Signatures of phase transitions and optical bistability for atoms in optical lattices

Radiative dipole-dipole interactions lead to a rich phenomenology of phases in an optical lattice of atoms when driven by a coherent field. They can also support intrinsic optical bistability, where it is possible for two such phases to coexist. Here, we investigate the different phases that emerge in an array of atoms and how they can be identified by studying the scattered light. We find that the onset of phases predicted by mean-field theory are revealed by large jumps in coherent and incoherent signals of the transmitted light. The presence of bistability can result in a strong cooperative and weak single-atom response from the array, with hysteresis upon sweeping the incident light frequency. We discuss how the phases depend on the low light intensity collective modes, and also determine the thresholds for the optical bistability in terms of the atomic cooperativity parameter and intensity of the incident light, in many cases obtaining analytical results.