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arXiv · 0712.0230

Experimental test of uncertainty relations for quantum mechanics on a circle

J. Rehacek·Z. Bouchal·R. Celechovsky·Z. Hradil·L. L. Sanchez-Soto
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Abstract

We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution. Intelligent states minimizing the uncertainty product under the constraint of a given uncertainty in angle or in angular momentum turn out to be given by Mathieu wave functions. We also discuss a number of physically feasible approximations to these optimal states. The theory is applied to the orbital angular momentum of a beam of photons and verified in an experiment that employs computer-controlled spatial light modulators both at the state preparation and analyzing stages.

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J. Rehacek, Z. Bouchal, R. Celechovsky, Z. Hradil, L. L. Sanchez-Soto. 2007-12-03. Experimental test of uncertainty relations for quantum mechanics on a circle. https://doi.org/10.1103/physreva.77.032110

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