Angular distributions and polarization correlations of the two-photon spherical states

TL;DR

This paper provides a detailed analysis of the angular distributions and polarization correlations in Landau's two-photon spherical states, revealing new correlation laws based on analyzer orientations.

Contribution

It introduces explicit polarization density matrices for different quantum numbers and uncovers novel polarization correlation behaviors.

Findings

Angular distributions are independent of parity for fixed J and M.

Derived polarization density matrices for various quantum states.

Discovered new polarization correlation laws involving sum of analyzer angles.

Abstract

We have analyzed in detail the angular polarization properties in the center of mass reference frame of Landau's two-photon spherical states in momentum space. The angular distributions for fixed values of $J$ and $M$ do not depend on the parity but are defined by two different functions of the polar angle between the relative momentum and the quantization axes. The two-photon polarization density matrices are derived for each values of $J$, $M$, and $P$. The linear polarization correlations of individual photons are analyzed in detail. We find, besides the usual correlation laws for $J\geq 2$ in terms of $sin$ and $cos$ of the angle between the orientation of the analyzers, correlations in terms of the sum of the orientation angles of the analyzers.