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 Physics , 2007, DOI: 10.1103/PhysRevLett.99.073002 Abstract: High resolution laser Stark excitation of np (60 < n < 85) Rydberg states of ultra-cold 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 eventual 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 indicates a major role of the nearest neighboring Rydberg atom.
 Physics , 2010, DOI: 10.1103/PhysRevA.82.053409 Abstract: Results of numerical Monte Carlo simulations for the Stark-tuned F\"orster resonance and dipole blockade between two to five cold rubidium Rydberg atoms in various spatial configurations are presented. The effects of the atoms' spatial uncertainties on the resonance amplitude and spectra are investigated. The feasibility of observing coherent Rabi-like population oscillations at a F\"orster resonance between two cold Rydberg atoms is analyzed. Spectra and the fidelity of the Rydberg dipole blockade are calculated for various experimental conditions, including nonzero detuning from the F\"orster resonance and finite laser linewidth. The results are discussed in the context of quantum-information processing with Rydberg atoms.
 Physics , 2001, Abstract: We show that the interaction between Rydberg atomic states can provide continuous spin squeezing of atoms with two ground states. The interaction prevents the simultaneous excitation of more than a single atom in the sample to the Rydberg state, and we propose to utilize this blockade effect to realize an effective collective spin hamiltonian J_x^2-J_y^2. With this hamiltonian the quantum mechanical uncertainty of the spin variable J_x+J_y can be reduced significantly.
 Physics , 2013, Abstract: Recent developments in the study of ultracold Rydberg gases demand an advanced level of experimental sophistication, in which high atomic and optical densities must be combined with excellent control of external fields and sensitive Rydberg atom detection. We describe a tailored experimental system used to produce and study Rydberg-interacting atoms excited from dense ultracold atomic gases. The experiment has been optimized for fast duty cycles using a high flux cold atom source and a three beam optical dipole trap. The latter enables tuning of the atomic density and temperature over several orders of magnitude, all the way to the Bose-Einstein condensation transition. An electrode structure surrounding the atoms allows for precise control over electric fields and single-particle sensitive field ionization detection of Rydberg atoms. We review two experiments which highlight the influence of strong Rydberg--Rydberg interactions on different many-body systems. First, the Rydberg blockade effect is used to pre-structure an atomic gas prior to its spontaneous evolution into an ultracold plasma. Second, hybrid states of photons and atoms called dark-state polaritons are studied. By looking at the statistical distribution of Rydberg excited atoms we reveal correlations between dark-state polaritons. These experiments will ultimately provide a deeper understanding of many-body phenomena in strongly-interacting regimes, including the study of strongly-coupled plasmas and interfaces between atoms and light at the quantum level.
 Physics , 2012, Abstract: Over the past few years we have built an apparatus to demonstrate the entanglement of neutral Rb atoms at optically resolvable distances using the strong interactions between Rydberg atoms. Here we review the basic physics involved in this process: loading of single atoms into individual traps, state initialization, state readout, single atom rotations, blockade-mediated manipulation of Rydberg atoms, and demonstration of entanglement.
 Physics , 2009, Abstract: We report on our recent progress on the manipulation of single rubidium atoms trapped in optical tweezers and the generation of entanglement between two atoms, each individually trapped in neighboring tweezers. To create an entangled state of two atoms in their ground states, we make use of the Rydberg blockade mechanism. The degree of entanglement is measured using global rotations of the internal states of both atoms. Such internal state rotations on a single atom are demonstrated with a high fidelity.
 Physics , 2008, DOI: 10.1038/nphys1183 Abstract: The dipole blockade between Rydberg atoms has been proposed as a basic tool in quantum information processing with neutral atoms. Here we demonstrate experimentally the Rydberg blockade of two individual atoms separated by 4 $\mu$m. Moreover, we show that, in this regime, the single atom excitation is enhanced by a collective two-atom behavior associated with the excitation of an entangled state. This observation is a crucial step towards the deterministic manipulation of entanglement of two or more atoms using the Rydberg dipole interaction.
 Physics , 2010, DOI: 10.1364/JOSAB.27.00A208 Abstract: We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus more specially the review on 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 F\"orster 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.
 Physics , 2009, DOI: 10.1016/j.physrep.2009.10.001 Abstract: Cold Rydberg atoms exposed to strong magnetic fields possess unique properties which open the pathway for an intriguing many-body dynamics taking place in Rydberg gases consisting of either matter or anti-matter systems. We review both the foundations and recent developments of the field in the cold and ultracold regime where trapping and cooling of Rydberg atoms have become possible. Exotic states of moving Rydberg atoms such as giant dipole states are discussed in detail, including their formation mechanisms in a strongly magnetized cold plasma. Inhomogeneous field configurations influence the electronic structure of Rydberg atoms, and we describe the utility of corresponding effects for achieving tightly trapped ultracold Rydberg atoms. We review recent work on large, extended cold Rydberg gases in magnetic fields and their formation in strongly magnetized ultracold plasmas through collisional recombination. Implications of these results for current antihydrogen production experiments are pointed out, and techniques for trapping and cooling of such atoms are investigated.
 Physics , 2009, DOI: 10.1103/PhysRevLett.104.010502 Abstract: We report the generation of entanglement between two individual $^{87}$Rb atoms in hyperfine ground states $|F=1,M=1>$ and $|F=2,M=2>$ which are held in two optical tweezers separated by 4 $\mu$m. Our scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. The entangled state is generated in about 200 ns using pulsed two-photon excitation. We quantify the entanglement by applying global Raman rotations on both atoms. We measure that 61% of the initial pairs of atoms are still present at the end of the entangling sequence. These pairs are in the target entangled state with a fidelity of 0.75.
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