Classification of spin and multipolar squeezing

TL;DR

This paper classifies different types of squeezing in collective spin systems, revealing their structure through unitary equivalence classes and exploring the limits of squeezing in su(2J+1) and su(4) systems.

Contribution

It introduces a classification scheme for spin and multipolar squeezing based on su(2J+1) algebra, linking squeezing limits to the structure of equivalence classes.

Findings

Squeezing can be classified into unitary equivalence classes.

Each class is characterized by su(2) subalgebras within su(2J+1).

The squeezing limit relates to the dimensionality of the class.

Abstract

We investigate various types of squeezing in a collective su(2J+1) system consisting of spin-J particles (J>1/2). We show that the squeezing in the collective su(2J+1) system can be classified into unitary equivalence classes, each of which is characterized by a set of squeezed and anti-squeezed observables forming an su(2) subalgebra in the su(2J+1) algebra. The dimensionality of the unitary equivalence class is fundamentally related to its squeezing limit. We also demonstrate the classification of the squeezing among the spin and multipolar observables in a collective su(4) system.