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 wavelengths. 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 wavelengths, about 5% around ten wavelengths, 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⁺.