Minimum uncertainty states of angular momentum and angular position

Pegg, D.T., Barnett, S.M., Zambrini, R., Franke-Arnold, S. and Padgett, M. (2005) Minimum uncertainty states of angular momentum and angular position. New Journal of Physics, 7(1), p. 62. (doi: 10.1088/1367-2630/7/1/062)

Abstract

The states of linear momentum that satisfy the equality in the Heisenberg uncertainty principle for position and momentum, that is the intelligent states, are also the states that minimize the uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the constrained minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the constrained minimum uncertainty product states for the angular case by means of instructive approximations, a numerical iterative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Padgett, Professor Miles and Franke-Arnold, Professor Sonja
• Authors: Pegg, D.T., Barnett, S.M., Zambrini, R., Franke-Arnold, S., and Padgett, M.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: New Journal of Physics
• Journal Abbr.: New J. Phys.
• Publisher: Institute of Physics Publishing Ltd.
• ISSN (Online): 1367-2630
• Published Online: 01 February 2005
• Copyright Holders: Copyright © 2005 IOP Publishing and Deutsche Physikalische Gesellschaft
• First Published: First published in New Journal of Physics 7(1):62
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher