Cooperative fluorescence effects for dipole-dipole interacting systems with experimentally relevant level configurations

The mutual dipole-dipole interaction of atoms in a trap can affect their fluorescence. Extremely large effects were reported for double jumps between different intensity periods in experiments with two and three Ba^+ ions for distances in the range of about ten wave lengths of the strong transition while no effects were observed for Hg^+ at 15 wave lengths. In this theoretical paper we study this question for configurations with three and four levels which model those of Hg^+ and Ba^+, respectively. For two systems in the Hg^+ configuration we find cooperative effects of up to 30% for distances around one or two wave lengths, about 5% around ten wave lengths, and, for larger distances in agreement with experiments, practically none. This is similar for two V systems. However, for two four-level configurations, which model two Ba^+ ions, cooperative effects are practically absent, and this latter result is at odds with the experimental findings for Ba^+.Comment: 9 pages, 5 figures, RevTeX4, to be published in Phys. Rev.

Random Series and Discrete Path Integral methods: The Levy-Ciesielski implementation

We perform a thorough analysis of the relationship between discrete and series representation path integral methods, which are the main numerical techniques used in connection with the Feynman-Kac formula. First, a new interpretation of the so-called standard discrete path integral methods is derived by direct discretization of the Feynman-Kac formula. Second, we consider a particular random series technique based upon the Levy-Ciesielski representation of the Brownian bridge and analyze its main implementations, namely the primitive, the partial averaging, and the reweighted versions. It is shown that the n=2^k-1 subsequence of each of these methods can also be interpreted as a discrete path integral method with appropriate short-time approximations. We therefore establish a direct connection between the discrete and the random series approaches. In the end, we give sharp estimates on the rates of convergence of the partial averaging and the reweighted Levy-Ciesielski random series approach for sufficiently smooth potentials. The asymptotic rates of convergence are found to be O(1/n^2), in agreement with the rates of convergence of the best standard discrete path integral techniques.Comment: 20 pages, 4 figures; the two equations before Eq. 14 are corrected; other typos are remove

Polaron effective mass

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