scholarly journals Quantum statistics on graphs

2010 ◽  
Vol 467 (2125) ◽  
pp. 212-233 ◽  
Author(s):  
J. M. Harrison ◽  
J. P. Keating ◽  
J. M. Robbins
Keyword(s):  
Quantum Hall ◽  
Tight Binding ◽  
Quantum Statistics ◽  
Metric Graphs ◽  
Molecular Physics ◽  
Binding Model ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Exchange Processes

Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph, concentrating on the simplest case of Abelian statistics for two particles. In spite of the fact that graphs are locally one dimensional, anyon statistics emerge in a generalized form. A given graph may support a family of independent anyon phases associated with topologically inequivalent exchange processes. In addition, for sufficiently complex graphs, there appear new discrete-valued phases. Our analysis is simplified by considering combinatorial rather than metric graphs—equivalently, a many-particle tight-binding model. The results demonstrate that graphs provide an arena in which to study new manifestations of quantum statistics. Possible applications include topological quantum computing, topological insulators, the fractional quantum Hall effect, superconductivity and molecular physics.

scholarly journals Competing ν = 5/2 fractional quantum Hall states in confined geometry

2016 ◽  
Vol 113 (44) ◽  
pp. 12386-12390 ◽  
Author(s):  
Hailong Fu ◽  
Pengjie Wang ◽  
Pujia Shan ◽  
Lin Xiong ◽  
Loren N. Pfeiffer ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Filling Factor ◽  
Fault Tolerant ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Quantum Point ◽  
Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

QUANTUM COMPUTING WITH NON-ABELIAN QUASIPARTICLES

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1372-1378 ◽  
Author(s):  
N. E. BONESTEEL ◽  
L. HORMOZI ◽  
G. ZIKOS ◽  
S. H. SIMON
Keyword(s):  
Dimensional Space ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Operations ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
Two Space Dimensions ◽  
Topological Quantum Computation

In topological quantum computation quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum operations are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum operations depend only on the topology of the braids formed by these world-lines. We describe recent work showing how to find braids which can be used to perform arbitrary quantum computations using a specific kind of quasiparticle (those described by the so-called Fibonacci anyon model) which are thought to exist in the experimentally observed ν = 12/5 fractional quantum Hall state.

scholarly journals A Josephson relation for fractionally charged anyons

Science ◽  
2019 ◽  
Vol 363 (6429) ◽  
pp. 846-849 ◽  
Author(s):  
M. Kapfer ◽  
P. Roulleau ◽  
M. Santin ◽  
I. Farrer ◽  
D. A. Ritchie ◽  
...  
Keyword(s):  
Quantum Hall ◽  
Dynamical Property ◽  
Electron Systems ◽  
Dimensional Electron ◽  
Fractional Quantum ◽  
Time Resolved ◽  
Quantum Phases ◽  
Fractional Charge ◽  
Fractional Quantum Hall ◽  
Topological Quantum

Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the fractional quantum Hall effect (FQHE). Their dynamics are of utmost importance for topological quantum phases and possible decoherence-free quantum information approaches, but observing these dynamics experimentally is challenging. Here, we report on a dynamical property of anyons: the long-predicted Josephson relation fJ = e*V/h for charges e* = e/3 and e/5, where e is the charge of the electron and h is Planck’s constant. The relation manifests itself as marked signatures in the dependence of photo-assisted shot noise (PASN) on voltage V when irradiating contacts at microwaves frequency fJ. The validation of FQHE PASN models indicates a path toward realizing time-resolved anyon sources based on levitons.

scholarly journals Andreev reflection of fractional quantum Hall quasiparticles

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
M. Hashisaka ◽  
T. Jonckheere ◽  
T. Akiho ◽  
S. Sasaki ◽  
J. Rech ◽  
...  
Keyword(s):  
Andreev Reflection ◽  
Quantum Hall ◽  
Many Body ◽  
Fractional Quantum ◽  
Body Effect ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Body State ◽  
Topological Quantum ◽  
Integer Quantum

AbstractElectron correlation in a quantum many-body state appears as peculiar scattering behaviour at its boundary, symbolic of which is Andreev reflection at a metal-superconductor interface. Despite being fundamental in nature, dictated by the charge conservation law, however, the process has had no analogues outside the realm of superconductivity so far. Here, we report the observation of an Andreev-like process originating from a topological quantum many-body effect instead of superconductivity. A narrow junction between fractional and integer quantum Hall states shows a two-terminal conductance exceeding that of the constituent fractional state. This remarkable behaviour, while theoretically predicted more than two decades ago but not detected to date, can be interpreted as Andreev reflection of fractionally charged quasiparticles. The observed fractional quantum Hall Andreev reflection provides a fundamental picture that captures microscopic charge dynamics at the boundaries of topological quantum many-body states.

scholarly journals Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene

2014 ◽  
Vol 1 (4) ◽  
pp. 564-579 ◽  
Author(s):  
Xi Lin ◽  
Ruirui Du ◽  
Xincheng Xie
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
High Mobility ◽  
Fractional Quantum Hall Effect ◽  
Coulomb Interactions ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Technical Developments ◽  
Topological Quantum

Abstract The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally, FQHE has been observed in high-mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.

scholarly journals Exact Modular $S$ Matrix for ${\mathbb Z}_{k}$ Parafermion Quantum Hall Islands and Measurement of Non-Abelian Anyons

2021 ◽  
Vol 62 ◽  
pp. 1-28
Author(s):  
Lachezar S. Georgiev ◽  
Keyword(s):  
Quantum Hall ◽  
Affine Lie Algebras ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Topological Quantum ◽  
S Matrix ◽  
Topological Quantum Computation ◽  
Charged Sector ◽  
Coset Models

Using the decomposition of rational conformal filed theory characters for the $\Z_k$ parafermion quantum Hall droplets for general $k=2,3,\dots$, we derive analytically the full modular $S$ matrix for these states, including the $\uu$ parts corresponding to the charged sector of the full conformal field theory and the neutral parafermion contributions corresponding to the diagonal affine coset models. This precise neutral-part parafermion $S$ matrix is derived from the explicit relations between the coset matrix and those for the numerator and denominator of the coset and the latter is expressed in compact form due to the level-rank duality between the affine Lie algebras $\widehat{\frak{su}(k)_2}$ and $\widehat{\frak{su}(2)_k}$. The exact results obtained for the $S$ matrix elements are expected to play an important role for identifying interference patterns of fractional quantum Hall states in Fabry-P\'erot interferometers which can be used to distinguish between Abelian and non-Abelian statistics of quasiparticles localized in the bulk of fractional quantum Hall droplets as well as for nondestructive interference measurement of Fibonacci anyons which can be used for universal topological quantum computation

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