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IEEE Journal of Quantum Electronics

Quantum jump statistics for two-atom systems

Maciej Lewenstein

Published Jul 1, 1988• 17 citations
Publisher

Abstract

The quantum jump statistics in the fluorescence intensity from two three-level atoms is studied. A rate-equation description valid for strong driving fields is derived, and a partial analysis of quantum jump statistics which goes beyond the strong-excitation limit is presented. As the main result, it is shown that collective effects, such as unusual intensity levels and double quantum jumps, can occur in two-atom systems. However, their observation requires that the atoms be localized within a wavelength of light.>

DOI
10.1109/3.980

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The quantum jump statistics in the fluorescence intensity from two three-level atoms is studied. A rate-equation description valid for strong driving fields is derived, and a partial analysis of quantum jump statistics which goes beyond the strong-excitation limit is presented. As the main result, it is shown that collective effects, such as unusual intensity levels and double quantum jumps, can occur in two-atom systems. However, their observation requires that the atoms be localized within a wavelength of light.>
We study analytically the effect of the dipole-dipole interaction on the statistics of the fluorescent radiation emitted from a system of two two-level atoms resonantly driven by a coherent field. For some interatomic separations, an inhibition of fluorescence occurs, which is reminiscent of the recently discussed quantum-jump phenomenon in a single three-level atom. This is reflected in the behaviors of the intensity correlation function, Mandel's Q parameter, and the time-dependent fluorescence spectrum. It is argued that this quantum-jump-like behavior arises from the coupling between the symmetric states and the antisymmetric state caused by the dipole-dipole interaction.
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.
Complete density-matrix equations and a one-photon counting probability are used to examine the photon statistics of fluorescence light of a single three-level atom, weakly coupled to an external cavity of low QQQ value. The internal structure of the atom is supposed to be characterized by a weak and a strong transition. The strong transition is coherently driven by an external laser field, whereas no external field is acting on the weak transition. In free space the system exhibits quantum jumps. By placing the atom within the mirrors of an external cavity, tuned close to the transition frequency of the two upper levels, modifications in the quantum jump behavior of the atom are shown due to a modified spontaneous decay rate between the two states. In particular, it is demonstrated that the effect of the cavity is to modify the repetition rate of quantum jumps into the metastable dark state and the average duration of bright periods of fluorescence, whereas the average duration of dark periods is not changed in first order of the spontaneous decay rates involved. In view of current experiments in our laboratory a quantitative analysis is presented for the special case of a single indium ion located between the mirrors of a high-order symmetric confocal cavity.
We analyze the macroscopic quantum jumps (sudden interruptions in the fluorescence on a macroscopic time scale) that are produced when a pair of two-level atoms separated by a distance d is irradiated by a strong laser having wavelength ${\ensuremath{\lambda}}_{0}$, with ${\ensuremath{\lambda}}_{0}$\ensuremath{\gg}d. Included in the analysis is the dipole-dipole coupling of the atoms, the ac Stark effect, and the role played by a term that is present in the atom-laser field interaction Hamiltonian when k\ensuremath{\cdot}d\ensuremath{\ne}0 (k is the wave vector of the laser field and d is the vector connecting the two atoms). Our treatment is based on frequency-resolved delay functions, an extension of a concept developed by Reynaud, Dalibard, and Cohen-Tannoudji [IEEE J. Quantum Electron. 24, 1395 (1988)], which is shown to be useful to study frequency-resolved photon statistics. As examples, we study the statistics of the fluorescence produced by the two-atom system as well as those in the components of the fluorescent triplet produced by a single two-level atom.
We consider the effect of dipole-dipole interaction on the quantum jumps in a system of two three-level atoms in a ssV configuration interacting with coherent fields. We show that the intensity-intensity correlation for the strong transition shows additional fluctuations for some interatomic separations between the atoms signifying three levels of fluorescence. It is argued that the intermediate level of fluorescence arises from the coupling between the symmetric and antisymmetric states caused by the dipole-dipole interaction.