Berry phase and its applications

Abstract

The generalizations of the theory of Berry phase to nonadiabiatic and nocyclic cases are elabolated in this thesis. We bave given a way to see the geometrical meaning og Berry phase appearing in a nonadiabatic case by introducin the Lewis invariant method and the concept of generalised parmeter space. Our theoretical elabolation for a nonadiabatic and cyclic case was applied to obtain the semiclassical quantization rule for a system composed of two nonadiabatically interacting ones. We also show that there are two different observable geometrical phases which have the same value if the evolution is cyslic. The first is the relative phase difference between the phases for two different paths in the projective Hibert space, which have the same end points and the second is an absolute value of Berry phase for an evolution curve. In the later case the reference state to measure the phase change should be equal to the initial state. These considerations for noncyclic evolutions have a number of applications in quantm optics. We report experiments by use of single mode optical fivers in this thesis. Finally, the fact that a particle in a potetial well with which a boundary ot it is moving can memorize the history of motion of that boundary through a nonintegrable (history dependent) object, Berry phase is discussed by use of the Gaussian wave packet approximation and the Lewis invarinat method in order to treat a time-independent case and a time-dependent one, respectively. In later case, the evolutions are generally noncyclic.