Recent theoretical advances on superradiant phase transitions

The Dicke model describing a single-mode boson field coupled to two-level systems is an important paradigm in quantum optics. In particular, the physics of ``superradiant phase transitions'' in the ultrastrong coupling regime is the subject of a vigorous research activity in both cavity and circuit QED. Recently, we explored the rich physics of two interesting generalizations of the Dicke model: (i) A model describing the coupling of a boson mode to two independent chains A and B of two-level systems [1], where chain A is coupled to one quadrature of the boson field and chain B to the orthogonal quadrature. This original model leads to a quantum phase transition with a double symmetry breaking and a fourfold ground state degeneracy. (ii) A generalized Dicke model with three-level systems [2,3] including the diamagnetic term. In contrast to the case of two-level atoms for which no-go theorems exist, in the case of three-level system we prove that the Thomas-Reich-Kuhn sum rule does not always prevent a superradiant phase transition.\\[4pt] [1] P. Nataf, A. Baksic and C. Ciuti, Phys. Rev. A {\bf 86}, 013832 (2012).\\[0pt] [2] C. Ciuti and P. Nataf, Phys. Rev. Lett. {\bf 109}, 179301 (2012).\\[0pt] [3] A. Baksic, P. Nataf, and C. Ciuti, arXiv:1206.3213 (2012).