Experimental investigation of the uncertainty principle for radial degrees of freedom

Zhang, Z., Zhang, D., Qiu, X., Chen, Y., Franke-Arnold, S. and Chen, L. (2022) Experimental investigation of the uncertainty principle for radial degrees of freedom. Photonics Research, 10(9), pp. 2223-2228. (doi: 10.1364/PRJ.443691)

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Abstract

While the uncertainty principle for linear position and linear momentum, and more recently for angular position and angular momentum, is well established, its radial equivalent has so far eluded researchers. Here we exploit the logarithmic radial position, ln r , and hyperbolic momentum, P H , to formulate a rigorous uncertainty principle for the radial degree of freedom of transverse light modes. We show that the product of their uncertainties is bounded by Planck’s constant, Δ ln r · Δ P H ≥ ℏ / 2 , and identify a set of radial intelligent states that satisfy the equality. We illustrate the radial uncertainty principle for a variety of intelligent states, by preparing transverse light modes with suitable radial profiles. We use eigenmode projection to measure the corresponding hyperbolic momenta, confirming the minimum uncertainty bound. Optical systems are most naturally described in terms of cylindrical coordinates, and our radial uncertainty relation provides the missing piece in characterizing optical quantum measurements, providing a new platform for the fundamental tests and applications of quantum optics.

Item Type:Articles
Additional Information:Funding. Program for New Century Excellent Talents in University of China (NCET-13-0495); Natural Science Foundation of Fujian Province of China for Distinguished Young Scientists (2015J06002); Fundamental Research Funds for the Central Universities at Xiamen University (20720190057); National Natural Science Foundation of China (12004318, 12034016, 61975169).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Franke-Arnold, Professor Sonja
Authors: Zhang, Z., Zhang, D., Qiu, X., Chen, Y., Franke-Arnold, S., and Chen, L.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Photonics Research
Publisher:Optica Publishing Group
ISSN:2327-9125
ISSN (Online):2327-9125
Published Online:26 July 2022
Copyright Holders:Copyright © 2022 Chinese Laser Press
First Published:First published in Photonics Research 10(9): 2223-2228
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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