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 nonequilibrium 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 18 lattice sites. We show that bistability significantly strengthens the spatial correlations and the entanglement.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 nonequilibrium 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 18 lattice sites. We show that bistability significantly strengthens the spatial correlations and the entanglement.

arXiv:1305.2208Physical Review ANov 22, 201355 citations

Spatial correlations of Rydberg excitations in optically driven atomic ensembles

David Petrosyan, Michael Höning, Michael Fleischhauer

We study many-body correlations in the stationary state of a continuously driven, strongly interacting dissipative system. Specifically, we examine resonant optical excitations of Rydberg states of atoms interacting via long-range dipole-dipole and van der Waals potentials employing numerical and analytical techniques. Collection of atoms within a blockade distance form a ``superatom'' that can accommodate at most one Rydberg excitation. The superatom excitation probability saturates to $\frac{1}{2}$ for coherently driven atoms but is significantly higher in the presence of dephasing, approaching unity as the number of atoms increases. Using the exact numerical solution of the density-matrix equations for a small system, we demonstrate that strong dephasing of the optically driven dipoles renders the many-body problem amenable to semiclassical Monte Carlo simulations. We employ the Monte Carlo algorithm for a large number of atoms and find that in the steady state of a uniformly driven, extended one-dimensional system, the saturation of superatoms leads to quasicrystallization of Rydberg excitations whose correlations exhibit damped spatial oscillations. We show that the behavior of the system under the van der Waals interaction potential can be approximated by a rate-equations model based on a ``hard-rod'' interatomic potential, and by solving it we obtain the period and correlation length for the density wave of Rydberg excitations.We study many-body correlations in the stationary state of a continuously driven, strongly interacting dissipative system. Specifically, we examine resonant optical excitations of Rydberg states of atoms interacting via long-range dipole-dipole and van der Waals potentials employing numerical and analytical techniques. Collection of atoms within a blockade distance form a ``superatom'' that can accommodate at most one Rydberg excitation. The superatom excitation probability saturates to $\frac{1}{2}$ for coherently driven atoms but is significantly higher in the presence of dephasing, approaching unity as the number of atoms increases. Using the exact numerical solution of the density-matrix equations for a small system, we demonstrate that strong dephasing of the optically driven dipoles renders the many-body problem amenable to semiclassical Monte Carlo simulations. We employ the Monte Carlo algorithm for a large number of atoms and find that in the steady state of a uniformly driven, extended one-dimensional system, the saturation of superatoms leads to quasicrystallization of Rydberg excitations whose correlations exhibit damped spatial oscillations. We show that the behavior of the system under the van der Waals interaction potential can be approximated by a rate-equations model based on a ``hard-rod'' interatomic potential, and by solving it we obtain the period and correlation length for the density wave of Rydberg excitations.

arXiv:1212.2423Physical Review AMay 28, 201376 citations

Probing Quantum Statistics and Spatial Correlations with Ultralong-Range Rydberg Molecules

T. C. Killian

Bulletin of the American Physical SocietyMay 28, 20190 citations

Spontaneous dipole-dipole interactions in many-body, driven, dissipative Rydberg systems

J. Maslek, Thomas Boulier, Eric Magnan +5 more

Bulletin of the American Physical SocietyMar 16, 20170 citations

\frac{1}{2}

for coherently driven atoms but is significantly higher in the presence of dephasing, approaching unity as the number of atoms increases. Using the exact numerical solution of the density-matrix equations for a small system, we demonstrate that strong dephasing of the optically driven dipoles renders the many-body problem amenable to semiclassical Monte Carlo simulations. We employ the Monte Carlo algorithm for a large number of atoms and find that in the steady state of a uniformly driven, extended one-dimensional system, the saturation of superatoms leads to quasicrystallization of Rydberg excitations whose correlations exhibit damped spatial oscillations. We show that the behavior of the system under the van der Waals interaction potential can be approximated by a rate-equations model based on a ``hard-rod'' interatomic potential, and by solving it we obtain the period and correlation length for the density wave of Rydberg excitations.