Minimum uncertainty measurements of angle and angular momentum

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

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• Entanglement of Orbital Angular Momentum States of Photons
• Triggered qutrits for Quantum Communication protocols
• Quantization of the canonically conjugate pair angle and orbital angular momentum
• On the uncertainty relations and squeezed states for the quantum mechanics on a circle
• Elliptical Squeezed States and Rydberg Wave Packets

Cited by in corpus (14)

• Tutorial: Optical quantum metrology
• Orbital angular momentum in phase space
• Experimental test of uncertainty relations for quantum mechanics on a circle
• Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry
• Radon transform on the cylinder and tomography of a particle on the circle
• Full quantum reconstruction of vortex states
• Vortex entanglement in Bose-Einstein condensates coupled to Laguerre-Gauss beams
• Non-negative Wigner functions for orbital angular momentum states
• Robustness of raw quantum tomography
• Fundamental quantum limits in ellipsometry
• Uncertainty relations revisited
• Angular performance measure for tighter uncertainty relations
• Nondiffracting beams for vortex tomography
• Generalized uncertainty relations