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Entangled quantum heat engines based on two-qubit XXZ model with Dzyaloshinski-Mariya interaction

Wang Tao Huang Xiao-Li Liu Yang Xu Huan

Entangled quantum heat engines based on two-qubit XXZ model with Dzyaloshinski-Mariya interaction

Wang Tao, Huang Xiao-Li, Liu Yang, Xu Huan
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  • We construct an entangled quantum heat engine based on two-coupled-qubit XXZ model with Dzyaloshinski-Mariya interaction. The work done and the heat transfer are discussed according to the definition first given by Kieu, The relations between the entanglement and heat transfer, work output and efficiency are analyzed for different anisotropic parameters. The results show that the second law of thermodynamics holds in entangled systems and the isolines for the efficiency are looped curves. When the anisotropic parameter Δ is small enough, the heat engine can operate in both C1 > C2 and C1C2, however, when Δ is large, the heat engine operates in C1 > C2 only.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11105064).
    [1]

    Scovil H E D, Schulz-DuBois E O 1959 Phys. Rev. Lett. 2 262

    [2]

    Geva E, Kosloff R 1992 J. Chem. Phys. 97 4398

    [3]

    Lloyd S 1997 Phys. Rev. A 56 3374

    [4]

    Kosloff R, Geva E, Gordon J 2000 J. Appl. Phys. 87 8093

    [5]

    Feldmann T, Kosloff R 2000 Phys. Rev. E 61 4774

    [6]

    He J Z, Chen J C, Hua B 2002 Phys. Rev. E 65 036145

    [7]

    Wu F, Chen L G, Sun F R, Wu C, Li Q 2006 Phys. Rev. E 73 016103

    [8]

    Wang J H, He J Z, Xin Y 2007 Phys. Scr. 75 227

    [9]

    Rezek Y, Kosloff R 2006 New J. Phys. 8 83

    [10]

    Bender C M, Brody D C, Meister B K 2000 J. Phys. A 33 4427

    [11]

    Quan H T, Liu Y X, Sun C P, Nori F 2007 Phys. Rev. E 76 031105

    [12]

    Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122

    [13]

    Henrich M J, Mahler G, Michel M 2007 Phys. Rev. E 75 051118

    [14]

    Abe S, Okuyama S 2011 Phys. Rev. E 83 021121

    [15]

    Wang J H, He J Z, He X 2011 Phys. Rev. E 84 041127

    [16]

    Wang J H, He J Z 2012 J. Appl. Phys. 11 043505

    [17]

    Wang J H, Xiong S Q, He J Z, Liu J T 2012 Acta Phys. Sin. 61 080509 (in Chinese) [王建辉, 熊双泉, 何济洲, 刘江涛 2012 物理学报 61 080509]

    [18]

    Scully M O, Zubairy M S, Agarwal G S, Walther H 2003 Science 299 862

    [19]

    Scully M O 2010 Phys. Rev. Lett. 104 207701

    [20]

    Dorfman K E, Kim M B, Svidzinsky A A 2011 Phys. Rev. A 84 053829

    [21]

    Scully M O, Chapin K R, Dorfman K E, Kim M B, Svidzinsky A A 2011 Proc. Natl. Acad. Sci. 108 15097

    [22]

    Quan H T 2009 Phys. Rev. E 79 041129

    [23]

    Perrot P 1998 A to Z of Thermodynamics (New York: Oxford university press) p26, 103

    [24]

    Kieu T D 2004 Phys. Rev. Lett. 93 140403

    [25]

    Kieu T D 2006 Eur. Phys. J. D 39 115

    [26]

    Chen J, Yan Z 1998 J. Appl. Phys. 84 1791

    [27]

    Amico L, Fazio R, Osterloh A, Vedral V 2008 Rev. Mod. Phys. 80 517

    [28]

    Guo Z, Yan L S, Pan W, Luo B, Xu M F 2011 Acta Phys. Sin. 60 060301 (in Chinese) [郭 振, 闫连山, 潘 伟, 罗 斌, 徐明峰 2011物理学报 60 060301]

    [29]

    Lu D M 2011 Acta Phys. Sin. 60 090302 (in Chinese) [卢道明 2011 物理学报 60 090302]

    [30]

    Zhang T, Liu W T, Chen P X, Li C Z 2007 Phys. Rev. A 75 062102

    [31]

    Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese) [张英丽, 周 斌 2011 物理学报 60 120301]

    [32]

    He J Z, He X, Zheng J 2012 Chin. Phys. B 21 050303

    [33]

    Xie L J, Zhang D Y, Tang S Q, Zhan X G, Gao F 2009 Chin. Phys. B 18 3203

    [34]

    Wang H, Liu S Q, He J Z 2009 Phys. Rev. E 79 041113

    [35]

    Zhang G F 2008 Eur. Phys. J. D 49123

    [36]

    Dzyaloshkii I 1958 J. Phys. Chem. Sol. 4 241

    [37]

    Moriya T 1960 Phys. Rev. Lett. 4 228

    [38]

    Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901

    [39]

    Wootters W K 1998 Phys. Rev. Lett. 80 2245

    [40]

    Tong D M 2010 Phys. Rev. Lett. 104 12401

    [41]

    Zeng J Y 2007 Quantum Mechanics (Vol. 2) (Beijing: Science Press) p203 (in Chinese) [曾谨言 2007 量子力学 (卷II) (北京: 科学出版社)第203页]

    [42]

    Marzlin P K, Sanders B C 2004 Phys. Rev. Lett. 93 160408

    [43]

    Tong D M, Singh K, Kwek L C, Oh C H 2005 Phys. Rev. Lett. 95 110407

    [44]

    Tong D M, Singh K, Kwek L C, Oh C H 2007 Phys. Rev. Lett. 98 150402

    [45]

    Rigolin G, Ortiz G 2012 Phys. Rev. A 85 062111

  • [1]

    Scovil H E D, Schulz-DuBois E O 1959 Phys. Rev. Lett. 2 262

    [2]

    Geva E, Kosloff R 1992 J. Chem. Phys. 97 4398

    [3]

    Lloyd S 1997 Phys. Rev. A 56 3374

    [4]

    Kosloff R, Geva E, Gordon J 2000 J. Appl. Phys. 87 8093

    [5]

    Feldmann T, Kosloff R 2000 Phys. Rev. E 61 4774

    [6]

    He J Z, Chen J C, Hua B 2002 Phys. Rev. E 65 036145

    [7]

    Wu F, Chen L G, Sun F R, Wu C, Li Q 2006 Phys. Rev. E 73 016103

    [8]

    Wang J H, He J Z, Xin Y 2007 Phys. Scr. 75 227

    [9]

    Rezek Y, Kosloff R 2006 New J. Phys. 8 83

    [10]

    Bender C M, Brody D C, Meister B K 2000 J. Phys. A 33 4427

    [11]

    Quan H T, Liu Y X, Sun C P, Nori F 2007 Phys. Rev. E 76 031105

    [12]

    Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122

    [13]

    Henrich M J, Mahler G, Michel M 2007 Phys. Rev. E 75 051118

    [14]

    Abe S, Okuyama S 2011 Phys. Rev. E 83 021121

    [15]

    Wang J H, He J Z, He X 2011 Phys. Rev. E 84 041127

    [16]

    Wang J H, He J Z 2012 J. Appl. Phys. 11 043505

    [17]

    Wang J H, Xiong S Q, He J Z, Liu J T 2012 Acta Phys. Sin. 61 080509 (in Chinese) [王建辉, 熊双泉, 何济洲, 刘江涛 2012 物理学报 61 080509]

    [18]

    Scully M O, Zubairy M S, Agarwal G S, Walther H 2003 Science 299 862

    [19]

    Scully M O 2010 Phys. Rev. Lett. 104 207701

    [20]

    Dorfman K E, Kim M B, Svidzinsky A A 2011 Phys. Rev. A 84 053829

    [21]

    Scully M O, Chapin K R, Dorfman K E, Kim M B, Svidzinsky A A 2011 Proc. Natl. Acad. Sci. 108 15097

    [22]

    Quan H T 2009 Phys. Rev. E 79 041129

    [23]

    Perrot P 1998 A to Z of Thermodynamics (New York: Oxford university press) p26, 103

    [24]

    Kieu T D 2004 Phys. Rev. Lett. 93 140403

    [25]

    Kieu T D 2006 Eur. Phys. J. D 39 115

    [26]

    Chen J, Yan Z 1998 J. Appl. Phys. 84 1791

    [27]

    Amico L, Fazio R, Osterloh A, Vedral V 2008 Rev. Mod. Phys. 80 517

    [28]

    Guo Z, Yan L S, Pan W, Luo B, Xu M F 2011 Acta Phys. Sin. 60 060301 (in Chinese) [郭 振, 闫连山, 潘 伟, 罗 斌, 徐明峰 2011物理学报 60 060301]

    [29]

    Lu D M 2011 Acta Phys. Sin. 60 090302 (in Chinese) [卢道明 2011 物理学报 60 090302]

    [30]

    Zhang T, Liu W T, Chen P X, Li C Z 2007 Phys. Rev. A 75 062102

    [31]

    Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese) [张英丽, 周 斌 2011 物理学报 60 120301]

    [32]

    He J Z, He X, Zheng J 2012 Chin. Phys. B 21 050303

    [33]

    Xie L J, Zhang D Y, Tang S Q, Zhan X G, Gao F 2009 Chin. Phys. B 18 3203

    [34]

    Wang H, Liu S Q, He J Z 2009 Phys. Rev. E 79 041113

    [35]

    Zhang G F 2008 Eur. Phys. J. D 49123

    [36]

    Dzyaloshkii I 1958 J. Phys. Chem. Sol. 4 241

    [37]

    Moriya T 1960 Phys. Rev. Lett. 4 228

    [38]

    Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901

    [39]

    Wootters W K 1998 Phys. Rev. Lett. 80 2245

    [40]

    Tong D M 2010 Phys. Rev. Lett. 104 12401

    [41]

    Zeng J Y 2007 Quantum Mechanics (Vol. 2) (Beijing: Science Press) p203 (in Chinese) [曾谨言 2007 量子力学 (卷II) (北京: 科学出版社)第203页]

    [42]

    Marzlin P K, Sanders B C 2004 Phys. Rev. Lett. 93 160408

    [43]

    Tong D M, Singh K, Kwek L C, Oh C H 2005 Phys. Rev. Lett. 95 110407

    [44]

    Tong D M, Singh K, Kwek L C, Oh C H 2007 Phys. Rev. Lett. 98 150402

    [45]

    Rigolin G, Ortiz G 2012 Phys. Rev. A 85 062111

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Publishing process
  • Received Date:  24 October 2012
  • Accepted Date:  07 November 2012
  • Published Online:  20 March 2013

Entangled quantum heat engines based on two-qubit XXZ model with Dzyaloshinski-Mariya interaction

  • 1. School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11105064).

Abstract: We construct an entangled quantum heat engine based on two-coupled-qubit XXZ model with Dzyaloshinski-Mariya interaction. The work done and the heat transfer are discussed according to the definition first given by Kieu, The relations between the entanglement and heat transfer, work output and efficiency are analyzed for different anisotropic parameters. The results show that the second law of thermodynamics holds in entangled systems and the isolines for the efficiency are looped curves. When the anisotropic parameter Δ is small enough, the heat engine can operate in both C1 > C2 and C1C2, however, when Δ is large, the heat engine operates in C1 > C2 only.

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