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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.
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Keywords:
- spin coherent-states /
- variational method /
- Jaynes-Cummings model
[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
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[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
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