Uncertainty principle for angular position and angular momentum

By Sonja Franke-Arnold, Stephen M. Barnett, E. Yao, Jonathan Leach, Johannes Courtial, Miles J. Padgett. 2004

252 citations recorded by the source corpus.

The uncertainty principle places fundamental limits on the accuracy with which we are able to measure the values of different physical quantities (Heisenberg 1949 The Physical Principles of the Quantum Theory (New York: Dover); Robertson 1929 Phys. Rev. 34 127). This has profound effects not only on the microscopic but also on the macroscopic level of physical systems. The most familiar form of the uncertainty principle relates the uncertainties in position and linear momentum. Other manifestations include those relating uncertainty in energy to uncertainty in time duration, phase of an electromagnetic field to photon number and angular position to angular momentum (Vaccaro and Pegg 1990 J. Mod. Opt. 37 17; Barnett and Pegg 1990 Phys. Rev. A 41 3427). In this paper, we report the first observation of the last of these uncertainty relations and derive the associated states that satisfy the equality in the uncertainty relation. We confirm the form of these states by detailed measurement of the angular momentum of a light beam after passage through an appropriate angular aperture. The angular uncertainty principle applies to all physical systems and is particularly important for systems with cylindrical symmetry.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d9eec90ac4c9c9aba4e0435c65389b4284e22db0

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Citations in the corpus

Performance metrics and design considerations for a free-space optical orbital-angular-momentum–multiplexed communication link (2015, background): “, the received beam phase profile and the receiver aperture are concentric), then the power of the transmitted OAM mode does not spread into neighboring modes; this is due to the fact that orthogonality among different modes within a limited-size receiver aperture is still ensured based on recoverin”
Electron vortices: Beams with orbital angular momentum (2017, unknown): “However, the use of the knife-edge resulted in the mode broadening due to an approximate uncertainty principle for angular position and angular momentum (Franke-Arnold et al., 2004), so the measurement can not be taken for a vortex beam in a pure Landau state.”
Vortex knots in light (2004, background): “The design of phase-only holograms can be modified to control not only the phase structure of the diffracted beams but their intensity also [20, 21, 22].”
Orbital angular momentum: origins, behavior and applications (2011, background): “However, if one restricts the calculation of variance to a single 2π range, one obtains a practical measure of angular uncertainty and can show that there exists a simple uncertainty relationship for angular momentum, namely, 1`1φ > |1 − 2πPπ |/2 [159].”