Minimum Uncertainty Measurements of Angle and Angular Momentum

Z. Hradil, J. Řeháček, Z. Bouchal, R. Čelechovský, and L. L. Sánchez-Soto
Phys. Rev. Lett. 97, 243601 – Published 15 December 2006

Abstract

We present an accurate description of the conjugate pair angle–angular momentum in terms of the exponential of the angle instead of the angle itself, which leads to dispersion 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 discuss Gaussian approximations to these optimal states in terms of von Mises distributions. The theory is successfully applied to the spatial degrees of freedom of a photon and verified in an experiment that employs computer-controlled spatial light modulators at both the state preparation and the analyzing stages.

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  • Received 10 May 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.243601

©2006 American Physical Society

Authors & Affiliations

Z. Hradil1, J. Řeháček1, Z. Bouchal1, R. Čelechovský1, and L. L. Sánchez-Soto2

  • 1Department of Optics, Palacky University, 17. listopadu 50, 772 00 Olomouc, Czech Republic
  • 2Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain

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Issue

Vol. 97, Iss. 24 — 15 December 2006

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