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arXiv:0803.4481 · New Journal of Physics

Kinetic Monte Carlo modeling of dipole blockade in Rydberg excitation experiment

Amodsen Chotia, Matthieu Viteau, Thibault Vogt, D. Comparat, P. Pillet

Published Apr 30, 2008• 40 citations
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Abstract

We present a method to model the interaction and the dynamics of atoms excited to Rydberg states. We show a way to solve the optical Bloch equations for laser excitation of the frozen gas in good agreement with the experiment. A second method, the kinetic Monte Carlo (KMC) method, gives an exact solution of rate equations. Using a simple N -body integrator (Verlet), we are able to describe dynamic processes in space and time. Unlike more sophisticated methods, the KMC simulation offers the possibility of numerically following the evolution of tens of thousands of atoms within a reasonable computation time. The KMC simulation gives good agreement with dipole-blockade type of experiment. The role of ions and the individual particle effects are investigated.

DOI
10.1088/1367-2630/10/4/045031

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We present a method to model the interaction and the dynamics of atoms excited to Rydberg states. We show a way to solve the optical Bloch equations for laser excitation of the frozen gas in good agreement with the experiment. A second method, the kinetic Monte Carlo (KMC) method, gives an exact solution of rate equations. Using a simple N -body integrator (Verlet), we are able to describe dynamic processes in space and time. Unlike more sophisticated methods, the KMC simulation offers the possibility of numerically following the evolution of tens of thousands of atoms within a reasonable computation time. The KMC simulation gives good agreement with dipole-blockade type of experiment. The role of ions and the individual particle effects are investigated.
High resolution laser Stark excitation of np (60<n<85) Rydberg states of ultracold cesium atoms shows an efficient blockade of the excitation attributed to long-range dipole-dipole interaction. The dipole blockade effect is observed as a quenching of the Rydberg excitation depending on the value of the dipole moment induced by the external electric field. Effects of ions which could match the dipole blockade effect are discussed in detail but are ruled out for our experimental conditions. Analytic and Monte Carlo simulations of the excitation of an ensemble of interacting Rydberg atoms agree with the experiments and indicate a major role of the nearest neighboring Rydberg atom.
We develop a theoretical approach for the dynamics of Rydberg excitations in ultracold gases,with a realistically large number of atoms. We rely on the reduction of the single-atom Bloch equations to rate equations, which is possible under various experimentally relevant conditions. Here, we explicitly refer to a two-step excitation scheme. We discuss the conditions under which our approach is valid by comparing the results with the solution of the exact quantum master equation for two interacting atoms. Concerning the emergence of an excitation blockade in a Rydberg gas, our results are in qualitative agreement with experiment. Possible sources of quantitative discrepancy are carefully examined. Based on the two-step excitation scheme, we predict the occurrence of an antiblockade effect and propose possible ways to detect this excitation enhancement experimentally in an optical lattice, as well as in the gas phase.
The dipole blockade of Rydberg excitations is a hallmark of the strong interactions between atoms in these high-lying quantum states [M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010); D. Comparat and P. Pillet, J. Opt. Soc. Am. B 27, A208 (2010)]. One of the consequences of the dipole blockade is the suppression of fluctuations in the counting statistics of Rydberg excitations, of which some evidence has been found in previous experiments. Here we present experimental results on the dynamics and the counting statistics of Rydberg excitations of ultracold rubidium atoms both on and off resonance, which exhibit sub- and super-Poissonian counting statistics, respectively. We compare our results with numerical simulations using a novel theoretical model based on Dicke states of Rydberg atoms including dipole-dipole interactions, finding good agreement between experiment and theory.
It is shown that the two-step excitation scheme typically used to create an ultracold Rydberg gas can be described with an effective two-level rate equation, greatly reducing the complexity of the optical Bloch equations. This allows us to efficiently solve the many-body problem of interacting cold atoms with a Monte Carlo technique. Our results reproduce the observed excitation blockade effect. However, we demonstrate that an Autler-Townes double peak structure in the two-step excitation scheme, which occurs for moderate pulse lengths as used in the experiment, can give rise to an antiblockade effect. It is most pronounced for atoms arranged on a lattice. Since the effect is robust against a large number of lattice defects it should be experimentally realizable with an optical lattice created by CO2 lasers.
We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus especially on the review of the dipole–dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing the entanglement of the wave-functions of the atoms and opening a fascinating way for the realization of quantum bits and quantum gates. We consider then several works on the blockade effect in a large assembly of atoms for three different configurations: blockade through electric-field induced dipole, through Förster resonance, and in van der Waals interaction. The properties of coherence and cooperativity are analyzed. Finally, we treat the role of dipole–dipole interactions between Rydberg atoms responsible for Penning ionization. The perturbation of the dipole blockade by ions and the evolution of the Rydberg towards an ultracold plasma are discussed.
We have studied the evolution of Rydberg wave packets in the presence of interatomic dipole-dipole interactions in a frozen Rb gas. Rb atoms in a magneto-optical trap (MOT) are first laser excited to nsnsns Rydberg eigenstates. A picosecond THz pulse further excites them into coherent superposition states involving the initial-level and neighboring npnpnp states. A second, identical, time-delayed THz pulse probes the wave-packet dynamics. As the wave packets evolve they are influenced by dipole-dipole interactions, predominantly pairwise excitation-exchange processes of the form $|s\ensuremath{\rangle}|p\ensuremath{\rangle}\ensuremath{\leftrightarrow}|p\ensuremath{\rangle}|s\ensuremath{\rangle}$. The coherent electronic evolution of the ensemble dephases due to the variation in dipole-dipole coupling strength between atom pairs in the MOT. The experimental results are in good agreement with numerical calculations that simulate the interactions between nearest neighbors in a frozen gas.