Cooperative quantum jumps for three dipole-interacting atoms
Volker Hannstein, Gerhard C. Hegerfeldt · Physical Review A · 2004
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 $\mathsf{V}$ configuration and in what may be called a $\mathsf{D}$ 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 ${\mathrm{Hg}}^{+}$ ions the effects are negligible, in agreement with the experimental data. For three ${\mathrm{Ba}}^{+}$ ions this seems to indicate that the large cooperative effects observed experimentally cannot be explained by the dipole-dipole interaction.