  Influence of the self-phase modulation of quantum light on the induced
resonant excitation of a semiconductor quantum dot is studied analytically in
the case of the Kerr-nonlinearity of the medium. The phase nonlinearity is
found to result actually in a resonance detuning specific for each field photon
number state. This effect is shown to provide significant decrease of the
excitation efficiency accompanied at the same time by more regular excitation
dynamics obtained even for initial squeezed vacuum field state. The enhancement
of entanglement between semiconductor and field subsystems with growing
non-linearity is demonstrated. As a result, the formation of different types of
non-Gaussian field states is found with features being analyzed in details.
