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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.
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Keywords:
- two-mode Dicke model /
- ground-state energy /
- quantum phase transitions
[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
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[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 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 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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[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 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 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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