Dynamical correlation between quantum entanglement and intramolecular energy in molecular vibrations：An algebraic approach

doi:10.1088/1674-1056/23/7/073301

Abstract The dynamical correlation between quantum entanglement and intramolecular energy in realistic molecular vibrations is explored using the Lie algebraic approach. The explicit expression of entanglement measurement can be achieved using algebraic operations. The common and different characteristics of dynamical entanglement in different molecular vibrations are also provided. The dynamical study of quantum entanglement and intramolecular energy in small molecular vibrations can be helpful for controlling the entanglement and further understanding the intramolecular dynamics.

Keywords: quantum entanglement molecular vibration intramolecular energy Lie algebra

Received: 02 January 2014
Revised: 24 January 2014
Accepted manuscript online:

PACS:	33.15.-e	(Properties of molecules)
	33.20.Tp	(Vibrational analysis)
	03.67.Mn	(Entanglement measures, witnesses, and other characterizations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11147019 and 91021009).

Corresponding Authors: Feng Hai-Ran
E-mail: hairanfeng@mail.sdu.edu.cn

About author: 33.15.-e; 33.20.Tp; 03.67.Mn

Cite this article:

Feng Hai-Ran (冯海冉), Meng Xiang-Jia (孟祥佳), Li Peng (李鹏), Zheng Yu-Jun (郑雨军) Dynamical correlation between quantum entanglement and intramolecular energy in molecular vibrations：An algebraic approach 2014 Chin. Phys. B 23 073301

[1]	Brune M, Schmidt-Kaler F, Maali A, Dreyer J, Hagley E, Raimond J M and Haroche S 1996 Phys. Rev. Lett. 76 1800
[2]	Zheng X J, Xu H, Fang M F and Zhu K C 2010 Chin. Phys. B 19 034207
[3]	Cirac J I and Zoller P 1995 Phys. Rev. Lett. 74 4091
[4]	Schmidt-Kaler F, Häffner H, Riebe M, Gulde S, Lancaster G P T, Deuschle T, Becher C, Roos C F, Eschner J and Blatt R 2003 Nature 422 408
[5]	Jones J A and Mosca M 1998 J. Chem. Phys. 109 1648
[6]	Marx R, Fahmy A F, Myers J M, Bermel W and Glaser S J 2000 Phys. Rev. A 62 012310
[7]	Wei D X, Luo J, Yang X D, Sun X P, Zeng X Z, Liu M L, Ding S W and Zhan M S 2004 Chin. Phys. 13 817
[8]	Tesch C M, Kurtz L and Vivie-Riedle R 2001 Chem. Phys. Lett. 343 633
[9]	Tesch C M and Vivie-Riedle R 2002 Phys. Rev. Lett. 89 157901
[10]	Troppmann U, Tesch C M and Vivie-Riedle R 2003 Chem. Phys. Lett. 378 273
[11]	Vala J, Amitay Z, Zhang B, Leone S R and Kosloff R 2002 Phys. Rev. A 66 062316
[12]	Babikov D 2004 J. Chem. Phys. 121 7577
[13]	Tesch C M and Vivie-Riedle R 2004 J. Chem. Phys. 121 12158
[14]	Cheng T and Brown A 2006 J. Chem. Phys. 124 034111
[15]	Shioya K, Mishima K and Yamashita K 2007 Mol. Phys. 105 1283
[16]	Mishima K, Tokumo K and Yamashita K 2008 Chem. Phys. 343 61
[17]	Ryan R Z and Alex B 2010 J. Chem. Phys. 132 014307
[18]	Ohtsuki Y 2010 New J. Phys. 12 045002
[19]	Berrios E, Gruebele M, Shyshlov D, Wang L and Babikov D 2012 J. Phys. Chem. A 116 11347
[20]	Zhai L J, Zheng Y J and Ding S L 2012 Chin. Phys. B 21 070503
[21]	Troppmann U, Gollub C and Vivie-Riedle R 2006 New J. Phys. 8 100
[22]	Gu Y and Babikov D 2009 J. Chem. Phys. 131 034306
[23]	Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
[24]	Zheng Y J 2013 Molecular Structure and Algebraic Methods (Beijing: Science Press) (in Chinese)
[25]	Suzuki S, Mishima K and Yamashita K 2005 Chem. Phys. Lett. 410 358
[26]	Zhao M and Babikov D 2006 J. Chem. Phys. 125 024105
[27]	Weidinger D and Gruebele M 2007 Mol. Phys. 105 1999
[28]	Menzel-Jones C and Shapiro M 2007 Phys. Rev. A 75 052308
[29]	Ndong M, Lauvergnat D, Chapuisat X and Desouter-Lecomte M 2007 J. Chem. Phys. 126 244505
[30]	Mishima K and Yamashita K 2010 Chem. Phys. 367 63
[31]	Fujisaki H 2004 Phys. Rev. A 70 012313
[32]	Hou X W, Wan M F and Ma Z Q 2006 Chem. Phys. Lett. 426 469
[33]	Liu Y, Zheng Y, Ren W and Ding S 2008 Phys. Rev. A 78 032523
[34]	Liu D M, Peng D P and Hou X W 2008 Chin. Phys. Lett. 25 1263
[35]	Mishima K and Yamashita K 2009 Int. J. Quan. Chem. 109 1827
[36]	Hou X, Chen J and Ma Z 2009 Phys. Rev. A 79 022308
[37]	Hou X W and Cheng C M 2009 Chin. Phys. B 18 2719
[38]	Feng H R, Li P, Zheng Y J and Ding S L 2010 Prog. Theor. Phys. 123 215
[39]	McKemmish L K, McKenzie R H, Hush N S and Reimers J R 2011 J. Chem. Phys. 135 244110
[40]	Feng H R, Li P, Zheng Y J and Ding S L 2010 Acta Phys. Sin. 59 5246 (in Chinese)
[41]	Wei T C, Nemoto K, Goldbart P M, Kwiat P G, Munro W J and Verstraete F 2003 Phys. Rev. A 67 022110
[42]	Hou X W, Chen J H, Wan M F and Ma Z Q 2008 Eur. Phys. J. D 49 37
[43]	Fei S M 2010 Physics 39 0 (in Chinese)
[44]	Rungta P, Buzek V, Caves C M, Hillery M and Milburn G J 2001 Phys. Rev. A 64 042315
[45]	Chen K, Albeverio S and Fei S M 2005 Phys. Rev. Lett. 95 040504
[46]	Carvalho A R R, Mintert F and Buchleitner A 2004 Phys. Rev. Lett. 93 230501
[47]	Gao X H, Fei S M and Wu K 2006 Phys. Rev. A 74 050303
[48]	Meng Q, Zheng Y J and Ding S L 2001 Int. J. Quan. Chem. 81 154
[49]	Zheng Y J and Ding S L 2001 Phys. Rev. A 64 032720
[50]	Wang X Y and Ding S L 2004 Acta Phys. Sin. 53 423 (in Chinese)
[51]	Zheng Y J and Ding S L 2007 Int. J. Quan. Chem. 107 1008
[52]	Hou X W, Wan M F and Ma Z Q 2012 Chin. Phys. B 21 103301
[53]	Vadeiko I P, Miroshnichenko G P, Rybin A V and Timonen J 2003 Phys. Rev. A 67 053808
[54]	Batista C D and Ortiz G 2004 Adv. Phys. 53 1
[55]	Kikoin Y K and Kiselev M N 2004 arXiv:cond-mat/0407063v1
[56]	Rau A P R and Zhao W 2005 Phys. Rev. A 71 063822
[57]	Feng H R and Ding S L 2007 J. Phys. B: At. Mol. Opt. Phys. 40 69
[58]	Cooper I L and Gupta R K 1997 Phys. Rev. A 55 4112
[59]	Cooper I L 1998 J. Phys. Chem. A 102 9565
[60]	Feng H R, Liu Y, Zheng Y J, Ding S L and Ren W Y 2007 Phys. Rev. A 75 063417
[61]	Mirraphimi M, Turinici G and Rouchon P 2005 J. Phys. Chem. A 109 2631
[62]	Mirrahimi M, Rouchon P and Turinici G 2005 Automatica 41 1987
[63]	Ceng S 2006 Introduction to Quantum Mechanical System Control (Beijing: Scientific Press) (in Chinese)
[64]	Mirrahimi M and Handel R V 2007 SIAM J. Control Optim. 46 445
[65]	Beauchard K, Coron J M, Mirrahimi M and Rouchon P 2007 Syst. Control Lett. 56 388
[66]	Yu A P 2002 Ecological Indicators 2 123
[67]	Wang H, Hofheinz M, Ansmann M, Bialczak R C, Lucero E and Neeley M 2008 Phys. Rev. Lett. 101 240401
[68]	Zheng D S and Wu G Z 2002 Chem. Phys. Lett. 352 85
[69]	Wu G Z 2005 Nonlinearity and Chaos in Molecular Vibrations (Amsterdam: Elsevier)

[1]	Entanglement and thermalization in the extended Bose-Hubbard model after a quantum quench: A correlation analysis Xiao-Qiang Su(苏晓强), Zong-Ju Xu(许宗菊), and You-Quan Zhao(赵有权). Chin. Phys. B, 2023, 32(2): 020506.
[2]	Characterizing entanglement in non-Hermitian chaotic systems via out-of-time ordered correlators Kai-Qian Huang(黄恺芊), Wei-Lin Li(李蔚琳), Wen-Lei Zhao(赵文垒), and Zhi Li(李志). Chin. Phys. B, 2022, 31(9): 090301.
[3]	Nonreciprocal coupling induced entanglement enhancement in a double-cavity optomechanical system Yuan-Yuan Liu(刘元元), Zhi-Ming Zhang(张智明), Jun-Hao Liu(刘军浩), Jin-Dong Wang(王金东), and Ya-Fei Yu(於亚飞). Chin. Phys. B, 2022, 31(9): 094203.
[4]	Bright 547-dimensional Hilbert-space entangled resource in 28-pair modes biphoton frequency comb from a reconfigurable silicon microring resonator Qilin Zheng(郑骑林), Jiacheng Liu(刘嘉成), Chao Wu(吴超), Shichuan Xue(薛诗川), Pingyu Zhu(朱枰谕), Yang Wang(王洋), Xinyao Yu(于馨瑶), Miaomiao Yu(余苗苗), Mingtang Deng(邓明堂), Junjie Wu(吴俊杰), and Ping Xu(徐平). Chin. Phys. B, 2022, 31(2): 024206.
[5]	Influences of spin-orbit interaction on quantum speed limit and entanglement of spin qubits in coupled quantum dots M Bagheri Harouni. Chin. Phys. B, 2021, 30(9): 090301.
[6]	Nonlocal advantage of quantum coherence and entanglement of two spins under intrinsic decoherence Bao-Min Li(李保民), Ming-Liang Hu(胡明亮), and Heng Fan(范桁). Chin. Phys. B, 2021, 30(7): 070307.
[7]	Entanglement properties of GHZ and W superposition state and its decayed states Xin-Feng Jin(金鑫锋), Li-Zhen Jiang(蒋丽珍), and Xiao-Yu Chen(陈小余). Chin. Phys. B, 2021, 30(6): 060301.
[8]	Quantifying entanglement in terms of an operational way Deng-Hui Yu(于登辉) and Chang-Shui Yu(于长水). Chin. Phys. B, 2021, 30(2): 020302.
[9]	Reversion of weak-measured quantum entanglement state Shao-Jiang Du(杜少将), Yonggang Peng(彭勇刚), Hai-Ran Feng(冯海冉), Feng Han(韩峰), Lian-Wu Yang(杨连武), Yu-Jun Zheng(郑雨军). Chin. Phys. B, 2020, 29(7): 074202.
[10]	Qubit movement-assisted entanglement swapping Sare Golkar, Mohammad Kazem Tavassoly, Alireza Nourmandipour. Chin. Phys. B, 2020, 29(5): 050304.
[11]	Quantum speed limit time and entanglement in a non-Markovian evolution of spin qubits of coupled quantum dots M. Bagheri Harouni. Chin. Phys. B, 2020, 29(12): 124203.
[12]	Protecting the entanglement of two-qubit over quantum channels with memory via weak measurement and quantum measurement reversal Mei-Jiao Wang(王美姣), Yun-Jie Xia(夏云杰), Yang Yang(杨阳), Liao-Zhen Cao(曹连振), Qin-Wei Zhang(张钦伟), Ying-De Li(李英德), and Jia-Qiang Zhao(赵加强). Chin. Phys. B, 2020, 29(11): 110307.
[13]	Hidden Anderson localization in disorder-free Ising–Kondo lattice Wei-Wei Yang(杨薇薇), Lan Zhang(张欄), Xue-Ming Guo(郭雪明), and Yin Zhong(钟寅)†. Chin. Phys. B, 2020, 29(10): 107301.
[14]	Geometrical quantum discord and negativity of two separable and mixed qubits Tang-Kun Liu(刘堂昆), Fei Liu(刘飞), Chuan-Jia Shan(单传家), Ji-Bing Liu(刘继兵). Chin. Phys. B, 2019, 28(9): 090304.
[15]	Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis Zhi-Yuan Li(李志远). Chin. Phys. B, 2019, 28(6): 060301.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Dynamical correlation between quantum entanglement and intramolecular energy in molecular vibrations：An algebraic approach

Cite this article:

Online attention