Cooperative quantum jumps for three dipole-interacting atoms

Abstract

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

Simplified approach to double jumps for fluorescing dipole-dipole interacting atoms

“…For p 10 one has to take into account the decays from |s 23 decay rate by the steady state population of the initial level and adding up the different contributions then yields the same results for the transition rates as obtained by the Bloch equation approach in reference [20]. The same is also true for three dipole-interacting D systems [22].…”

“…The quasi-steady states are already known from the calculations for three three-level systems. As in reference [22] one can use a symmetrized basis analoguous to the Dicke basis for two atoms. This leads to the states |s ijk = 1 √ 6 |i |j |k + |j |k |i + |k |i |j + |i |k |j + |j |i |k + |k |j |i , (24a) |b ijj = 1 √ 6 2|i |j |j − |j |j |i − |j |i |j (25b)…”

“…The dimensionless parameter a (j) kl = 2πr kl /λ j is given by the inter-atomic distance r kl multiplied by the wave number 2π/λ j of this transition. In order to get a maximal effect of the dipole-dipole interaction we assume as in [22] that the atoms form an equilateral triangle (i.e. r kl = r) and that…”

“…This process is characterized by the transition rates between the different intensity periods. In references [18,20,22] they were calculated for different model level systems and different numbers of atoms using a perturbation approach based on the Bloch equation of the corresponding systems. This approach will be illustrated in the following by applying it to the simple case of a single three level system in a D-type configuration as depicted in figure 2.…”

“…Although this result contradicts the findings of references [3,4] a direct quantitative comparison with the experiments was not possible since explicit experimental data were only provided for three Ba + ions. For this reason three of the D and V systems were investigated in reference [22]. In comparison to two of either systems the cooperative effects found in this case are considerably higher, namely up to 170% deviation from the case of independent atoms.…”