  Atomic ensembles strongly interacting with light constitute rich
quantum-optical many-body systems, with the potential for observing cooperative
effects and dissipative nonequilibrium phase transitions. We theoretically
analyze the conditions under which a driven atomic ensemble in free space,
characterized by strong dipole-dipole interactions and large spatial extent,
can undergo a superradiant phase transition, also known as cooperative
resonance fluorescence. In an atomic array, stationary states that conserve the
collective pseudospin exhibit completely cooperative decay and undergo a
second-order phase transition in the large atom number limit. In contrast,
decay mechanisms on longer timescales that fail to conserve pseudospin can lead
to discontinuous first-order phase transition at a critical finite atom number,
disrupting cooperation despite sharing many similar observable characteristics.
A hallmark of the superradiant phase transition is an abrupt shift from total
light reflection off the atoms to rapidly increasing transmission, accompanied
by significant quantum fluctuations, as a function of light intensity.
