We present an experimental and theoretical study of the polarized photoluminescence spectrum of single semiconductor quantum dots in various charge states. We compare our high resolution polarization sensitive spectral measurements with a new many-carrier theoretical model, which was developed for this purpose. The model considers both the isotropic and anisotropic exchange interactions between all participating electron-hole pairs. With this addition, we calculate both the energies and polarizations of all optical transitions between collective, quantum dot confined charge carrier states. We succeed in identifying most of the measured spectral lines. In particular, the lines resulting from singly-, doubly- and triply- negatively charged excitons and biexcitons. We demonstrate that lines emanating from evenly charged states are linearly polarized. Their polarization direction does not necessarily coincide with the traditional crystallographic direction. It depends on the shells of the single carriers, which participate in the recombination process.
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