2007/12/03 by J. Rehacek, J. Řeháček, Zdeněk Bouchal +6 · 5 citations
Computer Science · Engineering · Physics and Astronomy · #Optical Polarization and Ellipsometry #Orbital Angular Momentum in Optics #Quantum Information and Cryptography #quant-ph
paper · pdf · doi:10.1103/physreva.77.032110
published as Phys. Rev. A 77, 032110 (2008) · 12 pages, 9 figures. Submitted for publication
arxiv created 2007/12/03 · openalex publication_date 2008/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution. Intelligent states minimizing the uncertainty product under the constraint of a given uncertainty in angle or in angular momentum turn out to be given by Mathieu wave functions. We also discuss a number of physically feasible approximations to these optimal states. The theory is applied to the orbital angular momentum of a beam of photons and verified in an experiment that employs computer-controlled spatial light modulators at both the state preparation and analyzing stages.