In this paper we analyze properties of the phase transition that appears in a
set of quantum optical models; Dicke, Tavis-Cummings, quantum Rabi, and finally
the Jaynes-Cummings model. As the light-matter coupling is increased into the
deep strong coupling regime, the ground state turns from vacuum to become a
superradiant state characterized by both atomic and photonic excitations. It is
pointed out that all four transitions are of the mean-field type, that quantum
fluctuations are negligible, and hence these fluctuations cannot be responsible
for the corresponding vacuum instability. In this respect, these are not
quantum phase transitions. In the case of the Tavis-Cummings and
Jaynes-Cummings models, the continuous symmetry of these models implies that
quantum fluctuations are not only negligible, but strictly zero. However, all
models possess a non-analyticity in the ground state in agreement with a
continuous quantum phase transition. As such, it is a matter of taste whether
the transitions should be termed quantum or not. In addition, we also consider
the modifications of the transitions when photon losses are present. For the
Dicke and Rabi models these non-equilibrium steady states remain critical,
while the criticality for the open Tavis-Cummings and Jaynes-Cummings models is
completely lost, i.e. in realistic settings one cannot expect a true critical
behaviour for the two last models.Comment: 25 pages (single column), 6 figure
