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

## TL;DR

This paper investigates the two-photon Dicke model, revealing a superradiant phase transition in the ultrastrong coupling regime before spectral collapse, and compares its critical behavior with the one-photon case.

## Contribution

It demonstrates the existence of a superradiant phase transition in the two-photon Dicke model and extends mean-field analysis with quantum fluctuations.

## Key findings

- Superradiant phase transition occurs before spectral collapse.
- Quantum fluctuations modify the critical behavior.
- Comparison with one-photon case highlights unique features.

## Abstract

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