Quantenstochastische Resonanz in atomaren Quantenpunkten (English shop)

Preview

Table of Contents, Datei (57 KB)
Extract, Datei (140 KB)

The ongoing advances in the ability to influence and control systems at the atomic level open up new possibilities for experimentally illuminating fundamental questions and models of open quantum systems. In this work, the dynamics of atomic quantum dots embedded in a quasi-one-dimensional Bose–Einstein condensate is described. The system dynamics is mapped onto the driven spin–boson model. On this basis it is shown that the proposed experiment allows, for the first time, the observation of a quantum stochastic resonance phenomenon. The first chapter provides an introductory summary of the theory of open quantum systems.

Starting from the classical Langevin equation with Ohmic and frequency-dependent damping, the quantum-mechanical influence functional method of Feynman and Vernon is subsequently addressed for both special and general initial conditions. Following this, and with a view to the experiment to be described and its translation into a formal theoretical model, the spin–boson model is treated. In this context, the experimentally relevant aspect of the initial preparation of the states and its integration into the theoretical models is also examined. The formally exact solution of the system dynamics is presented, and from it the expressions for the conditional propagation functions, the expectation values as well as the correlations and response functions of the populations and coherences are derived. By comparison with the generally valid exact quantum master equation, the irreducible kernels of the system dynamics can be identified self-consistently. Building on this, the extensions and modifications required for the description of a driven spin–boson model are presented. Finally, the system dynamics in the driven case is discussed in the limiting cases of the Markovian and the high-frequency regime. The following chapter presents an experiment in which atomic quantum dots are embedded in a Bose–Einstein condensate and which allows the observation of specific phenomena of a driven spin–boson model. First, the experimental setup and its theoretical description are laid out. Possible potential landscapes for the realisation of one or several atomic quantum dots as well as their advantages and disadvantages are discussed. Subsequently, the theories required to describe the experimentally manipulated systems are briefly outlined. These include the theory of the interaction between atoms and coherent light fields, the physics of Bose–Einstein condensation, the Bose–Hubbard model, collision processes as well as Raman coupling, and finally the Luttinger liquid model for describing low-energy excitations in one-dimensional systems. The transformations of the previously established theoretical descriptions onto the spin–boson model, as well as their range of validity, are set out in detail in the third chapter. As preparatory work, the hydrodynamic Hamiltonian of the Luttinger liquid model is diagonalised and an effective description is derived for the population of the quantum dots as well as their interaction with condensate atoms via collision processes and induced transitions. The effective description now available is then explicitly mapped onto the spin–boson model by means of a unitary transformation. The experimental quantities can thereupon be assigned to the basic quantities of the spin–boson model, such as the bias parameter and the tunnelling matrix element Δ. Finally, the damping parameter α is identified and the possibilities offered by the experiment for varying its value are investigated. The fourth chapter is divided into two parts: in the first part, starting from the theory of a driven spin–boson model presented in the first chapter, the phenomenon of quantum stochastic resonance is investigated. The dynamics is considered in various limiting cases and the approximation methods of the corresponding approximate descriptions, among them the NIBA, are explained. These make it possible to capture the dynamics by means of numerical simulations. In the data thus obtained, the signatures of quantum stochastic resonance can be traced, thereby substantiating the theoretical statements made. In the second part, the insights previously gained are transferred to the experiment presented in the second chapter. It is analysed in detail in which region of the parameter space prescribed by the experiment the various aspects of quantum stochastic resonance are observable. These considerations are supported by simulations using the parameters prescribed by the experiment. The results are interpreted and summarised in the fifth chapter. Further questions that could thematically follow on from this work are discussed. The appendix contains a brief overview of the theories of path integrals and of the Kubo formalism.