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自旋相干态变换和自旋-玻色模型的基于变分法的基态解析解

杨晓勇 薛海斌 梁九卿

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自旋相干态变换和自旋-玻色模型的基于变分法的基态解析解

杨晓勇, 薛海斌, 梁九卿

Spin coherent-state transformation and analytical solutions of ground-state based on variational-method for spin-Bose models

Yang Xiao-Yong, Xue Hai-Bin, Liang Jiu-Qing
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  • 提出一种基于自旋相干态变换求解自旋-玻色模型基态的变分法, 并将其用于单原子模型, 得到旋波近似和非旋波近似情形下的解析基态能量和波函数, 特别是在光场与原子的弱、强耦合区域都与数值对角化结果符合得很好. 另外, 该方法也可以直接用于求解任意原子数的Dicke模型基态和相应的量子相变研究, 而通常基于Holstein-Primakoff变换的变分法, 原则上只适用于原子数趋于无穷的热力学极限情形.
    We present a variational method for the ground-state solutions of the spin-Bose models by means of the spin coherent-state transformation. For the Jaynes-Cummings (J-C) models with and without the rotating-wave approximation, the ground-state energies obtained by this method are in perfect agreement with the results from numerical diagonalization in the whole region of the coupling between a light field and an atom. The present variational-method can be directly used to solve the ground-state energies of the Dicke models with arbitrary atom-numbers and furoher study the quantum phase transition; while the variational-method based on the Holstein-Primakoff transformation is only valid in principle for the thermodynamic limit with the atom-number tending to infinity.
    • 基金项目: 国家自然科学基金(批准号: 11204203, 11275118)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11204203, 11275118).
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    Jaynes E T, Cummings F W 1963 Proceedings of IEEE 51 89

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    Forn-Diaz P, Lisenfeld J, Marcos D, García-Ripoll J J, Solano E, Harmans C J P M, Mooij J E 2010 arXiv1005.1559

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    Schuster D I, Houck A A, Schreier J A, Wallraff A, Gambetta M, Blais A, Frunzio L, Majer J, Johnson B, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 445 515

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    Yu Y, Han S, Chu X, Wang Z 2002 Science 296 889

    [8]

    Chiorescu I, Bertet P, Semba K, Nakamura Y, Harmans C J P M, Mooij J E 2004 Nature 431 159

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    Deppe Frank, Mariantoni Matteo, Menzel E P, Marx A,Saito S, Kakuyanag K,Tanaka H, Meno T, Semba K, Takayanagi H, Solano E, Gross R 2008 Nature Physics 4 686

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    Fink J M, Göppl M, Baur M,Bianchetti R, Leek P J, Blais A, Wallraff A 2008 Nature 454 546

    [11]

    Hofheinz Max, Wang H, Ansmann M, Bialczak Radoslaw C, Lucero Erik, Neeley M, O'Connell A D, Sank D, Wenner J, Martinis John M, Cleland A N 2009 Nature 459 546

    [12]

    Liu T, Wang K L, Feng M 2009 Europhys. Lett. 86 54003

    [13]

    Dicke R H 1954 Phys. Rev. 93 99

    [14]

    Holstein T, Primakoff H 1940 Phys. Rev. 58 1098

    [15]

    Lai Y Z, Liang J Q, H J Wller-Kirsten, Zhou J G 1996 Phys. Rev. A 53 3691;1996 J. Phys. A. Math Gen. 29 1773

    [16]

    Chen Z D, Liang J Q, Shen S Q, Xie W F 2004 Phys. Rev. A 69 023611

    [17]

    Lian J L, Zhang Y W, Liang J Q 2012 Chin. Phys. Lett. 29 060302

    [18]

    Liang J Q, Wei L F 2011 Advances In Quantum Physics (Beijing: Science Press) p76 (in Chinese) [梁九卿, 韦联福 2011 量子物理新进展 (北京: 科学出版社) 第76页]

    [19]

    Chen Q H, Liu T, Zhang Y Y, Wang K L 2011 Europhys. Lett. 96 14003

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    Li X H, Wang K L, Liu T 2009 Chin. Phys. Lett. 26 044212

  • [1]

    Jaynes E T, Cummings F W 1963 Proceedings of IEEE 51 89

    [2]

    Raimond J M, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565

    [3]

    Hood C J, Lynn T W, Doherty A C, Parkins A S, Kimble H J 2000 Science 287 1447

    [4]

    Wallraff A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kuma S, Girvin S M, Schoelkopf R J 2004 Nature 431 162

    [5]

    Forn-Diaz P, Lisenfeld J, Marcos D, García-Ripoll J J, Solano E, Harmans C J P M, Mooij J E 2010 arXiv1005.1559

    [6]

    Schuster D I, Houck A A, Schreier J A, Wallraff A, Gambetta M, Blais A, Frunzio L, Majer J, Johnson B, Devoret M H, Girvin S M, Schoelkopf R J 2007 Nature 445 515

    [7]

    Yu Y, Han S, Chu X, Wang Z 2002 Science 296 889

    [8]

    Chiorescu I, Bertet P, Semba K, Nakamura Y, Harmans C J P M, Mooij J E 2004 Nature 431 159

    [9]

    Deppe Frank, Mariantoni Matteo, Menzel E P, Marx A,Saito S, Kakuyanag K,Tanaka H, Meno T, Semba K, Takayanagi H, Solano E, Gross R 2008 Nature Physics 4 686

    [10]

    Fink J M, Göppl M, Baur M,Bianchetti R, Leek P J, Blais A, Wallraff A 2008 Nature 454 546

    [11]

    Hofheinz Max, Wang H, Ansmann M, Bialczak Radoslaw C, Lucero Erik, Neeley M, O'Connell A D, Sank D, Wenner J, Martinis John M, Cleland A N 2009 Nature 459 546

    [12]

    Liu T, Wang K L, Feng M 2009 Europhys. Lett. 86 54003

    [13]

    Dicke R H 1954 Phys. Rev. 93 99

    [14]

    Holstein T, Primakoff H 1940 Phys. Rev. 58 1098

    [15]

    Lai Y Z, Liang J Q, H J Wller-Kirsten, Zhou J G 1996 Phys. Rev. A 53 3691;1996 J. Phys. A. Math Gen. 29 1773

    [16]

    Chen Z D, Liang J Q, Shen S Q, Xie W F 2004 Phys. Rev. A 69 023611

    [17]

    Lian J L, Zhang Y W, Liang J Q 2012 Chin. Phys. Lett. 29 060302

    [18]

    Liang J Q, Wei L F 2011 Advances In Quantum Physics (Beijing: Science Press) p76 (in Chinese) [梁九卿, 韦联福 2011 量子物理新进展 (北京: 科学出版社) 第76页]

    [19]

    Chen Q H, Liu T, Zhang Y Y, Wang K L 2011 Europhys. Lett. 96 14003

    [20]

    Li X H, Wang K L, Liu T 2009 Chin. Phys. Lett. 26 044212

计量
  • 文章访问数:  6202
  • PDF下载量:  1190
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-09-24
  • 修回日期:  2013-02-21
  • 刊出日期:  2013-06-05

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