Statistically induced phase transitions and anyons in 1D optical lattices

2010/09/30 by Tassilo Keilmann, Simon Lanzmich, Ian P. McCulloch +3 · 11 citations
Computer Science · Physics and Astronomy · #Anyon #Boson #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Context (archaeology) #Electron #Fermion #Fractional quantum Hall effect #Phase (matter) #Phase transition #Physics #Quantum #Quantum Hall effect #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum mechanics #Quantum phase transition #Quantum spin Hall effect #Superfluidity #Theoretical physics #Topological quantum computer #cond-mat.other #cond-mat.quant-gas #physics.atom-ph #quant-ph

paper · pdf · doi:10.1038/ncomms1353

published as Nature Commun. 2:361,2011 · 8 pages, 5 figures

openalex publication_date 2011/06/21 · arxiv created 2011/08/25 · arxiv updated 2011/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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 tunneling. The statistical angle can thus be controlled in situ by modifying the relative phase of external driving fields. This opens the fascinating possibility of smoothly transmuting bosons via anyons into fermions and of inducing a phase transition by the mere control of the particle statistics as a free parameter. In particular, we demonstrate how to induce a quantum phase transition from a superfluid into an exotic Mott-like state where the particle distribution exhibits plateaus at fractional densities.

Citations

• On the theory of identical particles
• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Coherent Transport of Neutral Atoms in Spin-Dependent Optical Lattice Potentials
• Imaging the Mott Insulator Shells by Using Atomic Clock Shifts
• Two-Dimensional Magnetotransport in the Extreme Quantum Limit
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• One-Dimensional Interacting Anyon Gas: Low-Energy Properties and Haldane Exclusion Statistics
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• The density-matrix renormalization group
• Light-induced effective magnetic fields for ultracold atoms in planar geometries

Cited by

• Anyonization of bosons in one dimension: an effective swap model
• The Anyonic Quantum Carnot Engine
• Luttinger liquid with complex forward scattering: Robustness and Berry phase
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Inhomogeneous hard-core bosonic mixture with checkerboard supersolid phase: Quantum and thermal phase diagram
• Quantum spin dynamics in a spin-orbit-coupled Bose-Einstein condensate
• Few- to many-vortex states of density-angular-momentum–coupled Bose-Einstein condensates
• Quantum walks of two interacting anyons in one-dimensional optical lattices
• Topological phases of lattice bosons with a dynamical gauge field
• Approaching off-diagonal long-range order for 1+1-dimensional relativistic anyons
• Ground-state properties of the one-dimensional unconstrained pseudo-anyon Hubbard model

Related

• Realization of 1D Anyons with Arbitrary Statistical Phase
• Fractional Statistics
• Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics
• Boson-Anyon-Fermion Mapping and Anyon Construction in One Dimension
• The Anyon Hubbard Model in One-Dimensional Optical Lattices