We model a quantum walk of identical particles that can change their exchange statistics by hopping across a domain wall in a 1D lattice. Such a "statistical boundary" is transparent to single particles and affects the dynamics only by swapping multiple particles arriving together. We find that the two-particle interference is dramatically altered by reflections of these bunched waves at the interface, producing strong measurable asymmetries. Depending on the phases on the two sides, a bunched wavepacket can get completely reflected or split into a superposition of a reflected wave and an antibunched wave. This leads to striking dynamics with two domain walls, where bunched waves can get trapped in between or fragment into multiple correlated single-particle wavepackets. These findings can be realized with density-dependent hopping in present-day atomic setups and open up a new paradigm of intrinsically many-body phenomena at statistical boundaries.
We investigate continuous-time quantum walks of two indistinguishable anyons in one-dimensional lattices with both on-site and nearest-neighbor interactions based on the fractional Jordan-Wigner transformation. It is shown that the two-body correlations in position space are symmetric about the initial sites of two quantum walkers in the Bose limit ($χ=0$ ) and Fermi limit ( $χ=1$), while in momentum space this happens only in the Bose limit. An interesting asymmetry arises in the correlation for most cases with the statistical parameter $χ$ varying in between. It turns out that the origin of …
Anyons - particles carrying fractional statistics that interpolate between bosons and fermions - have been conjectured to exist in low dimensional systems. In the context of the fractional quantum Hall effect (FQHE), quasi-particles made of electrons take the role of anyons whose statistical exchange phase is fixed by the filling factor. Here we propose an experimental setup to create anyons in one-dimensional lattices with fully tuneable exchange statistics. In our setup, anyons are created by bosons with occupation-dependent hopping amplitudes, which can be realized by assisted Raman tunneli…
We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical …
We investigate the dynamical properties of anyons confined in one-dimensional optical lattice combined with a weak harmonic trap using the exact numerical method based on a generalized Jordan-Wigner transformation. The density profiles, momentum distribution, occupation distribution and occupations of the lowest natural orbital are obtained for different statistical parameters. The density profiles of anyons display the same behaviors irrespective of statistical parameter in the full evolving period. While the behaviors dependent on statistical property are shown in the momentum distributions …
Using the fractional statistical properties of so-called anyonic particles, we present exact solutions for up to six strongly interacting particles in one-dimensional confinement that interpolate the usual bosonic and fermionic limits. Specifically, we consider two-component mixtures of anyons and use these to eludicate the mixing-demixing properties of both balanced and imbalanced systems. Importantly, we demonstrate that the degree of demixing depends sensitively on the external trap in which the particles are confined. We also show how one may in principle probe the statistical parameter of…
Anyons are particles with fractional statistics that exhibit a nontrivial change in the wavefunction under an exchange of particles. Anyons can be considered to be a general category of particles that interpolate between fermions and bosons. We determined the position of the critical points of the one-dimensional anyon-Hubbard model, which was mapped to a modified Bose-Hubbard model where the tunneling depends on the local density and the interchange angle. We studied the latter model by using the density matrix renormalization group method and observed that gapped (Mott insulator) and gapless…
Statistics-governed dynamical scaling in interacting anyonic chains
National University of Defense Technology（国防科技大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）；International Solvay Institutes（国际索尔维研究所）；Southern University of Science and Technology（南方科技大学）；Jilin University（吉林大学）
Exact statistical transmutation of quantum mixtures on a ring
Université Grenoble-Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；LPMMC（低压与分子磁性物理实验室）；Laboratoire Kastler Brossel（卡斯特勒-布罗塞尔实验室）；Collège de France（法兰西公学院）；ENS-Université PSL（巴黎高等师范学校-巴黎文理研究大学）；Sorbonne Université（索邦大学）；International Solvay Institutes（国际索尔维研究所）；Center for Nonlinear Phenomena and Complex Systems（非线性现象与复杂系统中心）；Université Libre de Bruxelles（布鲁塞尔自由大学）；Université Côte d’Azur（蔚蓝海岸大学）；Institut de Physique de Nice（尼斯物理研究所）；Institut Universitaire de France（法兰西学院）
Simons Center for Geometry and Physics, Stony Brook University（石溪大学西蒙几何与物理中心）；Center for Theoretical Physics – a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；INFN, Sezione di Torino（都灵意大利国家核物理研究所）；Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern（伯尔尼大学理论物理研究所爱因斯坦基础物理中心）；School of Physics and Astronomy, Tel Aviv University（特拉维夫大学物理与天文学学院）
Revealing Pseudo-Fermionization and Chiral Binding of One-Dimensional Anyons using Adiabatic State Preparation
Department of Physics, Harvard University（哈佛大学物理系）；Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（卡斯勒·布罗塞尔实验室，法兰西公学院，法国国家科学研究中心，巴黎文理研究大学，索邦大学）；JILA, NIST and Department of Physics, University of Colorado（JILA，美国国家标准与技术研究院和科罗拉多大学物理系）；Institut für Physik und Astronomie, Technische Universität Berlin（柏林工业大学物理与天文学研究所）；Naquidis Center, Institut d’Optique Graduate School（Naquidis中心，高等光学学院）
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…
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 2D or 1D quantum particles with intermediate statistics, interpolating between bosons and fermions. We study the ground state of a large number N of 2D anyons, in a scaling limit where the statistics parameter is proportional to the inverse of N. This means that the statistics is seen as a "perturbation from the bosonic end." We model this situation in the magnetic gauge picture by bosons interacting through long-range magnetic potentials. We assume that these effective statistical gauge potentials are generated by magnetic charges carried by each particle, smeared over discs of rad…
Observation of anyonic thermodynamics and generalized Pauli principle
State Key Laboratory of Photonics and Communications, School of Electronics, Peking University（光电通信国家重点实验室，电子学院，北京大学）；Institute of Carbon-based Thin Film Electronics, Peking University（碳基薄膜电子学研究所，北京大学）；Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（非线性现象与复杂系统中心，布鲁塞尔自由大学）
