Generalized intelligent states and SU(1,1) and SU(2) squeezing

TL;DR

This paper introduces generalized intelligent states (GIS) that minimize the Robertson-Schrödinger uncertainty relation, constructs GIS for SU(1,1) and SU(2) groups, and discusses their relation to known coherent states and squeezing properties.

Contribution

It provides a sufficient and necessary condition for GIS, constructs these states for SU(1,1) and SU(2), and clarifies their relation to existing coherent states and squeezing phenomena.

Findings

SU(1,1) GIS include all Perelomov and Barut-Girardello coherent states.

SU(2) GIS encompass Bloch coherent states.

GIS exhibit arbitrarily strong squeezing of observables.

Abstract

A sufficient condition for a state |\psi> to minimize the Robertson-Schr\"{o}dinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized intelligent states (GIS), exhibit arbitrarily strong squeezing (after Eberly) of A and B. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the Bloch CS are subset of SU(2) GIS.