Puebla, RicardoRelaño Pérez, ArmandoRetamosa Granado, Joaquín2023-06-192023-06-192013-02-19[1] R. H. Dicke, Phys. Rev. 93, 99 (1954). [2] K. Hepp and E. H. Lieb, Ann. Phys. (NY) 76, 360 (1973); Y. K. Wang and F. T. Hioe, Phys. Rev. A 7, 831 (1973); H. J. Carmichael, C. W. Gardiner, and D. F. Walls, Phys. Lett. A 46, 47 (1973). [3] C. Emary and T. Brandes, Phys. Rev. Lett. 90, 044101 (2003); Phys. Rev. E 67, 066203 (2003). [4] K. Baumann, R. Mottl, F. Brennecke, and T. Esslinger, Phys. Rev. Lett. 107, 140402 (2011). [5] K. Rzazewsky, K. Wodkiewicz, and W. Zakowicz, Phys. Rev. Lett. 35, 432 (1975); K. Rzazewsky and W. Wodkiewicz, Phys. Rev. A 13, 1967 (1976); J. M. Knight, Y. Aharonov, and G. T. C. Hsieh, ibid. 17, 1454 (1978); I. Bialynicki-Birula and K. Rzazewsky, ibid. 19, 301 (1979). [6] P. Nataf and C. Ciuti, Nature Commun. 1, 72 (2010); O. Viehmann, J. von Delft, and F. Marquardt, Phys. Rev. Lett. 107, 113602 (2011). [7] K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Nature (London) 464, 1301 (2010). [8] V. M. Bastidas, C. Emary, B. Regler, and T. Brandes, Phys. Rev. Lett. 108, 043003 (2012). [9] M. A. Alcalde, M. Bucher, C. Emary, and T. Brandes, Phys. Rev. E 86, 012101 (2012). [10] A. Altland and F. Haake, N. J. Phys 14, 073011 (2012). [11] J. Vidal and S. Dusuel, Europhys. Lett. 74, 817 (2006). [12] P. Pérez Fernández, P. Cejnar, J. M. Arias, J. Dukelsky, J. E. García Ramos, and A. Relaño, Phys. Rev. A 83, 033802 (2011). [13] P. Pérez Fernández, A. Relaño, J. M. Arias, P. Cejnar, J. Dukelsky, and J. E. García Ramos, Phys. Rev. E 83, 046208 (2011). [14] K. Banaszek, C. Radzewicz, K. Wodkiewicz, and J. S. Krasinski, Phys. Rev. A 60, 674 (1999); S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J. Raimond, and S. Haroche, Nature (London) 455, 510 (2008). [15] P. Reimann and M. Kastner, New. J. Phys. 14, 043020 (2012); A. J. Short, ibid. 13, 053009 (2011).1050-294710.1103/PhysRevA.87.023819https://hdl.handle.net/20.500.14352/33705© 2013 American Physical Society. The authors thank Borja Peropadre for his valuable comments. R.P. thanks J. M. Udias for his financial support. This work is supported in part by Spanish Government grants for the research projects FIS2009 11621-C02-01, FIS2009-07277, and CSPD-2007-00042 Ingenio2010, and by the Universidad Complutense de Madrid Grant No. UCM-910059.We study the phase diagram of the Dicke model in terms of the excitation energy and the radiation-matter coupling constant lambda. Below a certain critical value lambda(c), all the energy levels have a well-defined parity. For lambda > lambda(c) the energy spectrum exhibits two different phases separated by a critical energy E-c that proves to be independent of lambda. In the upper phase, the energy levels have also a well-defined parity, but below E-c the energy levels are doubly degenerated. We show that the long-time behavior of appropriate parity-breaking observables distinguishes between these two different phases of the energy spectrum. Steady states reached from symmetry-breaking initial conditions restore the symmetry only if their expected energies are above the critical. This fact makes it possible to experimentally explore the complete phase diagram of the excitation spectrum of the Dicke model.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.87.023819http://journals.aps.org/open access5362-Level AtomFieldCavityTermodinámica2213 Termodinámica