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

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

›› 2014, Vol. 23 ›› Issue (7): 73301-073301.doi: 10.1088/1674-1056/23/7/073301

• ATOMIC AND MOLECULAR PHYSICS • 上一篇下一篇

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

冯海冉^a, 孟祥佳^b, 李鹏^a, 郑雨军^b

a Department of Physics and Information Engineering, Jining University, Jining 273155, China;
b School of Physics, Shandong University, Jinan 250100, China

收稿日期:2014-01-02 修回日期:2014-01-24 出版日期:2014-07-15 发布日期:2014-07-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11147019 and 91021009).

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

Feng Hai-Ran (冯海冉)^a, Meng Xiang-Jia (孟祥佳)^b, Li Peng (李鹏)^a, Zheng Yu-Jun (郑雨军)^b

a Department of Physics and Information Engineering, Jining University, Jining 273155, China;
b School of Physics, Shandong University, Jinan 250100, China

Received:2014-01-02 Revised:2014-01-24 Online:2014-07-15 Published:2014-07-15
Contact: Feng Hai-Ran E-mail:hairanfeng@mail.sdu.edu.cn
About author:33.15.-e; 33.20.Tp; 03.67.Mn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11147019 and 91021009).

摘要/Abstract

摘要： 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.

关键词: quantum entanglement, molecular vibration, intramolecular energy, Lie algebra

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.

Key words: quantum entanglement, molecular vibration, intramolecular energy, Lie algebra

中图分类号: (Properties of molecules)

33.15.-e

33.20.Tp (Vibrational analysis) 03.67.Mn (Entanglement measures, witnesses, and other characterizations)

冯海冉, 孟祥佳, 李鹏, 郑雨军. Dynamical correlation between quantum entanglement and intramolecular energy in molecular vibrations：An algebraic approach[J]. , 2014, 23(7): 73301-073301.

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[J]. Chin. Phys. B, 2014, 23(7): 73301-073301.

参考文献 69

[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)

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

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

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