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arXiv:1306.0619 · Nature Communications

Direct measurement of a 27-dimensional orbital-angular-momentum state vector

Mehul Malik, Mohammad Mirhosseini, Martin P. J. Lavery, Jonathan Leach, Miles J. Padgett, Robert W. Boyd

Published Jan 20, 2014• 225 citations
arXivHTMLPDF
DOI
10.1038/ncomms4115

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The of a quantum state poses a unique challenge for experimentalists. Recently, the technique of measurement was proposed for characterizing a quantum state in-situ through sequential weak and strong measurements. While this method has been used for measuring polarization states, its real potential lies in the of states with a large dimensionality. Here we show the practical direct of a high-dimensional state vector in the discrete basis of orbital-angular momentum. Through weak measurements of orbital-angular momentum and strong measurements of angular position, we measure the complex probability amplitudes of a pure state with a dimensionality, d=27. Further, we use our method to directly observe the relationship between rotations of a state vector and the relative phase between its orbital-angular-momentum components. Our technique has important applications in high-dimensional classical and quantum information systems, and can be extended to characterize other types of large quantum states.
Berry phase of higher-dimensional orbital angular momentum of light is studied. When an N th order orbital state, described by a vector in (N + 1)-dimensional space, evolves through a closed path in space of orbital states, there will exist a higher order orbital Berry phase. We calculate this phase by using the matrix transformation theory. A direct measurement of the higher-order orbital Berry phase is also carried out by the interference method. The experimental results are in good agreement with the theoretical description, which shows that the Berry phase is proportional to the orbital angular momentum of light.