The density matrix approach has been employed to analyze the pump-probe spe
ctroscopic absorption spectra of small semiconductor nanocrystals popularly
known as quantum dots (QDs) under the strong confinement regime (SCR) with
sizes smaller than the bulk exciton Bohr radius such that the Coulombic in
teraction energy becomes negligible in comparison with the confinement ener
gy. The average time rate of absorption has been obtained by incorporating
the radiative and nonradiative decay processes as well as the inhomogeneous
broadening arising due to nonuniform QD sizes. The analytical results are
obtained for QDs duly irradiated by a strong near-resonant pump and a broad
band weak probe. Numerical estimations have been made for: (i) isolated QDs
and (ii) QD-arrays of GaAs and CdS. The results agree very well with the a
vailable experimental observations in CdS QDs. The results in the case of G
aAs QDs can lead one to experimentally estimate absorption/gain spectra in
the important III-V semiconducting microscopic structures. (C) 2001 Academi
c Press.