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Physical Review A

Quantum polarization distributions via marginals of quadrature distributions

Alfredo Luis

Published May 2, 2005• 24 citations
Publisher

Abstract

We derive quantum polarization distributions on the Poincar\'e sphere for two-mode fields as suitable marginals of the standard $s$-ordered quadrature distributions that include the Wigner function. We compare them with previously introduced distributions directly defined on the sphere from first principles. We apply this approach to some relevant field states such as coherent and number states.

DOI
10.1103/physreva.71.053801

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We derive quantum polarization distributions on the Poincar'e sphere for two-mode fields as suitable marginals of the standard sss-ordered quadrature distributions that include the Wigner function. We compare them with previously introduced distributions directly defined on the sphere from first principles. We apply this approach to some relevant field states such as coherent and number states.
Quantum optics entails polarization properties that cannot be fully described by the classical Stokes parameters. In this work, we characterize the polarization of classical as well as quantum fields by means of a probability distribution on the Poincar\'e sphere. This serves to define the degree of polarization of a field state as the distance between the corresponding polarization distribution and the uniform distribution representing unpolarized light. We apply this definition to relevant quantum field states such as SU(2) coherent, squeezed, number, and phase states.
We study nonclassical polarization states characterized by polarization distributions taking negative values. We consider two different families of polarization distributions that include polarization analogs of the Wigner function. We apply different measures of nonclassical behavior such as the nonclassical depth and the distance of the polarization distribution to its modulus. This approach is applied to relevant quantum field states such as one-photon states, SU(2) coherent states, quadrature coherent states, and twin number states. We examine observables allowing the detection of the negativity of the polarization distributions.
We introduce a probability distribution for polarization of three-dimensional quantum light fields as a marginal of the quadrature QQQ function for a three-mode field by removing the variables irrelevant for polarization (total intensity and global phase). The probability distribution turns out to be determined by projection on SU(3) coherent states. We introduce a degree of polarization as the distance between the polarization distribution and the uniform distribution associated with completely unpolarized light. We study the relation between two- and three-dimensional polarization by considering field states with a component in the vacuum state. We apply this formalism to some relevant field states.