Non-Abelian excitations are an interesting feature of many fractional quantum Hall phases, including those phases described by the Moore-Read (or Pfaffian) wave function. However, the detection of the non-Abelian quasiparticles is challenging. Here, we consider a system described by the Moore-Read wave function, and assume that impurity particles bind to its quasiholes. Then, the angular momentum of the impurities, reflected also by the impurity density, provides a useful witness of the physics of the non-Abelian excitations. By demanding that the impurities are constrained to the lowest Landau level, we are able to write down the corresponding many-body wave function describing both the Moore-Read liquid and the impurities. Through Monte Carlo sampling we determine the impurity angular momentum, and we show that it suggests a quantum-statistical parameter $α= aν-b +P/2$ for the quasiholes, where $α$ ranges from $0$ for bosons to $1$ for fermions. A reasonable agreement with the Monte Carlo results is obtained for $a=1/4$, $b=1/8$ and $P=0,1$ depending on the parity of the particle number in the Moore-Read liquid. This parity-dependence of the angular momentum serves as an unambiguous demonstration of the non-Abelian nature of the excitations. In addition to the studies of excitations in the Moore-Read liquid, we also apply our scheme to Laughlin liquids, for which we focus on interacting bosonic impurities. With this, the impurities themselves form Laughlin states, which allows for a study of hierarchical fractional quantum Hall states.
One of the hallmarks of quantum statistics, tightly entwined with the concept of topological phases of matter, is the prediction of anyons. Although anyons are predicted to be realized in certain fractional quantum Hall systems, they have not yet been unambiguously detected in experiment. Here we introduce a simple quantum impurity model, where bosonic or fermionic impurities turn into anyons as a consequence of their interaction with the surrounding many-particle bath. A cloud of phonons dresses each impurity in such a way that it effectively attaches fluxes/vortices to it and thereby convert…
Anyon-Impurity Bound States in Quantum-Engineered Fractional Chern Insulators
International Solvay Institutes（国际索尔维研究所）；Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（布鲁塞尔自由大学非线性现象与复杂系统中心）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig-Maximilians-Universität München（慕尼黑大学物理系及阿诺德·索末菲理论物理中心）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
The elementary excitations of a fractional quantum Hall liquid are quasiparticles or quasiholes which are neither bosons nor fermions, but so-called anyons. Here we study impurity particles immersed in a quantum Hall liquid which bind to the quasiholes via repulsive interactions with the liquid. We show that the angular momentum of an impurity is given by the multiple of a fractional "quantum" of angular momentum, and can directly be observed from the impurity density. In a system with several impurities bound to quasiholes, their total angular momentum interpolates between the values for free…
Interferometric Braiding of Anyons in Chern Insulators
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Libre de Bruxelles（布鲁塞尔自由大学）；Collège de France（法兰西公学院）；Sorbonne Université（索邦大学）；International Solvay Institutes（国际索尔维研究所）
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Max-Planck-Institute of Quantum Optics（马克斯·普朗克量子光学研究所）
Studies on experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step towards realizing the emerging fractional statistics for particles restricted to move on the sphere, instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest…
We demonstrate that identical impurities immersed in a two-dimensional many-particle bath can be viewed as flux-tube-charged-particle composites described by fractional statistics. In particular, we find that the bath manifests itself as an external magnetic flux tube with respect to the impurities, and hence the time-reversal symmetry is broken for the effective Hamiltonian describing the impurities. The emerging flux tube acts as a statistical gauge field after a certain critical coupling. This critical coupling corresponds to the intersection point between the quasiparticle state and the ph…
Anyons are exotic quasi-particles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-abelian statistics--a property that would help realize fault tolerant quantum computation. Non-abelian anyons have long been predicted to occur in the fractional quantum Hall (FQH) phases that form in two-dimensional electron gases (2DEG) in the presence of a large magnetic field, su ch as the $ν=\tfrac{5}{2}$ FQH state. However, direct experimental evidence of anyons and tests th…
The Kondo effect is an archetypical phenomenon in the physics of strongly correlated electron systems. Recent attention has focused on the application of Kondo physics to quantum information science by exploiting overscreened Kondo impurities with residual anyon-like impurity entropy. While this physics was proposed in the fine-tuned multi-channel Kondo setup or in the Majorana-based topological Kondo effect, we here study the Kondo effect with symplectic symmetry Sp(2k) and present details about the implementation which importantly only involves conventional s-wave superconductivity coupled t…
Local spectroscopy of anyons bound to charge traps
Princeton University（普林斯顿大学）；University of Leeds（利兹大学）；Flatiron Institute（平顿研究所）；Washington University in St. Louis（圣路易斯华盛顿大学）；National Institute for Materials Science（国立材料研究所）；University of Cambridge（剑桥大学）；University of California at Berkeley（加州大学伯克利分校）
Single anyons and anyon binding in a quantum Hall dot
University of California at Santa Barbara（加州大学圣塔芭芭拉分校）；University of California, Berkeley（加州大学伯克利分校）；Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）；National Institute for Materials Science（物质材料研究机构）
