Distance Dependence of Entanglement Generation via a Bosonic Environment

The search for methods to create and maintain entanglement has led to the idea of environmentally induced entanglement. Roughly speaking, the usually detrimental effect of coupling a non-interacting bipartite system to an environment is turned into an advantage by using the environment to mediate an indirect interaction, which can result in entanglement of the two parts of the system under certain conditions. Of course, care has to be taken to properly evaluate the conflicting influences of the environment. Only if the indirect interaction overcompensates for the decoherence, entanglement creation can be expected. It has been suggested that entanglement creation can be achieved in bosonic heat baths even over finite spatial separations with only a moderate polynomial decay of entanglement with distance. In this work, we look more closely at the distance dependence, for the first time employing an oscillator model that is both exactly solvable and includes dissipation. We numerically prove that entanglement creation is, in fact, extremely distance-sensitive and it is not possible to entangle objects which are further apart than approximately their own size. Additionally, we suggest an approach how to mitigate the distance dependence. It comes at the cost of geometrically modifying the bath modes by imposing physical boundary conditions resulting in a gap in the spectrum. This is implemented by placing the system inside of an infinitely long superconducting cavity. An experimental implementation of this could be feasible

The Impact of Decoherence and Dissipation on Cosmological Systems and on the Generation of Entanglement

The physics of open quantum systems, and therefore the phenomenon of decoherence, has become important in many branches of research. Within this thesis, we investigate the system--environment interaction in the context of different problems. The influence of decoherence is ubiquitous and, due to the scale independence of quantum theory, not limited to microscopic systems. One of the great open problems in theoretical physics is the appearance of a cosmological constant which differs by many orders of magnitude from the theoretical predicted value. In the first part of this thesis we will address this question within the framework of quantum mechanics. The considerations are based on a quantum mechanical model which explains the value of the cosmological constant without introducing extremely small numbers. Decoherence, based on the uncontrollable entanglement with the environment, can explain the localization of the vacuum energy to the classical observed value. The model mentioned above allows, in principle, the tunneling into a universe with a different vacuum energy. We investigate the modification of the tunneling rate due to dissipative effects which follow from the system--bath interaction. Closely related to the cosmological constant problem and subject of the second part of this thesis is the spontaneous decay of a quantum field vacuum. Using a semiclassical approximation it is possible to investigate this process within the framework of the path integral formalism. We discuss the quantum--to--classical transition of the spontaneously nucleated vacuum bubbles. Furthermore, we investigate the dependence of the decay rate on the space-time backgrounds. The third part of this thesis is dedicated to the interaction between quantum systems and their environment in a different context. We investigate the generation of entanglement between two systems which are interacting indirectly with each other through the coupling to a heat bath. The interaction--induced entanglement will be destroyed rapidly through decoherence and dissipation. We will show that it is possible to generate a significant amount of entanglement by imposing certain boundary conditions to the bath. Furthermore, the dependence of the entanglement generation on the spatial separation of the systems will be analyzed. Specifically we will examine the bathinduced entanglement of oscillators and spins