We applied low temperature diffraction limited confocal optical microscopy to spatially resolve, and spectroscopically study photoluminescence from single self-assembled semiconductor quantum dots. Using selective wavelength imaging we unambiguously demonstrated that a single photoexcited quantum dot emits light in a few very narrow spectral lines. By solving numerically a many body Hamiltonian for a model quantum dot, we show that the multi-line emission spectrum is due to optical transitons between confined exciton multiplexes. We explain the measured spectrum and its dependence on the power of either cw or pulsed excitation by analytically solving the coupled rate equations for the excitation relaxation between these exciton multiplexes.
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