Signatures of optical phase transitions in super- and subradiant arrays of atoms

Resonant light interacting with matter can support different phases of a polarizable medium, and optical bistability where two such phases coexist. Here we identify signatures of optical phase transitions and optical bistability mapped onto scattered light in planar arrays of cold atoms. Methods on how to explore such systems in superradiant, and extreme subradiant states existing outside the light cone, are proposed. The cooperativity threshold and intensity regimes for the intrinsic optical bistability, supported by resonant dipole-dipole interactions alone, are derived in several cases of interest analytically. Subradiant states require lower intensities, but stronger cooperativity for the existence of non-trivial phases than superradiant states. The transmitted light reveals the onset of phase transitions and bistability that are predicted by mean-field theory as large jumps in coherent and incoherent signals and hysteresis. In the quantum solution, traces of phase transitions are identified in enhanced quantum fluctuations of excited level populations.