Trapping Abelian anyons in fractional quantum Hall droplets

Abstract

We study the trapping of Abelian anyons (quasiholes and quasiparticles) by a local potential (e.g., induced by an AFM tip) in a microscopic model of fractional quantum Hall liquids with long-range Coulomb interaction and edge confining potential. We find, in particular, at Laughlin filling fraction $\nu =1/3$, both quasihole and quasiparticle states can emerge as the ground state of the system in the presence of the trapping potential. As expected, we find the presence of an Abelian quasihole has no effect on the edge spectrum of the quantum liquid, unlike in the non-Abelian case [Phys. Rev. Lett. {\bf 97}, 256804 (2006)]. Although quasiholes and quasiparticles can emerge generically in the system, their stability depends on the strength of the confining potential, the strength and the range of the trapping potential. We discuss the relevance of the calculation to the high-accuracy generation and control of individual anyons in potential experiments, in particular, in the context of topological quantum computing.

8 pages, 8 figures

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• Non-Abelian Braiding of Lattice Bosons
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Quasiparticle tunneling in the Moore-Read fractional quantum Hall State
• Anyonic braiding via quench dynamics in fractional quantum Hall liquids
• Neutral excitation and bulk gap of the Fractional Quantum Hall liquids in disk geometry
• Edge reconstruction of fractional quantum Hall liquids with spin degrees of freedom
• Fractionally charged impurity states of a fractional quantum Hall system
• Bulk and edge quasihole tunneling amplitudes in the Laughlin state
• Sensing the binding and unbinding of anyons at impurities
• Developments in the applications of density functional theory to fractional quantum Hall systems