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The controllability of current quantum technologies allows to implementspin-boson models where two-photon couplings are the dominating terms oflight-matter interaction. In this case, when the coupling strength becomescomparable with the characteristic frequencies, a spectral collapse can takeplace, i.e. the discrete system spectrum can collapse into a continuous band.Here, we analyze the thermodynamic limit of the two-photon Dicke model, whichdescribes the interaction of an ensemble of qubits with a single bosonic mode.We find that there exists a parameter regime where two-photon interactionsinduce a superradiant phase transition, before the spectral collapse occurs.Furthermore, we extend the mean-field analysis by considering second-orderquantum fluctuations terms, in order to analyze the low-energy spectrum andcompare the critical behavior with the one-photon case.

Superradiant phase transition in the ultrastrong coupling regime of the two-photon Dicke model