Many-body effects in ultrafast nonlinear spectroscopy

We develop a theory of many-body effects in pump-probe and wave-mixing nonlinear spectroscopies. We focus on the femtosecond dynamics arising from Coulomb and Pauli interactions among optically-excited carriers. We interpret the coherent nonlinear optical response of semiconductors and metals by mapping it onto the linear response of a "dressed" system consisting of two uncoupled bands and characterized by effective optical transition matrix elements, electron/hole dispersions, and interaction potentials. We achieve this for any pulse duration by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. Our theory describes all many-body correlations that contribute to a given order in the optical fields but also treats important interaction effects to infinite order. In addition, it provides a physically-transparent way to interpret such experiments by distinguishing between two different optical nonlinearities, each leading to different dynamics: (i) renormalization of the optical transition matrix elements, and (ii) response of the system to the renormalization of the electron/hole dispersions and interaction potentials.