Steady-state crystallization of Rydberg excitations in an optically   driven lattice gas
  We study resonant optical excitations of atoms in a one-dimensional lattice to the Rydberg states interacting via the van der Waals potential which suppresses simultaneous excitation of neighboring atoms. Considering two- and three-level excitation schemes, we analyze the dynamics and stationary state of the continuously-driven, dissipative many-body system employing time-dependent density-matrix renormalization group (t-DMRG) simulations. We show that two-level atoms can exhibit only nearest neighbor correlations, while three-level atoms under dark-state resonant driving can develop finite-range crystalline order of Rydberg excitations. We present an approximate rate equation model whose analytic solution yields qualitative understanding of the numerical results. 
Michael Hoening, Dominik Muth, David Petrosyan, Michael Fleischhauer
quant-ph cond-mat.quant-gas