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Decoherence is central to our understanding of the transition from the quantum to the classical world. It is also a way of probing the dynamics of interacting many-body systems. Photoexcited semiconductors are such systems in which the transient dynamics can be studied in considerable detail experimentally. Recent advances in spectroscopy of semiconductors provide powerful tools to explore many-body physics in new regimes. An appropriate theoretical framework is necessary to describe new physical effects now accessible for observation. We present a possible approach in this thesis, and discuss results of its application to an experimentally relevant scenario. The major portion of this thesis is devoted to a formalism for the multi-dimensional Fourier spectroscopy of semiconductors. A perturbative treatment of the electromagnetic field is used to derive a closed set of differential equations for the multi-particle correlation functions, which take into account the many-body effects up to third order in the field. A diagrammatic method is developed, in which we retain all features of the double-sided Feynman diagrams for bookkeeping the excitation scenario, and complement them by allowing for the description of interactions. We apply the formalism to study decoherence between the states of optically excited excitons embedded in an electron gas, and compare it with the decoherence between these states and the ground state. We derive a dynamical equation for the two-time correlation functions of excitons, and compare it with the corresponding equation for the interband polarization. It is argued, and verified by numerical calculation, that the decay of Raman coherence depends sensitively on how differently the superimposed exciton states interact with the electron gas, and that it can be much slower than the decay of interband polarization. We also present a new numerical approach based on the length gauge for modeling the time-dependent laser-semiconductor interaction. The interaction in the length gauge involves the position operator for electrons, as opposed to the momentum operator in the velocity gauge. The approach is free of the unphysical divergences that arise in the velocity gauge. It is invariant under local gauge symmetry of the Bloch functions, and can handle arbitrary electronic structure and temporal dependence of the fields.

Decoherence is central to our understanding of the transition from the quantum to the classical world. It is also a way of probing the dynamics of interacting many-body systems. Photoexcited semiconductors are such systems in which the transient dynamics can be studied in considerable detail experimentally. Recent advances in spectroscopy of semiconductors provide powerful tools to explore many-body physics in new regimes. An appropriate theoretical framework is necessary to describe new physical effects now accessible for observation. We present a possible approach in this thesis, and discuss results of its application to an experimentally relevant scenario. The major portion of this thesis is devoted to a formalism for the multi-dimensional Fourier spectroscopy of semiconductors. A perturbative treatment of the electromagnetic field is used to derive a closed set of differential equations for the multi-particle correlation functions, which take into account the many-body effects up to third order in the field. A diagrammatic method is developed, in which we retain all features of the double-sided Feynman diagrams for bookkeeping the excitation scenario, and complement them by allowing for the description of interactions. We apply the formalism to study decoherence between the states of optically excited excitons embedded in an electron gas, and compare it with the decoherence between these states and the ground state. We derive a dynamical equation for the two-time correlation functions of excitons, and compare it with the corresponding equation for the interband polarization. It is argued, and verified by numerical calculation, that the decay of Raman coherence depends sensitively on how differently the superimposed exciton states interact with the electron gas, and that it can be much slower than the decay of interband polarization. We also present a new numerical approach based on the length gauge for modeling the time-dependent laser-semiconductor interaction. The interaction in the length gauge involves the position operator for electrons, as opposed to the momentum operator in the velocity gauge. The approach is free of the unphysical divergences that arise in the velocity gauge. It is invariant under local gauge symmetry of the Bloch functions, and can handle arbitrary electronic structure and temporal dependence of the fields.