  We consider a one-dimensional lattice of atoms with laser excitation to a
Rydberg state and spontaneous emission. The atoms are coupled due to the
dipole-dipole interaction of the Rydberg states. This driven-dissipative system
has a broad range of non-equilibrium phases, such as antiferromagnetic ordering
and bistability. Using the quantum trajectory method, we calculate the spatial
correlation function throughout the parameter space for up to 20 lattice sites.
We show that bistability significantly strengthens the spatial correlations and
entanglement.
