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

Spatial correlations of one dimensional driven-dissipative systems of Rydberg atoms