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The stream of photons emitted by a single quantum system such as a molecule or a nanocrystal is often statistically characterized by the distribution of delays between consecutive photons, or by the autocorrelation function of the intensity, or by the distributions of on- and off-times. We derive and discuss general relations between their Laplace transforms, addressing the influence of detection yield and background. Our analytical treatment applies to any distribution of delays and to random telegraph signals, including nonexponential distributions. We examine the special case of systems switching between two states characterized by different distributions of delays, where the switching can obey various statistics. We show that the second-order autocorrelation function keeps track of long-time fluctuations which are obviously lost in averaging the distributions of delays. We apply our formalism to random telegraphs, in particular to those with power-law distributions of on- and/or of off-times, which are encountered in the blinking of single semiconductor nanocrystals.

A study is presented of the orientation of single 2.3, 8.9-dibenzanthanthrene molecules in n-tetradecane as a function of their spatial position on a length scale of 2 mm down to a few hundreds of nanometers at 1.4 K, which allows us to obtain structural information about this host/guest system. In the confocal detection volume of ∼10 µm 3 the guest molecules show two preferential orientations. A broad distribution of orientations of about (17˚is observed around these two mean orientations. The mean orientations exhibit long-range order even over a distance of 2 mm with gradual variations on a micrometer scale. Over distances smaller than the lateral dimension of the confocal detection volume these variations disappear almost completely whereas the widths of the distributions remain qualitatively the same. The results do not point to the presence of a polycrystalline structure which contradicts the common picture of Shpol'skii systems.