Wigner distribution of a general angular-momentum state: Applications to a collection of two-level atoms

Abstract

The general theory of quantum angular momentum is used to derive the unique Wigner distribution function for arbitrary angular-momentum states. We give the explicit distribution for atomic angular-momentum Dicke states, coherent states, and squeezed states that correspond to a collection of N two-level atoms. These Wigner functions W(\ensuremath{\theta},cphi) are represented as a pseudoprobability distribution in spherical phase space with spherical coordinates \ensuremath{\theta} and cphi on the surface of a sphere of radius \ensuremath{\Elzxh} \ensuremath{\surd}j(j+1) where j is the total angular-momentum eigenvalue.