Uncertainty principle for angular position and angular momentum

Franke-Arnold, S., Barnett, S. M. , Yao, E., Leach, J., Courtial, J. and Padgett, M. (2004) Uncertainty principle for angular position and angular momentum. New Journal of Physics, 6(103), (doi:10.1088/1367-2630/6/1/103)

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Publisher's URL: http://dx.doi.org/10.1088/1367-2630/6/1/103


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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Courtial, Dr Johannes and Padgett, Professor Miles and Barnett, Professor Stephen and Yao, Dr Eric and Leach, Mr Jonathan
Authors: Franke-Arnold, S., Barnett, S. M., Yao, E., Leach, J., Courtial, J., and Padgett, M.
Subjects:Q Science > QC Physics
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:New Journal of Physics
Publisher:Institute of Physics Publishing Ltd.
ISSN (Online):1367-2630

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