Research On The Theory Of Landau-Zener Tunneling Effect

Landau-Zener tunneling between energy levels is an important quantum phenomenon. It describes the quantum tunneling between adjacent levels in a system driven by an outer field. This tunneling effect exists in a variety of systems, such as chemical systems, nuclear systems and spin systems. This thesis describes the basic model of the linear Landau-Zener tunneling effect as well as the system's behavior in different driven fields. And based on that, we present the nonlinear two-level Landau-Zener model, and also describe the nonlinear Landau-Zener tunneling effect of BEC. The structure of the thesis is as follows:1. The discovery and study of Landau-Zener tunneling, as well as the latest research progress, are briefly reviewed.2. The basic theory of Landau-Zener tunneling effect is introduced. This is done by first giving a simple derivation of quantum adiabatic theory. Meanwhile, the conditions of using quantum adiabatic theory are mentioned. After that, two methods of describing Landau-Zener tunneling are introduced, which are Landau's adiabatic transition model and Zener's model respectively.3. The behavior of linear Landau-Zener tunneling in different driven fields are presented, which includes the standard Landau-Zener model (two-level linear model), the Landau-Zener effect in uniform field, and the Landau-Zener tunneling under three extreme conditions in periodic driven field. Analysis shows that tunneling can be suppressed under the limit of both high-frequency and low-frequency, while resonance will occur in the weak coupling limit.4. Based on both numerical simulation and analytic solution, the nonlinear two-level model is given. Result shows that tunneling between levels appears when the nonlinear intensity exceeds a certain threshold value, even in the adiabatic approximation.5. Introduction to the nonlinear Landau-Zener tunneling effect of BEC. The basic concepts of BEC is described first, followed by the analysis of nonlinear Landau-Zener tunneling effect in optical lattices, which shows that the Bloch band develops a loop at the edge of the Brillouin zone. Finally the condition of tunneling in a double-well potential is depicted.