Figure 1:
(a) The rich dynamical behavior of the atoms in the lattice is determined by a competition between the coherent excitation of Rydberg states, the interaction among excited atoms, and dissipation caused by radiative decay. (b)-(d) Exaggerated sketch of the three phases that can be assumed. The stationary fixed-point solutions of the nonlinear mean field equations either (b) exhibit a uniform density of Rydberg atoms or (c) a checkered density distribution that breaks the sublattice symmetry. (d) A Hopf bifurcation can lead to an instability that gives rise to an oscillatory steady-state solution in which the density difference between the two sublattices oscillates in time.