Second Phase Transition in an Open-System Dicke Model with Spontaneous Emission

Spin-boson models, which describe the interaction between atoms and harmonic oscillators, lie at the heart of quantum information science. In particular the Dicke model [1] with its famous ``superradiant'' phase transition [2] constitutes a standard model in quantum optics and has been recently realized [3,4]. Adding noise to such models can lead to novel phases and allows for the observation of ``dissipative phase transitions'' in steady state [5]. We consider a finite-size open-system Dicke model with spontaneous emission. In this model, the superradiant phase transition can be observed in steady-state. In addition, we find a second phase transition which solely occurs in the harmonic oscillator and results in nonstationarity. The corresponding critical coupling exhibits a different scaling with the number of atoms compared to that of the superradiant phase transition. As a result, qualitatively different dynamics depending on the size of the system can be observed.

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[5] E. M. Kessler et al., Phys. Rev. A 86, 012116 (2012).