  A detailed understanding of the population and coherence dynamics in
optically driven individual emitters in solids and their signatures in
ultrafast nonlinear-optical signals is of prime importance for their
applications in future quantum and optical technologies. In a combined
experimental and theoretical study on exciton complexes in single semiconductor
quantum dots we reveal a detailed picture of the dynamics employing three-beam
polarization-resolved four-wave mixing (FWM) micro-spectroscopy. The
oscillatory dynamics of the FWM signals in the exciton-biexciton system is
governed by the fine-structure splitting and the biexciton binding energy in an
excellent quantitative agreement between measurement and analytical
description. The analysis of the excitation conditions exhibits a dependence of
the dynamics on the specific choice of polarization configuration, pulse areas
and temporal ordering of driving fields. The interplay between the transitions
in the four-level exciton system leads to rich evolution of coherence and
population. Using two-dimensional FWM spectroscopy we elucidate the
exciton-biexciton coupling and identify neutral and charged exciton complexes
in a single quantum dot. Our investigations thus clearly reveal that FWM
spectroscopy is a powerful tool to characterize spectral and dynamical
properties of single quantum structures.
