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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Weak measurements with non-integer orbital angular momentum states

Jörg B. Götte

Published Feb 25, 2014• 1 citation
Publisher

Abstract

Weak measurements typically require two non-orthogonal states, which are not eigenstates of an observable. This is why weak values of the orbital angular momentum operator seem counterintuitive or involve additional auxiliary observables, such as polarization. We show how the use of states emerging from spiral phase plates or holograms with fractional step height can be used to construct weak values of the orbital angular momentum operator.

DOI
10.1117/12.2041671

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Weak measurements typically require two non-orthogonal states, which are not eigenstates of an observable. This is why weak values of the orbital angular momentum operator seem counterintuitive or involve additional auxiliary observables, such as polarization. We show how the use of states emerging from spiral phase plates or holograms with fractional step height can be used to construct weak values of the orbital angular momentum operator.
Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional Gaussian distribution can provide, in turn, key information about quantum correlations that can be relevant for quantum information applications. Here we demonstrate that by employing two-dimensional pointer states endowed with orbital angular momentum (OAM), it is possible to extract weak values of the higher order moments of single-particle operators, an inaccessible quantity with Gaussian pointer states only. We provide a specific example that illustrates the advantages of our method both in terms of signal enhancement and information retrieval.
We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital angular momentum bases, is used to estimate angular rotations. This is done by an amplification of both the real and imaginary parts of the weak-value of a polarization operator that has been coupled to the pointer, which is a spatial mode, via a spin-orbit coupling. Our experiment demonstrates the first realization of weak-value amplification in the azimuthal degree of freedom. We have achieved effective amplification factors as large as 100, providing a sensitivity that is on par with more complicated methods that employ quantum states of light or extremely large values of orbital angular momentum.