Minimum uncertainty measurements of angle and angular momentum

Z. Hradil, J. Rehacek, Z. Bouchal, R. Celechovsky, L. L. Sanchez-Soto

Published 2006-05-16Version 1

The uncertainty relations for angle and angular momentum are revisited. We use the exponential of the angle instead of the angle itself and adopt dispersion as a natural measure of resolution. We find states that minimize the uncertainty product under the constraint of a given uncertainty in angle or in angular momentum. These states are described in terms of Mathieu wave functions and may be approximated by a von Mises distribution, which is the closest analogous of the Gaussian on the unit circle. We report experimental results using beam optics that confirm our predictions.