  The Dicke model is a paradigmatic quantum-optical model describing the
interaction of a collection of two-level systems with a single bosonic mode.
Effective implementations of this model made it possible to observe the
emergence of superradiance, i.e., cooperative phenomena arising from the
collective nature of light-matter interactions. Via reservoir engineering and
analogue quantum simulation techniques, current experimental platforms allow us
not only to implement the Dicke model, but also to design more exotic
interactions, such as the two-photon Dicke model. In the Hamiltonian case, this
model presents an interesting phase diagram characterized by two quantum
criticalities: a superradiant phase transition and a spectral collapse, that
is, the coalescence of discrete energy levels into a continuous band. Here, we
investigate the effects of both qubit and photon dissipation on the phase
transition and on the instability induced by the spectral collapse. Using a
mean-field decoupling approximation, we analytically obtain the steady-state
expectation values of the observables signaling a symmetry breaking,
identifying a first-order phase transition from the normal to the superradiant
phase. Our stability analysis unveils a very rich phase diagram, which features
stable, bistable, and unstable phases depending on dissipation rate.
