A theoretical investigation is presented of the statistics of excitons in
quantum dots (QDs) of different sizes. A formalism is developed to build the
exciton creation operator in a dot from the single exciton wavefunction and it
is shown how this operator evolves from purely fermionic, in case of a small
QD, to purely bosonic, in case of large QDs. Nonlinear optical emission spectra
of semiconductor microcavities containing single QDs are found to exhibit a
peculiar multiplet structure which reduces to Mollow triplet and Rabi doublet
in fermionic and bosonic limits, respectively.Comment: Extensively expanded revision, 14 pages, 12 figures, submitted to
Phys. Rev.