Berry's phase for coherent states of Landau levels

TL;DR

This paper calculates the Berry phases for coherent and squeezed states of Landau levels, linking them to the Aharonov-Bohm effect and exploring both Abelian and non-Abelian phases during adiabatic magnetic field changes.

Contribution

It provides the first detailed calculation of Berry phases for Landau level coherent states, including both Abelian and non-Abelian cases, with physical interpretations.

Findings

Abelian Berry phase is analogous to the Aharonov-Bohm effect.

Non-Abelian Berry phase is derived for adiabatic magnetic field evolution.

Coherent states are interpreted as resulting from adiabatic magnetic flux movement.

Abstract

The Berry phases for coherent states and squeezed coherent states of Landau levels are calculated. Coherent states of Landau levels are interpreted as a result of a magnetic flux moved adiabatically from infinity to a finite place on the plane. The Abelian Berry phase for coherent states of Landau levels is an analog of the Aharonov- Bohm effect. Moreover, the non-Abelian Berry phase is calculated for the adiabatic evolution of the magnetic field B.