Aspects of coherent states of nonlinear algebras

TL;DR

This paper explores the properties of nonlinear $su(2)$ and $su(1,1)$ coherent states, revealing their interrelations, statistical and geometric features, and Berry's phase, advancing understanding of their mathematical structure.

Contribution

It introduces the relation between nonlinear $su(1,1)$ Barut-Girardello and Perelomov coherent states via Laplace transform and analyzes their statistical and geometrical properties.

Findings

Nonlinear $su(1,1)$ coherent states are connected by Laplace transform.

Statistical properties of these states are characterized.

Geometrical aspects and Berry's phase are derived.

Abstract

Various aspects of coherent states of nonlinear $su(2)$ and $su(1,1)$ algebras are studied. It is shown that the nonlinear $su(1,1)$ Barut-Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived.