Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.

Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.

In the present thesis the dynamics of the correlations between an open quantum system and its environment is investigated. This becomes feasible by means of a very useful representation of the total system-environment state. General conditions for separability and entanglement of the latter are derived, and investigated in the framework of an open quantum two-level system, which is coupled to a dissipative and a dephasing environment.

Diese Arbeit beschäftigt sich mit dem polarisations-, intensitäts- und temperaturabhängigen Dephasierungsverhalten kohärent angeregter Exzitonen, Biexzitonen und Trionen in Quantentrögen, Quantendrähten und Quanteninseln. Die Experimente, die an II-VI-Halbleiternano- strukturen durchgeführt wurden, basieren auf einer nichtlinear optischen Methode der Ultrakurzzeitspektroskopie, der Vierwellenmischung. Phasenrelaxation und Wechselwirkungsprozesse der resonant angeregten Quasiteilchen werden durch erweiterte optische Blochgleichungen theoretisch beschrieben. Um die Bedeutung von Korrelationen höherer Ordnung von Exzitonen in ZnSe Quantentrögen zu ermitteln, wird die Methode der Multiwellenmischung entwickelt. Durch Anwendung von modernen Halbleiterblochgleichungen bis zur 5. Ordnung in den anregenden Feldern gelingt die Beschreibung der beobachteten Spektren. / In this theses the polarization, intensity and temperature dependent dephasing behavior of coherently excited excitons, biexcitons, and trions are investigated in quantum wells, quantum wires and quantum islands. The experiments, applied to II-VI semiconductor nanostructures, base on a nonlinear optical method of ultrashorttime spectroscopy, the four-wave mixing. Phase relaxation and interaction processes of the resonantly excited quasi-particles are described by extended optical bloch equations. The importance of higher order correlations of excitons in ZnSe quantum wells is investigated. Therefore a new method has been developed, the so called multi-wave mixing. The application of modern semiconductor bloch equations up to fifth order in the exciting fields results in a successful description of the observed spectra.

Diese Arbeit beschäftigt sich mit dem polarisations-, intensitäts- und temperaturabhängigen Dephasierungsverhalten kohärent angeregter Exzitonen, Biexzitonen und Trionen in Quantentrögen, Quantendrähten und Quanteninseln. Die Experimente, die an II-VI-Halbleiternano- strukturen durchgeführt wurden, basieren auf einer nichtlinear optischen Methode der Ultrakurzzeitspektroskopie, der Vierwellenmischung. Phasenrelaxation und Wechselwirkungsprozesse der resonant angeregten Quasiteilchen werden durch erweiterte optische Blochgleichungen theoretisch beschrieben. Um die Bedeutung von Korrelationen höherer Ordnung von Exzitonen in ZnSe Quantentrögen zu ermitteln, wird die Methode der Multiwellenmischung entwickelt. Durch Anwendung von modernen Halbleiterblochgleichungen bis zur 5. Ordnung in den anregenden Feldern gelingt die Beschreibung der beobachteten Spektren. / In this theses the polarization, intensity and temperature dependent dephasing behavior of coherently excited excitons, biexcitons, and trions are investigated in quantum wells, quantum wires and quantum islands. The experiments, applied to II-VI semiconductor nanostructures, base on a nonlinear optical method of ultrashorttime spectroscopy, the four-wave mixing. Phase relaxation and interaction processes of the resonantly excited quasi-particles are described by extended optical bloch equations. The importance of higher order correlations of excitons in ZnSe quantum wells is investigated. Therefore a new method has been developed, the so called multi-wave mixing. The application of modern semiconductor bloch equations up to fifth order in the exciting fields results in a successful description of the observed spectra.

In the present thesis the dynamics of the correlations between an open quantum system and its environment is investigated. This becomes feasible by means of a very useful representation of the total system-environment state. General conditions for separability and entanglement of the latter are derived, and investigated in the framework of an open quantum two-level system, which is coupled to a dissipative and a dephasing environment.