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arXiv:cond-mat/0304568 · Physical Review Letters

Revisiting the Hanbury Brown–Twiss Setup for Fractional Statistics

Smitha Vishveshwara

Published Nov 7, 2003• 60 citations
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Abstract

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.

DOI
10.1103/physrevlett.91.196803

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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.
We investigate the parity and time-reversal symmetry in the Hanbury Brown-Twiss experiment. For this purpose, we develop a general scattering matrix framework founded on the concatenation of many individual compounded scattering processes on the setup. Within such scattering formulation, we propose a theoretical and experimental mechanism which provides how to measure the symmetry of the system through the correlation function of a pair of particles transmitted through the leads. The correlation function naturally reveal the quantum statistics of both bosons and fermions and demonstrate a very preponderant role of PT-symmetry on the HBT experiment.
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 Hanbury Brown-Twiss experiment has proved to be an effective means of measuring two-point correlation function of identical particles. We analyze experimental observation of stripes formation of a phase fluctuating Bose-Einstein condensates in a highly elongated 3D traps [Dettmer {\em et al.}, Phys. Rev. Lett. {\bf 87}, 160406 (2001)] by means of axial two-point correlation functions. We also predict that the stripes are present in quasi-1D Bose gas in the mean-field as well as in the hard-core bosons regimes. These stripes can be realized by measuring the axial two-point correlation functions by using the Bragg interferometric method which is similar to the original Hanbury Brown and Twiss experimental setup.
We analyze a Hanbury Brown-Twiss geometry in which particles are injected from two independent sources into a mesoscopic conductor in the quantum Hall regime. All partial waves end in different reservoirs without generating any single-particle interference; in particular, there is no single-particle Aharonov-Bohm effect. However, exchange effects lead to two-particle Aharonov-Bohm oscillations in the zero-frequency current cross correlations. We demonstrate that this is related to two-particle orbital entanglement, detected via violation of a Bell inequality. The transport is along edge states and only adiabatic quantum point contacts and normal reservoirs are employed.
We present the first study of the statistics of GHz photons in quantum circuits, using Hanbury Brown and Twiss correlations. The super-Poissonian and Poissonian photon statistics of thermal and coherent sources, respectively, made of a resistor and a radio frequency generator, are measured down to the quantum regime at milli-Kelvin temperatures. As photon correlations are linked to the second and fourth moments of current fluctuations, this experiment, which is based on current cryogenic electronics, may become a standard for probing electron/photon statistics in quantum conductors.