双模Dicke模型的一级量子相变

俞立先; 梁奇锋; 汪丽蓉; 朱士群

doi:10.7498/aps.63.134204

摘要

多光场与多粒子相互作用的多模Dicke模型不但存在着更为丰富的量子相，而且在量子信息中有着重要的应用. 本文运用Holstein-Primakoff变换和玻色扩展法研究双模Dicke模型的基态特性并从理论上发现了一个新的一级量子相变. 该相变在实验上可以通过测量平均光子数或原子布居数进行观察.

关键词:

The multi-mode Dicke model, which describes many atoms interacting with the multi-mode photons, has attracted much attention; it not only exhibits rich quantum phases, but also has an important application in quantum information. In this paper, we explore the ground-state properties of the two-mode Dicke model by the Holstein-Primakoff transformation and Boson expansion method, and theoretically predict a new first-order quantum phase transition. In the experiment, this quantum phase transition could be detected by measuring the mean-photon number or the atom population.

Keywords:

作者及机构信息

1.
苏州大学物理科学与技术学院, 苏州 215006;

2.
绍兴文理学院数理信息学院, 绍兴 312000;

3.
山西大学激光光谱研究所, 太原 030006

基金项目: 国家自然科学基金（批准号：11074184，11275129，61275211）、浙江省自然科学基金（批准号：LY13A040001）和浙江省教育厅科研项目（批准号：Y201122352）资助的课题.

Authors and contacts

1.
School of Physical Science and Technology, Soochow University, Suzhou 215006, China;

2.
Department of Physics, Shaoxing University, Shaoxing 312000, China;

3.
Laser Spectroscopy Laboratory, Shanxi University, Taiyuan 030006, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11074184, 11275129, 61275211), the Natural Science Foundation of Zhejiang Province, China (Grant No. LY13A040001), and the Scientific Research Fundation of the Education Department of Zhejiang Province, China (Grant No. Y201122352).

参考文献

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[3]	Safi I, Saleur H 2004 Phys. Rev. Lett. 93 126602
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[9]	Li S C, Fu L B, Li F L 2013 Phys. Rev. A 88 013602
[10]	Wang Li, Libin Fu 2013 Phys. Rev. A 87 053612
[11]	Zhang X Z, Song Z 2013 Phys. Rev. A 87 012114
[12]	Liu N 2013 Acta Phys. Sin. 62 013402 (in Chinese)[刘妮 2013 物理学报 62 013402]
[13]	Dicke R H 1954 Phys. Rev. 93 99
[14]	Hepp K, Lieb E H 1973 Ann. Phys. 76 360
[15]	Wang Y K, Hioe F T 1973 Phys. Rev. A 7 831
[16]	Emary C, Brandes T 2003 Phys. Rev. E 67 066203
[17]	Castaños O, Nahmad-Achar E, López-Peña R, Hirsch J G 2012 Phys. Rev. A 86 023814
[18]	Song L J, Yan D, Ma J, Wang X G 2009 Phys. Rev. E 79 046220
[19]	Lambert N, Emary C, Brandes T 2005 Phys. Rev. A 71 053804
[20]	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 物理学报 59 3695]
[21]	Baumann K, Guerlin C, Brennecke F, Esslinger T 2010 Nature 464 1301
[22]	Nataf P, Ciuti C 2010 Nat. Commun. 1 7 2
[23]	Chen G, Chen Z D, Liang J Q 2007 Phys. Rev. A 76 055803
[24]	Hepp K, Lieb E H 1973 Ann. Phys. 76 360
[25]	Emeljanov V I, Klimontovich Y L 1976 Phys. Lett. 59 366
[26]	Tolkunov D, Solenov D 2007 Phys. Rev. B 75 024402
[27]	Buchhold M, Strack P, Sachdev S, Diehl S 2013 Phys. Rev. A 87 063622
[28]	Strack P, Sachdev S 2011 Phys. Rev. Lett. 107 277202
[29]	Wickenbrock A, Hemmerling M, Robb G R M, Emary C, Renzoni F 2013 Phys. Rev. A. 87 043817
[30]	Larson J, Levin S 2009 Phys. Rev. Lett. 103 013602
[31]	Larson J 2011 Phys. Rev. A 83 052103
[32]	Larson J 2008 Phys. Rev. A 78 033833
[33]	Tavis M, Cummings F W 1968 Phys. Rev. 170 379
[34]	Holstein T, Primakoff H 1949 Phys. Rev. 58 1098
[35]	Emary C, Brandes T 2003 Phys. Rev. E 67 066203
[36]	Bell S, Crighton J S 1981 Chem. Phys. Lett. 82 122

施引文献

[1]	Sachdev S 1999 Quantum Phase Transitions (UK:Cambridge UniversityPress)
[2]	Vojta M 2003 Rep. Prog. Phys. 66 2069
[3]	Safi I, Saleur H 2004 Phys. Rev. Lett. 93 126602
[4]	Goldstein M, GefenY, Berkovits R 2011 Phys. Rev. B 83 245112
[5]	Zhu S L 2006 Physics 35 11 (in Chinese) [朱诗亮 2006 物理 35 11]
[6]	Leviatan A, Macek M 2012 Phys. Lett. B 714 110
[7]	Goussev A, Jalabert R A, Pastawski H M, Wisniacki D 2012 Scholarpedia 7 11687
[8]	Tsang M 2013 Phys. Rev. A 88 021801
[9]	Li S C, Fu L B, Li F L 2013 Phys. Rev. A 88 013602
[10]	Wang Li, Libin Fu 2013 Phys. Rev. A 87 053612
[11]	Zhang X Z, Song Z 2013 Phys. Rev. A 87 012114
[12]	Liu N 2013 Acta Phys. Sin. 62 013402 (in Chinese)[刘妮 2013 物理学报 62 013402]
[13]	Dicke R H 1954 Phys. Rev. 93 99
[14]	Hepp K, Lieb E H 1973 Ann. Phys. 76 360
[15]	Wang Y K, Hioe F T 1973 Phys. Rev. A 7 831
[16]	Emary C, Brandes T 2003 Phys. Rev. E 67 066203
[17]	Castaños O, Nahmad-Achar E, López-Peña R, Hirsch J G 2012 Phys. Rev. A 86 023814
[18]	Song L J, Yan D, Ma J, Wang X G 2009 Phys. Rev. E 79 046220
[19]	Lambert N, Emary C, Brandes T 2005 Phys. Rev. A 71 053804
[20]	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 物理学报 59 3695]
[21]	Baumann K, Guerlin C, Brennecke F, Esslinger T 2010 Nature 464 1301
[22]	Nataf P, Ciuti C 2010 Nat. Commun. 1 7 2
[23]	Chen G, Chen Z D, Liang J Q 2007 Phys. Rev. A 76 055803
[24]	Hepp K, Lieb E H 1973 Ann. Phys. 76 360
[25]	Emeljanov V I, Klimontovich Y L 1976 Phys. Lett. 59 366
[26]	Tolkunov D, Solenov D 2007 Phys. Rev. B 75 024402
[27]	Buchhold M, Strack P, Sachdev S, Diehl S 2013 Phys. Rev. A 87 063622
[28]	Strack P, Sachdev S 2011 Phys. Rev. Lett. 107 277202
[29]	Wickenbrock A, Hemmerling M, Robb G R M, Emary C, Renzoni F 2013 Phys. Rev. A. 87 043817
[30]	Larson J, Levin S 2009 Phys. Rev. Lett. 103 013602
[31]	Larson J 2011 Phys. Rev. A 83 052103
[32]	Larson J 2008 Phys. Rev. A 78 033833
[33]	Tavis M, Cummings F W 1968 Phys. Rev. 170 379
[34]	Holstein T, Primakoff H 1949 Phys. Rev. 58 1098
[35]	Emary C, Brandes T 2003 Phys. Rev. E 67 066203
[36]	Bell S, Crighton J S 1981 Chem. Phys. Lett. 82 122

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