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Dicke模型中的量子相变在三十多年前已被预言, 该模型描述的是N个二能级原子与单模腔场集体耦合的系统. 在标准Dicke模型的基础上加入原子光的非线性相互作用和含时外场驱动, 使用含时幺正变换和Holstein-Primafoff变换方法从理论上推导出基态能量表达式. 并且给出了丰富的相图,而且这些性质最近已有文献从实验上验证. 本文主要呈现了非线性相互作用和外场驱动对量子相变的影响.
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关键词:
- Dicke 模型 /
- 量子相变 /
- Holstein-Primafoff变换
When an atomic ensemble is coupled with a cavity field governed by the well-known Dicke model , an important quantum phase transition (QPT) from the normal phase to the superradiant phase occurs, which was predicted more than 30 years ago. In this paper, both the atom-photon nonlinear interaction and the driving field are added to the Dicke's Hamiltonian. With the method of Holstein-Primafoff transformation, the ground state energy is given by the theoretical calculation, and the rich phase figures are presented. Meanwhile, these properties are observed experimentally. We mainly dicuss the effects of the atom-photon nonlinear interaction and the driving field on QPT.[1] Brennecke F, Donner T, Ritter S, Bourdel T, Köhl M, Esslinger T 2007 Nature 450 268
[2] Colombe Y, Steinmetz T, Dubois G, Linke F, Hunger D, Reichel J 2007 Nature 450 272
[3] Brennecke F, Ritter S, Donner T, Esslinger T 2008 Science 322 235
[4] Maschler C, Ritsch H 2005 Phys. Rev. Lett. 95 260401
[5] Chen G, Wang X G, Liang J Q, Wang Z D 2008 Phys. Rev. A 78 023634
[6] Morrison S, Parkins A S 2008 Phys. Rev. Lett. 100 040403
[7] Larson J, Damski B, Morigi G, Lewenstein M 2008 Phys. Rev. Lett. 100 050401
[8] Larson J, Martikainen J P 2010 Phys. Rev. A 82 033606
[9] Gopalakrishnan S, Lev B L, Goldbart P M 2009 Nat. Phys. 5 845
[10] Szirmai G, Nagy D, Domokos P 2009 Phys. Rev. Lett. 102 080401
[11] Bastidas V M, Emary C, Regler B, Brandes T 2012 Phys. Rev. Lett. 108 043003
[12] Hepp K, Lieb E H 1973 Ann. Phys. (N. Y.) 76 360
[13] Hioes F T 1973 Phys. Rev. A 8 1440
[14] Song L J, Yan D, Gai Y J, Wang Y B 2010 Acta Phys. Sin. 59 3695 (in Chinese) [宋立军, 严冬, 盖永杰, 王玉波 2010 59 3695]
[15] Song L J, Yan D, Gai Y J, Wang Y B 2011 Acta Phys. Sin. 60 020302 (in Chinese) [宋立军,严冬,盖永杰,王玉波 2011 60 020302]
[16] Baumann K, Guerlin C, Brennecke F, Esslinger T 2010 Nature 464 1301
[17] Baumann K, Mottl R, Brennecke F, Esslinger T 2011 Phys. Rev. Lett. 107 140402
[18] Viehmann O, von Delft J, Marquardt F 2011 Phys. Rev. Lett. 107 113602
[19] Nagy D, Kónya G, Szirmai G, Domokos P 2010 Phys. Rev. Lett. 104 130401
[20] Keeling J, Bhaseen M J, Simons B D 2010 Phys. Rev. Lett. 105 043001
[21] Liu N, Lian J L, Ma J, Xiao L T, Chen G , Liang J Q, Jia S T 2011 Phys. Rev. A 83 033601
[22] Xu C T, Liang J Q 2006 Phys. Rev. A 356 206
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[1] Brennecke F, Donner T, Ritter S, Bourdel T, Köhl M, Esslinger T 2007 Nature 450 268
[2] Colombe Y, Steinmetz T, Dubois G, Linke F, Hunger D, Reichel J 2007 Nature 450 272
[3] Brennecke F, Ritter S, Donner T, Esslinger T 2008 Science 322 235
[4] Maschler C, Ritsch H 2005 Phys. Rev. Lett. 95 260401
[5] Chen G, Wang X G, Liang J Q, Wang Z D 2008 Phys. Rev. A 78 023634
[6] Morrison S, Parkins A S 2008 Phys. Rev. Lett. 100 040403
[7] Larson J, Damski B, Morigi G, Lewenstein M 2008 Phys. Rev. Lett. 100 050401
[8] Larson J, Martikainen J P 2010 Phys. Rev. A 82 033606
[9] Gopalakrishnan S, Lev B L, Goldbart P M 2009 Nat. Phys. 5 845
[10] Szirmai G, Nagy D, Domokos P 2009 Phys. Rev. Lett. 102 080401
[11] Bastidas V M, Emary C, Regler B, Brandes T 2012 Phys. Rev. Lett. 108 043003
[12] Hepp K, Lieb E H 1973 Ann. Phys. (N. Y.) 76 360
[13] Hioes F T 1973 Phys. Rev. A 8 1440
[14] Song L J, Yan D, Gai Y J, Wang Y B 2010 Acta Phys. Sin. 59 3695 (in Chinese) [宋立军, 严冬, 盖永杰, 王玉波 2010 59 3695]
[15] Song L J, Yan D, Gai Y J, Wang Y B 2011 Acta Phys. Sin. 60 020302 (in Chinese) [宋立军,严冬,盖永杰,王玉波 2011 60 020302]
[16] Baumann K, Guerlin C, Brennecke F, Esslinger T 2010 Nature 464 1301
[17] Baumann K, Mottl R, Brennecke F, Esslinger T 2011 Phys. Rev. Lett. 107 140402
[18] Viehmann O, von Delft J, Marquardt F 2011 Phys. Rev. Lett. 107 113602
[19] Nagy D, Kónya G, Szirmai G, Domokos P 2010 Phys. Rev. Lett. 104 130401
[20] Keeling J, Bhaseen M J, Simons B D 2010 Phys. Rev. Lett. 105 043001
[21] Liu N, Lian J L, Ma J, Xiao L T, Chen G , Liang J Q, Jia S T 2011 Phys. Rev. A 83 033601
[22] Xu C T, Liang J Q 2006 Phys. Rev. A 356 206
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