  We develop a theory describing the effects of many-particle Coulomb
correlations on the coherent ultrafast nonlinear optical response of
semiconductors and metals. Our approach is based on a mapping of the nonlinear
optical response of the ``bare'' system onto the linear response of a
``dressed'' system. The latter is characterized by effective time-dependent
optical transition matrix elements, electron/hole dispersions, and interaction
potentials, which in undoped semiconductors are determined by the
single-exciton and two-exciton Green functions in the absence of optical
fields. This mapping is achieved by eliminating the optically-induced charge
fluctuations from the Hamiltonian using a Van Vleck canonical transformation.
It takes into account all many-body contributions up to a given order in the
optical fields as well as important Coulomb-induced quantum dynamics to all
orders in the optical field. Our approach allows us to distinguish between
optical nonlinearities of different origins and provides a physically-intuitive
interpretation of their manifestations in ultrafast coherent nonlinear optical
spectroscopy.
