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arXiv:quant-ph/9903034 · Physical Review A

Cooperative effects in the light and dark periods of two dipole-interacting atoms

Almut Beige, Gerhard C. Hegerfeldt

Published Mar 1, 1999• 32 citations
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Abstract

If an atom is able to exhibit macroscopic dark periods, or electron shelving, then a driven system of two atoms has three types of fluorescence periods (dark, single, and double intensity). We propose to use the average durations of these fluorescence types as a simple and easily accessible indicator of cooperative effects. As an example, we study two dipole-interacting V systems by simulation techniques. We show that the durations of the two types of light periods exhibit marked separation-dependent oscillations and that they vary in phase with the real part of the dipole-dipole coupling constant.

DOI
10.1103/physreva.59.2385

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If an atom is able to exhibit macroscopic dark periods, or electron shelving, then a driven system of two atoms has three types of fluorescence periods (dark, single, and double intensity). We propose to use the average durations of these fluorescence types as a simple and easily accessible indicator of cooperative effects. As an example, we study two dipole-interacting V systems by simulation techniques. We show that the durations of the two types of light periods exhibit marked separation-dependent oscillations and that they vary in phase with the real part of the dipole-dipole coupling constant.
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+.
The control and manipulation of the atomic translational and internal degrees of freedom via atom-laser interaction is an essential tool in modern quantum optical experiments which allows for a large variety of applications. The present work is concerned with theoretical investigations which may shed some light on certain experiments in this field.In the first part of this work, cooperative effects in the fluorescence of dipole-dipole interacting atoms in a trap are studied. The famous macroscopic quantum jumps can occur for a single atom with a metastable state when illuminated by light. Then periods of fluorescence of fixed intensity alternate stochastically with dark periods. If one has two or three such atoms in a trap, there are dark periods and periods of single and multiple intensity, from overlap. The statistics of these periods is influenced by the dipole-dipole interaction between the atoms in a sensitive manner. This work is concerned with a theoretical description of these effects, including a discussion of the seemingly contradictory experimental results which have been obtained in this context. The main result indicates that the huge rate of double and triple jumps reported for three trapped Ba+ ions can in fact not be attributed to the dipole-dipole interaction.In the second part, the possible use of an evanescent wave atomic mirror as a measuring device for the properties of an atomic wave packet is investigated. The idea is taken from an experiment, in which such a mirror was used for the temporal diffraction of a cloud of laser cooled atoms dropping out of a magneto-optical trap. A model for the investigation of the atomic wave function with such a mirror is given, and the outcomes of different set-ups are investigated. The main result shows that with such a mirror one can sample the mod-squared of a spread-out wave function, and this opens the way for a realistic possibility for measuring this otherwise not easily accessible quantity.
The temporal behavior of a single quantum system may contain information, for instance, about macroscopic dark periods in electron shelving, which is washed out or even lost in ensemble averages. The same is true in principle for spectral information. For example, for an atom with light and dark periods one might try to spectrally analyze the light emitted in a light period of given length or, more generally, the light emitted into one solid angle while monitoring the temporal emission in another solid angle. Considering different emission behaviors one may get different spectra, i.e., spectra that are dependent on the conditions imposed. In this paper, such questions, in particular the notion of spectrum in a light period, are studied. To this end we generalize the recent quantum jump approach to include resonance-fluorescence spectra of single atoms. We explicitly show that the theory developed in this paper easily generalizes, e.g., to absorption spectra. We apply the theory to a V system that has one metastable level and that may exhibit intermittent fluorescence when driven by two lasers. We show that the spectrum of resonance fluorescence of the complete ensemble differs substantially from that observed in a light period. A physical explanation of this behavior is presented. \textcopyright{} 1996 The American Physical Society.
The well-known three-level system of Dehmelt [Bull. Am. Phys. Soc. 20, 60 (1975)] exhibits macroscopic dark periods because one of the upper levels is metastable. In this paper we show that one can also have the same phenomenon for a three-level-atom system with both upper states rapidly decaying to the ground state, provided (a) their level separation is very small and (b) their dipole moments for the ground-state transition are parallel. For suitably chosen laser parameters we also exhibit an exact nonradiating solution of the complete time development for atom plus radiation field. This leads to the surprising effect that the atom, after emission of a number of photons, will stop to fluoresce although still irradiated by the laser. The mean number of photons emitted before this switching off of the atom is calculated, as well as the mean duration of the dark periods for the general case.
The intensity correlation function of lquotlquotlquotblinkingrquotrquotrquot quantum systems
Explicit expressions are determined for the photon correlation function of ``blinking'' quantum systems, i.e. systems with different types of fluorescent periods. These expressions can be used for a fit to experimental data and for obtaining system parameters therefrom. For two dipole-dipole interacting VVV systems the dependence on the dipole coupling constant is explicitly given and shown to be particularly pronounced if the strong driving is reduced. We propose to use this for an experimental verification of the dipole-dipole interaction.