commun. 10 1581
[10] Gärttner M, Hauke P and Rey A M 2018 Phys. Rev. Lett. 120 040402
[11] Riddell J and Sorensen E S 2019 Phys. Rev. B 99 054205
[12] Fan R, Zhang P, Shen H and Zhai H 2017 Sci. Bull. 62 707
[13] Hosur P, Qi X L, Roberts D A and Yoshida B 2016 J. High Energy Phys. 2016 4
[14] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[15] Bender C M, Boettcher S and Meisinger P N 1999 J. Math. Phys. 40 2201
[16] Bender C M 2007 Rep. Prog. Phys. 70 947
[17] Longhi S 2018 Europhys. Lett. 120 64001
[18] Klaiman S, Günther U and Moiseyev N 2008 Phys. Rev. Lett. 101 080402
[19] Guo A, Salamo G J, Duchesne D, Morandotti R, Volatier-Ravat M, Aimez V, Siviloglou G A and Christodoulides D N 2008 Phys. Rev. Lett. 103 093902
[20] Cartarius H and Wunner G 2012 Phys. Rev. A 86 013612
[21] Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M and Kip D 2010 Nat. Phys. 6 192
[22] Ramezani H, Kottos T, El-Ganainy R and Christodoulides D N 2010 Phys. Rev. A 82 043803
[23] Barashenkov I V, Suchkov S V, Sukhorukov A A, Dmitriev S V and Kivshar Y S 2012 Phys. Rev. A 86 053809
[24] Sukhorukov A A, Xu Z and Kivshar Y S 2010 Phys. Rev. A 82 043818
[25] Makris K G, El-Ganainy R, Christodoulides D N and Musslimani Z H 2011 Int. J. Theor. Phys. 50 1019
[26] Benisty H, Degiron A, Lupu A, De Lustrac A, Chénais S, Forget S, Besbes M, Barbillon G, Bruyant A, Blaize S and Lérondel G 2011 Opt. Express 19 18004
[27] Miri M A, Cotrufo M and Alù A 2019 Opt. Lett. 44 3558
[28] Hang C, Gabadadze G and Huang G 2017 Phys. Rev. A 95 023833
[29] Li L, Lee C H and Gong J 2020 Phys. Rev. Lett. 124 250402
[30] Zhang D W, Zhao Y X, Liu R B, Xue Z Y, Zhu S L and Wang Z D 2016 Phys. Rev. A 93 043617
[31] Wang X and Wu J H 2016 Opt. Express 24 4289
[32] Li J, Harter A K, Liu J, de Melo L, Joglekar Y N and Luo L 2019 Nat. Commun. 10 855
[33] Cao Y, Li Y and Yang X 2021 Phys. Rev. B 103 075126
[34] Gong J and Wang Q H 2015 Phys. Rev. A 91 042135
[35] Chitsazi M, Li H, Ellis F M and Kottos T 2017 Phys. Rev. Lett. 119 093901
[36] Harter A K and Joglekar Y N 2020 Prog. Theor. Experiment. Phys. 2020 12A106
[37] Huang K Q, Wang J Z, Zhao W L and Liu J 2021 J. Phys.:Condens. Matter. 33 055402
[38] Zhao W L, Gong P, Wang J and Wang Q 2020 Chin. Phys. B 29 120302
[39] Zhao W L, Wang J, Wang X and Tong P 2020 Phys. Rev. E 99 042201
[40] Zhao W L, Zhou L, Liu J, Tong P and Huang K 2020 Phys. Rev. A 102 062213
[41] Huang K Q, Zhao W L and Li Z 2021 Phys. Rev. A 104 052405
[42] Zhao W L 2022 Phys. Rev. Res. 4 023004
[43] Rossini D, Benenti G and Casati G 2006 Phys. Rev. A 74 036209
[44] Bandyopadhyay J N 2009 Europhys. Lett. 85 50006
[45] Adachi S, Toda M and Ikeda K 1988 Phys. Rev. Lett. 61 659
[46] Graham R and Kolovsky A R 1966 Phys. Lett. A. 222 47
[47] Park H K and Kim S W 2003 Phys. Rev. A 67 060102
[48] Zhao W L and Jie Q L 2009 Commun. Theor. Phys. 51 465
[49] Zhao W L, Jie Q L and Zhou B 2010 Commun. Theor. Phys. 54 247
[50] Zhao W L and Jie Q L 2020 Chin. Phys. B 29 080302
[51] Gadway B, Reeves J, Krinner L and Schneble D 2013 Phys. Rev. Lett. 110 190401
[52] Rozenbaum E B and Galitski V 2017 Phys. Rev. B 95 064303
[53] Wang W G, He L and Gong J 2012 Phys. Rev. Lett. 108 070403
[54] Wang W G 2020 Phys. Rev. E 102 012127
[55] Breuer H, Laine E and Piilo J 2009 Phys. Rev. Lett. 103 210401
[56] Toikka L A and Andreanov A 2019 arXiv:1901.09362v1[cond-mat.mes-hall]
[57] Smith A, Knolle J, Moessner R and Kovrizhin D L 2019 Phys. Rev. Lett. 123 086602
[58] McGinley M, Nunnenkamp A and Knolle J 2019 Phys. Rev. Lett. 122 020603
[59] Roy N and Sharma A 2021 J. Phys.:Condens. Matter. 33 334001
[60] Yoshida B and Yao N Y 2019 Phys. Rev. X 9 011006
[61] Harrow A W, Kong L, Liu Z W, Mehraban S and Shor P W 2021 PRX Quantum 2 020339
[62] Knap M 2018 Phys. Rev. B 98 184416
[63] Sharma K K and Gerdt V P 2021 Quantum Inform. Process. 20 195
[64] Styliaris G, Anand N and Zanardi P 2021 Phys. Rev. Lett. 126 030601
[65] Zanardi P and Anand N 2021 Phys. Rev. A 103 062214
[66] Bergamasco P D, Carlo G G and Rivas A M F 2019 Phys. Rev. Res. 1 033044

Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators

Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators

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