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We study the phase diagram of the Dicke model in terms of the excitationenergy and the radiation-matter coupling constant $\lambda$. Below a certaincritical value $\lambda_c$ of the coupling constant $\lambda$ all the energylevels have a well-defined parity. For $\lambda > \lambda_c$ the energyspectrum exhibits two different phases separated by a critical energy $E_c$that proves to be independent of $\lambda$. In the upper phase, the energylevels have also a well defined parity, but below $E_c$ the energy levels aredoubly degenerated. We show that the long-time behavior of appropriateparity-breaking observables distinguishes between the different phases of theenergy spectrum of the Dicke model. Steady states reached fromsymmetry-breaking initial conditions restore the symmetry only if theirexpected energies are above the critical. This fact makes it possible toexperimentally explore the complete phase diagram of the excitation spectrum ofthe Dicke model.

Excited-state phase transition leading to symmetry-breaking steady states in the Dicke model