Minimum uncertainty measurements of angle and angular momentum
arXiv:quant-ph/0605137 · doi:10.1103/PhysRevLett.97.243601
Abstract
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.
4 pages, two eps color figures. Submitted for publication