The geometric phase in a simple model

Apoorva G. Wagh, Veer Chand Rakhecha

Nathan A. Hagen, Luis A. Garza-Soto

We show how geometric phases derive from the elementary geometry of waves, and that geometric phases can be calculated from simple geometric transformations.

J. Anandan

A. T. Rezakhani, Paolo Zanardi A

Geometric phase of an open quantum system that is interacting with a thermal environment (bath) is studied through some simple examples. The system is considered to be a simple spin-half particle which is weakly coupled to the bath. It is seen that even in this regime the geometric phase can vary with temperature. In addition, we also consider the system under an adiabatically time-varying magnetic field which is weakly coupled to the bath. An important feature of this model is that it reveals existence of a temperature scale in which adiabaticity condition is preserved and beyond which the geometric phase is varying quite rapidly with temperature. This temperature is exactly the one in which the geometric phase vanishes. This analysis has some implications in realistic implementations of geometric quantum computation.

Miguel Angel Alonso, Mark R. Dennis

We give a simple description of the Pancharatnam-Berry geometric phase and some of its applications in optics. Geometric phases are a universal phenomenon, but we focus here on the case of geometric phases caused by changes in polarization. The geometric origin of this phase is explained by analogy with the motion of an imaginary creature living on a small planet, inspired by Saint-Exupéry’s “The Little Prince”.