Non-Abelian Interferometry

Parsa Bonderson, Kirill Shtengel, Johannes K. Slingerland

Parsa Bonderson, Kirill Shtengel, Johannes K. Slingerland

We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular S-matrix. In particular, this result applies to fractional quantum Hall interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed nu = 12/5 plateau.

F. De Martini, G. Denardo, Anton Zeilinger

Ángel S. Sanz, Salvador Miret-Artés

Parsa Bonderson

This thesis is primarily a study of the measurement theory of non-Abelian anyons through interference experiments. We give an introduction to the theory of anyon models, providing all the formalism necessary to apply standard quantum measurement theory to such systems. This formalism is then applied to give a detailed analysis of a Mach-Zehnder interferometer for arbitrary anyon models. In this treatment, we find that the collapse behavior exhibited by a target anyon in a superposition of states is determined by the monodromy of the probe anyons with the target. Such measurements may also be used to gain knowledge that would help to properly identify the anyon model describing an unknown system. The techniques used and results obtained from this model interferometer have general applicability, and we use them to also describe the interferometry measurements in a two point-contact interferometer proposed for non-Abelian fractional quantum Hall states. Additionally, we give the complete description of a number of important examples of anyon models, as well as their corresponding quantities that are relevant for interferometry. Finally, we give a partial classification of anyon models with small numbers of particle types.

Suk Bum Chung, Michael Stone

To detect non-Abelian statistics in the $\ensuremath{\nu}=12∕5$ quantum Hall state through interferometry, we apply an analysis similar to the ones proposed for the non-Abelian $\ensuremath{\nu}=5∕2$ quantum Hall state. The result is that the amplitude of the Aharonov-Bohm oscillation of this interference is dependent on the internal states of quasiholes, but, in contrast to the $\ensuremath{\nu}=5∕2$ quantum Hall state, independent of the number of quasiholes. However, if the quasiholes are in a superposition state, it is necessary for the interferometer to have certain additional features to obtain the coefficients.