Correlations, Dynamics, and Interferometry of Anyons in the Lowest Landau Level
arXiv:1905.00442 · doi:10.1088/1742-5468/ab3aef
Abstract
In this article, we present a systematic study of quantum statistics and dynamics of a pair of anyons in the lowerst Landau level (LLL), of direct relevance to quasiparticle excitations in the quantum Hall bulk. We develop the formalism for such a two-dimensional setting of two charged particles subject to a transverse field, including fractional angular momentum states and the related algebra stemming from the anyonic boundary condition, coherent state descriptions of localized anyons, and bunching features associated with such anyons. We analyze the dynamic motion of the anyons in a harmonic trap, emphasizing phase factors emerging from exchange statistics. We then describe non-equilibrium dynamics upon the application of a saddle potential, elaborating on its role as a squeezing operator acting on LLL coherent states, and its action as a beam splitter for anyons. Employing these potential landscapes as building blocks, we analyze anyon dynamics in a quantum Hall bulk interferometer. We discuss parallels between the presented LLL setting and other realms, extensively in the context of quantum optics, whose formalism we heavily borrow from, and briefly in that of black hole phenomena.
28 pages, 6 figures, 1 table
References in corpus (11)
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- Room-Temperature Quantum Hall Effect in Graphene
- Camparison of the Hanbury Brown-Twiss effect for bosons and fermions
- Interferometry of non-Abelian Anyons
- Anyonic Braiding in Optical Lattices
- Quench dynamics and parity blocking in Majorana wires
- Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics
- Landau levels of cold atoms in non-Abelian gauge fields
- Detecting Non-Abelian Anyons by Charging Spectroscopy
- Scattering Theory for Quantum Hall Anyons in a Saddle Point Potential
- Quasi-particle propagation in quantum Hall systems
Cited by in corpus (5)
- Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons
- Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit
- Anyonic Mach-Zehnder interferometer on a single edge of a 2D electron gas
- Natural orbitals and their occupation numbers for free anyons in the magnetic gauge
- Dynamics of "Classical" Bosons, Fermions, and beyond