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An Uncertainty Relation for the Orbital Angular Momentum Operator

Hossein Fakhri, M. Sayyah-Fard

Foundations of PhysicsJan 30, 20166 citations

Remark on the uncertainty between angle and angular momentum

K. Kraus

The European Physical Journal AAug 1, 196526 citations

Uncertainty relation between angle and orbital angular momentum: interference effect in electron vortex beams

Sh. Tanimura

The uncertainty relation between angle and orbital angular momentum had not been formulated in a similar form as the uncertainty relation between position and linear momentum because the angle variable is not represented by a quantum mechanical self-adjoint operator.Instead of the angle variable operator, we introduce the complex position operator Ẑ = x + iŷ and interpret the order parameter µ = Ẑ / Ẑ † Ẑ as a measure of certainty of the angle distribution.We prove the relation between the uncertainty of angular momentum and the angle order parameter.We also prove its generalizations and discuss experimental methods for testing these relations.The uncertainty relation between angle and orbital angular momentum had not been formulated in a similar form as the uncertainty relation between position and linear momentum because the angle variable is not represented by a quantum mechanical self-adjoint operator.Instead of the angle variable operator, we introduce the complex position operator Ẑ = x + iŷ and interpret the order parameter µ = Ẑ / Ẑ † Ẑ as a measure of certainty of the angle distribution.We prove the relation between the uncertainty of angular momentum and the angle order parameter.We also prove its generalizations and discuss experimental methods for testing these relations.

arXiv:1411.0823Nanosystems Physics Chemistry MathematicsApr 16, 20153 citations

Experimental test of uncertainty relations for quantum mechanics on a circle

Jaroslav Řeháček, Zdeněk Bouchal, Radek Čelechovský +2 more

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 at both the state preparation and analyzing stages.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 at both the state preparation and analyzing stages.

arXiv:0712.0230Physical Review AMar 24, 200833 citations

Quantum Description of the Angular Coordinate and Angular Momentum

Stephen Mark Barnett, Alison M. Yao, Filippo M. Miatto +13 more

We review the formulation of the operator for rotation angles and the corresponding uncertainty relation. The orbital angular momentum of light allows us to test these ideas and also to explore angular entanglement.

International Conference on Quantum InformationJan 1, 20110 citations

Orbital Angular Momentum

WORLD SCIENTIFIC eBooksFeb 6, 20240 citations

Uncertainty of orbital angular momentum and angle - theory

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