The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution of those m
ultipoles and work out the corresponding extremal pure states. We find that SU(2) coherent states are maximal to any order whereas the converse case of minimal states (which can be seen as the most quantum ones) is investigated for a diverse range of the number of photons. Taking advantage of the Majorana representation, we recast the problem as that of distributing a number of points uniformly over the surface of the Poincare sphere.
Rotated quadratures carry the phase-dependent information of the electromagnetic field, so they are somehow conjugate to the photon number. We analyze this noncanonical pair, finding an exact uncertatinty relation, as well as a couple of weaker inequ
alities obtained by relaxing some restrictions of the problem. We also find the intelligent states saturating that relation and complete their characterization by considering extra constraints on the second-order moments of the variables involved. Using these moments, we construct performance measures tailored to diagnose photon-added and Schrodinger catlike states, among others.
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.
We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations
of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes.
We advocate a simple multipole expansion of the polarisation density matrix. The resulting multipoles appear as successive moments of the Stokes variables and can be obtained from feasible measurements. In terms of these multipoles, we construct a wh
ole hierarchy of measures that accurately assess higher-order polarization fluctuations.
We set forth a method to analyze the orbital angular momentum of a light field. Instead of using the canonical formalism for the conjugate pair angle-angular momentum, we model this latter variable by the superposition of two independent harmonic osc
illators along two orthogonal axes. By describing each oscillator by a standard Wigner function, we derive, via a consistent change of variables, a comprehensive picture of the orbital angular momentum. We compare with previous approaches and show how this method works in some relevant examples.
We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the first one
corresponding to the classical picture on the Poincare sphere. We employ the particular case of the $Q$ function to formulate a whole hierarchy of measures that properly assess higher-order polarization correlations.
