Unpolarized states and hidden polarization

TL;DR

This paper introduces a multipolar expansion framework for quantum polarization states, defining higher-order unpolarized states and revealing the concept of hidden polarization in quantum optics.

Contribution

It develops a multipolar expansion approach to characterize unpolarized states at various orders and explores the emergence of hidden polarization within this framework.

Findings

First-order unpolarized states match classical polarization states

Higher-order unpolarized states correspond to fully invariant quantum states

Hidden polarization naturally arises in the multipolar expansion context

Abstract

We capitalize on a multipolar expansion of the polarisation density matrix, in which multipoles appear as successive moments of the Stokes variables. When all the multipoles up to a given order $K$ vanish, we can properly say that the state is $K$th-order unpolarized, as it lacks of polarization information to that order. First-order unpolarized states coincide with the corresponding classical ones, whereas unpolarized to any order tally with the quantum notion of fully invariant states. In between these two extreme cases, there is a rich variety of situations that are explored here. The existence of \textit{hidden} polarisation emerges in a natural way in this context.