  We present results on both the intensity and phase-dynamics of the transient
non-linear optical response of a single quantum dot (SQD).
  The time evolution of the Four Wave Mixing (FWM) signal on a subpicosecond
time scale is dominated by biexciton effects. In particular, for the
cross-polarized excitation case a biexciton bound state is found. In this
latter case, mean-field results are shown to give a poor description of the
non-linear optical signal at small times. By properly treating exciton-exciton
effects in a SQD, coherent oscillations in the FWM signal are clearly
demonstrated. These oscillations, with a period corresponding to the inverse of
the biexciton binding energy, are correlated with the phase dynamics of the
system's polarization giving clear signatures of non-Markovian effects in the
ultrafast regime.
