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arXiv:quant-ph/0308046 · Physical Review A

Intensity interferometry with anyons

T. D. Gutierrez

Published Jun 22, 2004• 6 citations
arXivHTMLPDF

Abstract

A pairwise correlation function in relative momentum space is discussed as a tool to characterize the properties of an incoherent source of noninteracting Abelian anyons. This is analogous to the Hanbury-Brown Twiss effect for particles with fractional statistics in two dimensions. In particular, using a flux tube model for anyons, the effects of source shape and quantum statistics on a two-particle correlation function are examined. Such a tool may prove useful in the context of quantum computing and other experimental applications where studying anyon sources are of interest.

DOI
10.1103/physreva.69.063614

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A pairwise correlation function in relative momentum space is discussed as a tool to characterize the properties of an incoherent source of noninteracting Abelian anyons. This is analogous to the Hanbury-Brown Twiss effect for particles with fractional statistics in two dimensions. In particular, using a flux tube model for anyons, the effects of source shape and quantum statistics on a two-particle correlation function are examined. Such a tool may prove useful in the context of quantum computing and other experimental applications where studying anyon sources are of interest.
We present a study of a Hanbury Brown-Twiss interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate Hanbury Brown-Twiss cross correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmutation from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought of as intermediate between bosons and fermions.
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θθθ. θ=0,πθ= 0, πθ=0,π correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, θθθ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of non-abelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern--Simons terms. The crossings of one-dimensional anyons on a ring are uni-directional, such that a fractional phase θθθ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently the anyon behavior predicted for quasiparticles in the ν=1/3ν= 1/3ν=1/3 fractional quantum Hall state has been observed both in scattering and in interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.
The Hanbury Brown-Twiss experiment has proved to be an effective means of probing statistics of particles. Here, in a setup involving edge-state quasiparticles in a fractional quantum Hall system, we show that a variant of the experiment composed of two sources and two sinks can be used to unearth fractional statistics. We find a clearcut signature of the statistics in the equal-time current-current correlation function for quasiparticle currents emerging from the two sources and collected at the sinks.
Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. However, the physics of anyons in one dimension remains largely unexplored. In this work, we realize Abelian anyons in one dimension with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase through a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks and observe the anyonic Hanbury Brown-Twiss effect as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of one-dimensional anyons.
Intensity interferometry (Hanbury Brown - Twiss effect) is an interesting and useful concept that is usually presented as a manifestation of the quantum statistics of indistinguishable particles. Here, by exploiting possibilities for project and entanglement, we substantially widen the scope of its central idea, removing the requirement of indistinguishability. We thereby potentially gain access to a host of new observables, including subtle polarization correlations and entanglement itself. Our considerations also shed light on the physical significance of superselection.
In spite of the predilections of the authors, the work of Hanbury Brown and Twiss on intensity interferometry may have had a more powerful impact on quantum optics than on astronomy. That it could have such an impact on quantum optics is even more surprising when one considers that the their results are more easily explained in the context of classical optics than quantum optics. Nevertheless for more than 50 years, quantum optics has been inspired by intensity interferometry and continues to add new variations and insights. I will discuss experiments using cold atoms, both bosons and fermions, and from sources both coherent and incoherent. The observations yield useful information concerning what happens in atomic systems both when they interact with each other and when they interact with light.