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Register a new userTrapping Abelian anyons in fractional quantum Hall droplets
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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 $ u = 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.
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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 $ u = 7/3$ FQH state through detection of the predicted statistical phase angle of $2pi/3$, consistent with a change of the anyonic particle number by one. The $ u = 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 $pi$ 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.
This paper has been superseded by a new preprint: Kun Yang and Bertrand I. Halperin, arXiv:0901.1429.
The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined anyons, may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.
The interplay between interaction and disorder-induced localization is of fundamental interest. This article addresses localization physics in the fractional quantum Hall state, where both interaction and disorder have nonperturbative consequences. We provide compelling theoretical evidence that the localization of a single quasiparticle of the fractional quantum Hall state at filling factor $ u=n/(2n+1)$ has a striking {it quantitative} correspondence to the localization of a single electron in the $(n+1)$th Landau level. By analogy to the dramatic experimental manifestations of Anderson localization in integer quantum Hall effect, this leads to predictions in the fractional quantum Hall regime regarding the existence of extended states at a critical energy, and the nature of the divergence of the localization length as this energy is approached. Within a mean field approximation these results can be extended to situations where a finite density of quasiparticles is present.
We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury-Brown and Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.
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