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 ϩ ions for distances in the range of about ten wave lengths of the strong transition while no effects were observed for Hg ϩ at 15 wavelengths. In this theoretical paper we study this question for configurations with three and four levels, which model those of Hg ϩ and Ba ϩ , respectively. For two systems in the Hg ϩ 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 ϩ ions, cooperative effects are practically absent, and this latter result is at odds with the experimental findings for Ba ϩ .
Abstract. We investigate the three-dimensional formulation of a recently proposed operational arrival-time model. It is shown that within typical conditions for optical transitions the results of the simple one-dimensional version are generally valid. Differences that may occur are consequences of Doppler and momentum-transfer effects. Ways to minimize these are discussed.
We investigate the effect of the dipole-dipole interaction on the quantum
jump statistics of three atoms. This is done for three-level systems in a V
configuration and in what may be called a D configuration. The transition rates
between the four different intensity periods are calculated in closed form.
Cooperative effects are shown to increase by a factor of 2 compared to two of
either three-level systems. This results in transition rates that are, for
distances of about one wavelength of the strong transition, up to 100% higher
than for independent systems. In addition the double and triple jump rates are
calculated from the transition rates. In this case cooperative effects of up to
170% for distances of about one wavelength and still up to 15% around 10
wavelengths are found. Nevertheless, for the parameters of an experiment with
Hg+ ions the effects are negligible, in agreement with the experimental data.
For three Ba+ ions this seems to indicate that the large cooperative effects
observed experimentally cannot be explained by the dipole-dipole interaction.Comment: 9 pages, 9 figures. Revised version, to be published in PR
A simplified scheme for the investigation of cooperative effects in the quantum jump statistics of small numbers of fluorescing atoms and ions in a trap is presented. It allows the analytic treatment of three dipole-dipole interacting four-level systems which model the relevant level scheme of Ba + ions. For the latter, a huge rate of double and triple jumps was reported in a former experiment and the huge rate was attributed to the dipoledipole interaction. Our theoretical results show that the effect of the dipole-dipole interaction on these rates is at most 5% and that for the parameter values of the experiment there is practically no effect. Consequently it seems that the dipole-dipole interaction can be ruled out as a possible explanation for the huge rates reported in the experiment.
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