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arXiv · 1112.3400

Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect

Sanghun An·P. Jiang·H. Choi·W. Kang·S. H. Simon·L. N. Pfeiffer·K. W. West·K. W. Baldwin
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Abstract

In this paper, we report on the study of Abelian and non-Abelian statistics through Fabry-Perot interferometry of fractional quantum Hall (FQH) systems. Our detection of phase slips in quantum interference experiments demonstrates a powerful, new way of detecting braiding of anyons. We confirm the Abelian anyonic braiding statistics in the $ν= 7/3$ FQH state through detection of the predicted statistical phase angle of $2π/3$, consistent with a change of the anyonic particle number by one. The $ν= 5/2$ FQH state is theoretically believed to harbor non-Abelian anyons which are Majorana, meaning that each pair of quasiparticles contain a neutral fermion orbital which can be occupied or unoccupied and hence can act as a qubit. In this case our observed statistical phase slips agree with a theoretical model where the Majoranas are strongly coupled to each other, and strongly coupled to the edge modes of the interferometer. In particular, an observed phase slip of approximately $π$ is interpreted as a sudden flip of a qubit, or entry of a neutral fermion into the interferometer. Our results provide compelling support for the existence of non-Abelian anyons.

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Sanghun An, P. Jiang, H. Choi, W. Kang, S. H. Simon, L. N. Pfeiffer, K. W. West, K. W. Baldwin. 2011-12-15. Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect. https://arxiv.org/abs/1112.3400

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