An Uncertainty Relation for the Orbital Angular Momentum Operator

Franke-Arnold Franke-Arnold, Roberta Zambrini, S. S.Barnett +5 more

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.

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.

Shlomo Ruschin, Y. Ben-Aryeh

Wei Li, Shengmei Zhao

Abstract The inseparability of quantum correlation requires that the particles in the composite system be treated as a whole rather than treated separately, a typical example is the Einstein–Podolsky–Rosen (EPR) paradox. In this paper, we provide a theoretical study on the uncertainty relations of two kinds of bipartite observables in two-photon orbital angular momentum (OAM) entanglement, that is, the relative distance and centroid of the two photons at azimuth. We find that the uncertainty relations of the bipartite observables holds in any two-photon state, and they are separable in two-photon OAM entanglement. In addition, the entangled state behaves as a single particle in the bipartite representation. Finally, we find that the uncertainty relations of the bipartite observables can be used to manipulate the degree of the entanglement of an EPR state. Graphic abstract

John Robert Shewell