scholarly journals Topological edge states of anyon pairs emulated in electric circuits

2021 ◽  
Vol 2015 (1) ◽  
pp. 012127
Author(s):  
A D Rozenblit ◽  
N A Olekhno ◽  
A A Dmitriev ◽  
P S Seregin ◽  
M A Gorlach
Keyword(s):  
Electric Circuit ◽  
Quantum Statistics ◽  
Edge States ◽  
Fractional Quantum ◽  
Electric Circuits ◽  
Numerical Studies ◽  
Topological Quantum ◽  
Theoretical Predictions ◽  
Topological States ◽  
Geometrical Imperfections

Abstract Recent advances in two-particle topological quantum states demonstrate resilience to geometrical imperfections and hold perspectives for robust quantum computations. In this context, particles with fractional quantum statistics, the so-called anyons, attract especial attention. In particular, topological edge states of anyon pairs in one-dimensional chains of coupled cavities were recently predicted to demonstrate localization at one or another edge of the array depending on details of the quantum statistics. In this paper, propose an equivalent electric circuit serving as a classical emulator of such topological states. Detailed numerical studies of resonances in the circuit fully support theoretical predictions, pointing towards future experimental realizations of anyonic states analogs in electrical circuits.

scholarly journals 4D spinless topological insulator in a periodic electric circuit

2020 ◽  
Vol 7 (8) ◽  
pp. 1288-1295 ◽  
Author(s):  
Rui Yu ◽  
Y X Zhao ◽  
Andreas P Schnyder
Keyword(s):  
Resonance Frequency ◽  
Frequency Spectrum ◽  
Topological Insulator ◽  
Electric Circuit ◽  
Band Structures ◽  
Electric Circuits ◽  
Higher Dimensional ◽  
Symmetry Properties ◽  
Boundary States ◽  
Topological States

Abstract According to the mathematical classification of topological band structures, there exist a number of fascinating topological states in dimensions larger than three with exotic boundary phenomena and interesting topological responses. While these topological states are not accessible in condensed matter systems, recent works have shown that synthetic systems, such as photonic crystals or electric circuits, can realize higher-dimensional band structures. Here, we argue that, because of its symmetry properties, the 4D spinless topological insulator is particularly well suited for implementation in these synthetic systems. We explicitly construct a 2D electric circuit lattice, whose resonance frequency spectrum simulates the 4D spinless topological insulator. We perform detailed numerical calculations of the circuit lattice and show that the resonance frequency spectrum exhibits pairs of 3D Weyl boundary states, a hallmark of the nontrivial topology. These pairs of 3D Weyl states with the same chirality are protected by classical time-reversal symmetry that squares to +1, which is inherent in the proposed circuit lattice. We also discuss how the simulated 4D topological band structure can be observed in experiments.

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 Topological Atomic Chains on 2D Hybrid Structure

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3289
Author(s):  
Tomasz Kwapiński ◽  
Marcin Kurzyna
Keyword(s):  
Tight Binding ◽  
Wide Band ◽  
Hybrid Structure ◽  
Spectral Density Function ◽  
Hybrid Structures ◽  
Function Technique ◽  
Edge States ◽  
Surface Singularities ◽  
Atomic Chains ◽  
Topological States

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

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 Sequential Reasoning in Electricity: Developing and Using a Three-Tier Multiple Choice Test

2017 ◽  
Vol 8 ◽  
Author(s):  
Hildegard Urban
Keyword(s):  
Multiple Choice ◽  
Electric Circuit ◽  
Choice Test ◽  
School Students ◽  
Reliable Measure ◽  
Electric Circuits ◽  
Multiple Choice Tests ◽  
Qualitative Understanding ◽  
In Series ◽  
Testing Electricity

Electricity is one of the areas in physics most studied in terms of learning difficulties. Misconceptions are strongly-held, stable cognitive structures, which differ from expert conception and affect how students understand scientific explanations. Therefore, there is a need for tests of conceptual understanding tests which are useful in diagnosing the nature of students’ misconceptions related to simple electric circuits and, in consequence, can serve as a valid and reliable measure of students’ qualitative understanding of simple electric circuits. As ordinary multiple choice tests with one-tier may overestimate the students’ correct as well as wrong answers, two- and three-tier tests were developed by researchers. Although, there is much research related to students’ conceptions in basic electricity, there is a lack of instruments for testing basic electricity concepts of students at grade 7, especially addressing an electric circuit as a system for a simple circuit of resistors and lamps in series. To address this gap, the context of the present study is an extension to the development of an already existing instrument developed by the author for testing electricity concepts of students at grade 7, specifically focusing on only two specific aspects in depth: first, to develop three-tier items for figuring out sequential reasoning, and second, to distinguish between misconceptions and lack of knowledge. The participants of the study included 339 secondary school students from grade 7 to 12 after instruction on electricity. Surprisingly, there are no dependences on students’ misconceptions either according to their gender or to their age. In conclusion, the findings of the study suggest that four items for uncovering students’ sequential reasoning can serve as a valid and reliable measure of students’ qualitative understanding of the systemic character of an electric circuit.

The Development of Physics Education Game on Direct Current Electric Circuit for Learners

2021 ◽  
Vol 1 (1) ◽  
pp. 50-62
Author(s):  
Jati Zen Ma'ruf
Keyword(s):  
Direct Current ◽  
Physics Education ◽  
Electric Circuit ◽  
Student Response ◽  
Educational Game ◽  
Average Score ◽  
Distribution Data ◽  
Response Sheet ◽  
Physics Learning ◽  
Electric Circuits

This study is the research of the development of physics education game application. This study has two purposes, namely to (1) developing multimedia for physics learning in the form of a physics education game on direct current electric circuits, (2) knowing the quality of educational game applications that have been produced according to experts, (3)knowing the user's (student's) response to the media of physics learning in the form of educational game applications related to direct current electrical circuit. The development procedure in this study refers to the Luther-Sutopo procedure consisting of the stage of concept, design, material collecting, assembly, testing, and distribution. Data collection techniques in the research in this study using a questionnaire. The research instrument in this study was a validation and assessment sheet which was adapted from the rubric for evaluating C. Stewart's educational game, student response sheets, and the game tester response sheet. Product validation and assessment uses a Likert scale with 4 scales and students' responses use the Guttman scale, while the game tester response sheet uses descriptive analysis. The results of this study are products in the form of simulation physics education game applications in direct current electric circuits, the results of the validation and assessment of material experts and media experts, the educational game application scored 3.8 and 3.3 in a very good category. The results of the user’s (student’s) response to the direct current electric circuit educational game application developed got an average score of 0.97 with the agreed category.

scholarly journals Photonic Topological States in a Two-Dimensional Gyrotropic Photonic Crystal

Crystals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 137 ◽  
Author(s):  
Xiao-Chen Sun ◽  
Cheng He ◽  
Xiao-Ping Liu ◽  
Yi Zou ◽  
Ming-Hui Lu ◽  
...  
Keyword(s):  
Transverse Magnetic ◽  
Quantum Spin ◽  
Necessary Condition ◽  
Complex Conjugate ◽  
Optical Parameters ◽  
Edge States ◽  
Quantum Spin Hall Effect ◽  
Pauli Matrices ◽  
Topological States ◽  
Complete Set

Time-reversal symmetry (TRS) of electrons is associated with an anti-unitary operator with T 2 = − 1 , which induces Kramers degeneracy and plays an important role in realizing the quantum spin Hall effect (QSHE). By contrast, TRS of photons is described by T b 2 = 1 . We point out that due to this difference, TRS is not the necessary condition for the construction of the photonic analogue of the QSHE. Instead, by constructing an artificial pseudo TRS T p with T p 2 = − 1 in a photonic system, one can realize the photonic Kramers degeneracy and a pair of topological protected edge states, a photonic analogue of the QSHE. Specifically, by retrieving the optical parameters of materials with the pseudo TRS, we propose a photonic topological insulator (PTI) utilizing a pair of double-degenerate transverse electric (TE) and transverse magnetic (TM) polarizations to mimic the spin up and down states of the electron. We demonstrate that the unidirectional polarization-dependent transportation of TE and TM edge states can be realized in this system based on computer simulations. For all possible symmetry types, we check the robustness of these topological states by using a complete set of impurities, including three Pauli matrices and one complex conjugate operator. The results show that the PTI is protected by the pseudo TRS T p . In general, an arbitrary pair of optical polarizations on the Bloch sphere can be utilized to construct photonic pseudospin states and the PTI. Our findings confirm the physical meaning of the pseudo TRS and may provide guidance for future PTI designs.

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