On the interpretation of wave function overlaps in quantum dots

Søren Stobbe, Jørn Märcher Hvam, Peter Lodahl

    Research output: Contribution to journalJournal articleResearchpeer-review


    The spontaneous emission rate of excitons strongly confined in quantum dots (QDs) is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission rate is proportional to the probability that the electron and the hole are located at the same point or region in space, i.e., they must coincide spatially to recombine. Here, we show that this interpretation is not correct even loosely speaking. By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap integral, and the probability of electrons and holes coinciding, and find that the frequency dependence of the envelope wave function overlap integral is very different from that expected from the common interpretation. We show that these theoretical considerations lead to predictions for measurements. We compare our qualitative predictions with recent measurements of the wave function overlap and find good agreement.
    Original languageEnglish
    JournalIPPS physica status solidi (b)
    Issue number4
    Pages (from-to)855-858
    Publication statusPublished - 2011


    • quantum dots
    • quantum optics
    • semiconductor physics


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