Steady-state crystallization of Rydberg excitations in an optically driven lattice gas

We study the conditions for attaining crystalline order in the stationary state of a continuously driven, open many-body system. Specifically, we consider resonant optical excitations of atoms in a one-dimensional lattice to the Rydberg states interacting via the van der Waals potential. Strong blockade of excitations at neighboring lattice sites steers the system toward a crystalline state while competing with the fluctuations associated with relaxation. We analyze the stationary state of the many-body system and the dynamics of its buildup employing numerically exact time-dependent density-matrix renormalization-group simulations for two- and three-level excitation schemes. We also present an approximate rate equation model which provides qualitative conditions for attaining crystalline order.