  We have simulated the time evolution of the photon number distribution in a
semiconductor quantum dot-microcavity system driven by chirped laser pulses and
compare with unchirped results. When phonon interactions with the dot are
disregarded - thus corresponding to the limit of atomic cavity systems -
chirped pulses generate photon number distributions that change their shape
drastically in the course of time. Phonons have a strong and qualitative impact
on the photon statistics. The asymmetry between phonon absorption and emission
destroys the symmetry of the photon distributions obtained for positive and
negative chirps. While for negative chirps transient distributions resembling
thermal ones are observed, for positive chirps the photon number distribution
still resembles its phonon-free counterpart but with overall smoother shapes.
In sharp contrast, using unchirped pulses of the same pulse area and duration
wave-packets are found that move up and down the Jaynes-Cummings ladder with a
bell-shape that changes little in time. For shorter pulses and lower driving
strength Rabi-like oscillations occur between low photon number states. For all
considered excitation conditions transitions between sub- and super-Poissonian
statistics are found at certain times. For resonant driving with low intensity
the Mandel parameter oscillates and is mostly negative, which indicates a
non-classical state in the cavity field. Finally, we show that it is possible
that the Mandel parameter dynamically approaches zero and still the photon
distribution exhibits two maxima and thus is far from being a Poissonian.
