  We study an array of two-level systems arranged on a lattice and illuminated
by an external plane wave which drives a dipolar transition between the two
energy levels. In this set up, the two-level systems are coupled by dipolar
interactions and subject to nonlocal dissipation, so behave as an open
many-body quantum system. We investigate the long-time dynamics of the system
at the mean-field level, and use this to determine a phase diagram as a
function of external drive and detuning. We find a multitude of phases
including antiferromagnetism, spin density waves, oscillations and phase
bistabilities. We investigate these phases in more detail and explain how
nonlocal dissipation plays a role in the long-time dynamics. Furthermore, we
discuss what features would survive in the full quantum description.
