  In this work, we study the driven-dissipative dynamics of a coherently-driven
spin ensemble with a squeezed, superradiant decay. This decay consists of a sum
of both raising and lowering collective spin operators with a tunable weight.
The model presents different critical non-equilibrium phases with a gapless
Liouvillian that are associated to particular symmetries and that give rise to
distinct kinds of non-ergodic dynamics. In Ref. [1] we focus on the case of a
strong-symmetry and use this model to introduce and discuss the effect of
dissipative freezing, where, regardless of the system size, stochastic quantum
trajectories initialized in a superposition of different symmetry sectors
always select a single one of them and remain there for the rest of the
evolution. Here, we deepen this analysis and study in more detail the other
type of non-ergodic physics present in the model, namely, the emergence of
non-stationary dynamics in the thermodynamic limit. We complete our description
of squeezed superradiance by analysing its metrological properties in terms of
spin squeezing and by analysing the features that each of these critical phases
imprint on the light emitted by the system.
