Canonical Transformation Approach to the Ultrafast Non–linear Optical Dynamics of Semiconductors

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. Typeset using REVTEX