Non-negative Wigner functions for orbital angular momentum states

2009/09/30 by I. Rigas, L. L. Sánchez-Soto, L. L. Sanchez-Soto +4
Physics and Astronomy · #Angular momentum #Angular momentum coupling #Angular momentum of light #Angular momentum operator #Azimuthal quantum number #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Eigenvalues and eigenvectors #Gaussian #Orbital Angular Momentum in Optics #Orbital angular momentum of light #Physics #Quantum #Quantum mechanics #Quantum optics and atomic interactions #Total angular momentum quantum number #Wigner distribution function #quant-ph

paper · pdf · doi:10.1103/physreva.81.012101

published as Phys. Rev. A 81, 012101 (2010) · 4 pages. Minor changes (including title). To appear in Physica. Review A

arxiv created 2009/12/07 · openalex publication_date 2010/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The Wigner function of a pure continuous-variable quantum state is non-negative if and only if the state is Gaussian. Here we show that for the canonical pair angle and angular momentum, the only pure states with non-negative Wigner functions are the eigenstates of the angular momentum. Some implications of this surprising result are discussed.

Citations

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