The spectra of the diffracted wave in femtosecond-four-wave mixing and their dependence on the polarization of the driving fields are shown to be a very sensitive probe for the fundamental scattering processes that govern the coherent dynamics in a semiconductor. We demonstrate that the total dephasing rate is the result of a delicate balance between self-energies and vertex corrections. Particle interactions of the polarization scattering type are shown to be important contributions to the nonlinear optical response in the coherent regime. The coherent dynamics of optical excitations in semiconductors is dominated by many-body effects. A number of studies employing transient four-wave mixing (FWM) demonstrated that a basic quantum-mechanical effect, i.e. , the Fock exchange between carriers, governs the coherent evolution of the excitation. ' This level of description, however, completely fails to explain the dependence of the FWM signal on the polarization of the driving fields, which has been subject to intense research only recently. For the case of resonant excitation of the exciton, different signal strengths, ' different decay times, and different temporal signatures have been observed for identical and orthogonal polarization of the two incident beams, respectively.Reference 9 has associated the different decay times to a spatially inhomogeneous coupling between different spin states originating from disorder in quantum-well samples. For ideal semiconductors the excitation-induced dephasing, ' which is based on excitonic screening, is able to explain the different signal strengths. In this case the polarization dependence is due to the fact that the direct Coulomb-scattering contributions vanish for orthogonal linear polarization, where only the contributions of exchange type remain. A consistent many-body treatment of resonant excitation of the exciton including vertex corrections and corresponding exchange contributions in addition to the excitonically screened Hartree-Fock self-energy has been formulated only for the quasiequilibrium limit, " however, is out of reach in the coherent regime.In this paper experimental data for excitation within the continuum of states are presented. For this case a consistent theoretical description based on carrier-carrier scattering can be worked out. We demonstrate that the polarization dependence of the FWM spectra reflects the different types of many-body processes in a very distinct way.In the experiment we employ a self-diffraction geometry of transient FWM using transform-limited, tunable, Gaussian optical pulses of 140-fs duration. Spectra of the diffracted wave are taken as a function of time de-lay between the two incident pulses. The spectral resolution is about 1 meV. We excite in the low density limit (total carrier density = 10' cm ) in order to be within the third-order perturbation regime. More details of the experimental setup can be found in Ref. 6. The two incident beams with wave vectors q& and q2, respectively, are linearly polarized either parallel...
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