Engineering the Coherency of Fractional and Non-Abelian Electronic Interferometers

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Interferometry with fractional and non-Abelian excitations is interesting and relevant because it can reveal the non-local physics of fractional statistical phases and can potentially form the basis for topological quantum computing. While there are beautiful examples for the interference of electrons, so far, experimental efforts at establishing anyonic interferometry were not successful. This leads to the feeling, shared by many, that in our description of anyon interferometry, and in our effort to detect fractional (Abelian and non-Abelian) statistics, we are missing some essential ingredients. Understanding the lack of experimental observation of interference patterns in the fractional quantum Hall regime is the main motivation behind this project. One should note, though, that our goals go beyond explaining this experimental stalemate. We plan to provide an in-depth theory as to the physical ingredients that hinder interference of anyons (Abelian and non-Abelian), as compared with electron interference. We will make a special effort to highlight the role of the exotic neutral modes that were, until recently, quite evasive, and now seem to be ubiquitous in the fractional quantum Hall edges. Finally, we will come up with engineered setups, in which the interference-impeding elements could be factored out.Successful execution of this project will provide us with a better understanding of the subtle physics involved in anyonic interferometry, and why it is so different from electronic (and certainly other types of) interferometry. Our study may pave the way to experimental protocols that allow for the observation of such interference patterns. This is anticipated to take place with carefully engineered setups and controlled protocols. Novel insight on fundamental questions and practical applications for the construction of quantum computing circuits is expected.