Quantum concepts in optical polarization

TL;DR

This paper reviews the quantum theory of light polarization, highlighting differences from classical optics, especially regarding quantum states, degrees of polarization, and applications in quantum technologies.

Contribution

It provides a comprehensive comparison of classical and quantum polarization properties, introducing new quantum degrees of polarization and discussing nonclassical states for quantum tech.

Findings

Quantum Stokes parameters require nested spheres due to photon number fluctuations.

Higher-order moments significantly affect quantum polarization states.

Quantum degrees of polarization differ in state ordering, unlike classical measures.

Abstract

We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincar\'e sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincar\'e space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored and their potential applications in quantum technologies are discussed.