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Physical Review Letters

Cooperative quantum jumps with two atoms

Maciej Lewenstein, Juha Javanainen

Published Sep 21, 1987• 32 citations
Publisher

Abstract

Quantum jumps in the fluorescence from two three-level atoms may display cooperative effects, such as unusual intensity levels and transitions from a state with both atoms radiating directly to darkness. However, to see these experimentally, the atoms have to be well within a wavelength of light.
DOI
10.1103/physrevlett.59.1289

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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\mathsf{V}V configuration and in what may be called a D\mathsf{D}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+{\mathrm{Hg}}^{+}Hg+ ions the effects are negligible, in agreement with the experimental data. For three Ba+{\mathrm{Ba}}^{+}Ba+ ions this seems to indicate that the large cooperative effects observed experimentally cannot be explained by the dipole-dipole interaction.
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+{\mathrm{Ba}}^{+}Ba+ ions for distances in the range of about ten wave lengths of the strong transition while no effects were observed for Hg+{\mathrm{Hg}}^{+}Hg+ at 15 wavelengths. In this theoretical paper we study this question for configurations with three and four levels, which model those of Hg+{\mathrm{Hg}}^{+}Hg+ and Ba+,{\mathrm{Ba}}^{+},Ba+, respectively. For two systems in the Hg+{\mathrm{Hg}}^{+}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+{\mathrm{Ba}}^{+}Ba+ ions, cooperative effects are practically absent, and this latter result is at odds with the experimental findings for Ba+.{\mathrm{Ba}}^{+}.Ba+.