Experimental test of uncertainty relations for quantum mechanics on a circle

Details Experimental test of uncertainty relations for quantum mechanics on a circle Experimental test of uncertainty relations for quantum mechanics on a circle

2007-12-03

arxiv.org/abs/0712.0230v1

Phys. Rev. A 77, 032110 (2008)

Physics

Quantum Physics

12 pages, 9 figures. Submitted for publication

Scientific paper

10.1103/PhysRevA.77.032110

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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