Charge Fractionalization on Quantum Hall Edges

We discuss the propagation and fractionalization of localized charges on the edges of quantum Hall bars of variable widths, where interactions between the edges give rise to Luttinger liquid behavior with a non-trivial interaction parameter g. We focus in particular on the separation of an initial charge pulse into a sharply defined front charge and a broader tail. The front pulse describes an adiabatically dressed electron which carries a non-integer charge, which is \sqrt{g} times the electron charge. We discuss how the presence of this fractional charge can, in principle, be detected through measurements of the noise in the current created by tunneling of electrons into the system. The results are illustrated by numerical simulations of a simplified model of the Hall bar.Comment: 15 page

Resonant tunneling in fractional quantum Hall effect: superperiods and braiding statistics

We study theoretically resonant tunneling of composite fermions through their quasi-bound states around a fractional quantum Hall island, and find a rich set of possible transitions of the island state as a function of the magnetic field or the backgate voltage. These considerations have possible relevance to a recent experimental study, and bring out many subtleties involved in deducing fractional braiding statistics.Comment: Phys. Rev. Lett. in pres

Decoherence of Anyonic Charge in Interferometry Measurements

We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target's topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges a and a' in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with a to give a'.Comment: 5 pages, 1 figure; v2: reference added, example added, clarifying changes made to conform to the version published in PR

Primary-Filling e/3 Quasiparticle Interferometer

We report experimental realization of a quasiparticle interferometer where the entire system is in 1/3 primary fractional quantum Hall state. The interferometer consists of chiral edge channels coupled by quantum-coherent tunneling in two constrictions, thus enclosing an Aharonov-Bohm area. We observe magnetic flux and charge periods h/e and e/3, equivalent to creation of one quasielectron in the island. Quantum theory predicts a 3h/e flux period for charge e/3, integer statistics particles. Accordingly, the observed periods demonstrate the anyonic statistics of Laughlin quasiparticles

Are there sharp fractional charges in Luttinger liquids?

We examine charge fractionalization by chiral separation in a one-dimensional fermion system described by Luttinger liquid theory. The focus is on the question of whether the fractional charges are quantum mechanically sharp, and in the analysis we make a distinction between the global charge, which is restricted by boundary conditions, and the local charge where a background contribution is subtracted. We show, by way of examples, that fractional charges of arbitrary values, all which are quantum mechanically sharp, can be introduced by different initial conditions. Since the system is gapless, excitations of arbitrary low frequency contribute to the fluctuations, it is important to make a precise definition of sharp charges, and this we we do by subtraction of the ground state contribution. We very briefly comment on the relevance of our analysis for proposed experiments.Comment: One reference update

Extreme points of the set of density matrices with positive partial transpose

We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for finding such extreme points and illustrate this by some examples.Comment: 4 pages, 2 figure

Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

In this letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read state expected to describe the observed FQHE plateau at nu=5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et. al. are also addressed.Comment: 5 pages, 2 eps figures v2: A few minor changes and citation corrections. In particular, the connection to cond-mat/9711087 has been clarified. v3: Minor changes: fixed references to Fig. 2, updated citations, changed a few words to conform to the version published in PR

Effective photon-photon interaction in a two-dimensional "photon fluid"

We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional ``photon fluid'' confined in a Fabry-Perot resonator. With the atoms modelled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the ``bare'' strength of the anharmonic term. The resulting expression for the non-linear Kerr susceptibility, is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity.Comment: 25 pages (revtex4), including 2 figure

Berry phases for composite fermions: effective magnetic field and fractional statistics

The quantum Hall superfluid is presently the only viable candidate for a realization of quasiparticles with fractional Berry phase statistics. For a simple vortex excitation, relevant for a subset of fractional Hall states considered by Laughlin, non-trivial Berry phase statistics were demonstrated many years ago by Arovas, Schrieffer, and Wilczek. The quasiparticles are in general more complicated, described accurately in terms of excited composite fermions. We use the method developed by Kjonsberg, Myrheim and Leinaas to compute the Berry phase for a single composite-fermion quasiparticle, and find that it agrees with the effective magnetic field concept for composite fermions. We then evaluate the "fractional statistics", related to the change in the Berry phase for a closed loop caused by the insertion of another composite-fermion quasiparticle in the interior. Our results support the general validity of fractional statistics in the quantum Hall superfluid, while also giving a quantitative account of corrections to it when the quasiparticle wave functions overlap. Many caveats, both practical and conceptual, are mentioned that will be relevant to an experimental measurement of the fractional statistics. A short report on some parts of this article has appeared previously.Comment: 14 pages, 9 figure