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Non-Abelian Anyons and Interferometry


Bonderson, Parsa Hassan (2007) Non-Abelian Anyons and Interferometry. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5NDZ-W890.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:anyon interferometry
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Thesis Committee:
  • Preskill, John P. (chair)
  • Kitaev, Alexei
  • Shtengel, Kirill
  • Yeh, Nai-Chang
Defense Date:23 May 2007
Record Number:CaltechETD:etd-06042007-101617
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2447
Deposited By: Imported from ETD-db
Deposited On:04 Jun 2007
Last Modified:05 Aug 2020 18:21

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