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Förster resonances in Rydberg atoms can be used to implement quantum logic gates of a quantum computer via long-range dipole-dipole interaction (DDI). As such gates imply coherent interaction of only two Rydberg atoms [1], or excitation of only one Rydberg atom due to dipole blockade effect [2], a prerequisite for implementing the quantum-information processing is the theoretical and experimental analysis of DDI for a small number of cold Rydberg atoms. Recently we have observed experimentally the Stark-tuned Förster resonance between 2-5 cold rubidium Rydberg atoms [3]. The resonance line shapes were in good agreement with numerical Monte-Carlo simulations. In this report we present the details of our Monte-Carlo simulations and some new theoretical results on DDI dynamics and dipole blockade for several Rydberg atoms. To investigate a particular Förster resonance Rb(37P,J=3/2)+Rb(37P,J=3/2)-->Rb(37S)+Rb(38S), we applied a simplified theoretical model that considered the interactions of 2 to 5 Rydberg atoms in the identical 37P(J=3/2,|M|=1/2) state. The atoms were randomly positioned in a small cubic volume. The time evolution of all possible quasimolecular states was obtained by numerically solving the Schrödinger equation. We accounted for all possible binary resonant interactions, as well as the always-resonant exchange interactions that may broaden the resonance. The initial positions were averaged over 500 random realizations. Calculated spectra for 2-5 atoms interacting for 0.515 microsecond in a cubic volume of 18 microns in size agree with our experimental resonances. The interaction time was chosen to fit the widths of the experimental resonances, while the volume corresponds to the conditions of our experiment. The theoretical spectra highlight several features, which will be discussed in this report. In particular, the ultimate resonance width is limited by the inverse interaction time. New numerical simulations have been done to find the appropriate experimental conditions to observe coherent Rabi-like population oscillations due to Förster resonance between two cold Rydberg atoms. We have shown that the two atoms should be spatially localized with <20% uncertainty for such observations. Finally, we investigated the possibility to observe the dipole blockade effect in a disordered ensemble of several Rydberg atoms. We have found that dipole blockade is observable for our Förster resonance if the mean distance between Rydberg atoms is below 5 microns. This work was supported by RFBR (Grants No. 09-02-90427 and No. 09-02-92428), by Consortium EINSTEIN, by the Russian Academy of Sciences, and by Dynasty Foundation. [1] D.Jaksh et al., Phys. Rev. Lett., 2000, v.85, p.2208. [2] M.D.Lukin et al., Phys. Rev. Lett., 2001, v.87, p.037901. [3] I.I.Ryabtsev et al., Phys. Rev. Lett., 2010, v.104, p.073003. |
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