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Science

Hanbury Brown and Twiss-Type Experiment with Electrons

William D. Oliver, Jungsang Kim, R.C. Liu, Y. Yamamoto

Published Apr 9, 1999• 354 citations
Publisher

Abstract

Fermion anti-bunching was directly observed by measuring the cross-covariance of the current fluctuations of partitioned electrons. A quantum point contact was used to inject single-mode electrons into a mesoscopic electron beam splitter device. The beam splitter output currents showed negative cross-covariance, indicating that the electrons arrived individually at the beam splitter and were randomly partitioned into two output channels. As the relative time delay between the outputs was changed, the observed ringing in the cross-covariance was consistent with the bandwidths used to monitor the fluctuations. The result demonstrates a fermion complement to the Hanbury Brown and Twiss experiment for photons.

DOI
10.1126/science.284.5412.299

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Fermion anti-bunching was directly observed by measuring the cross-covariance of the current fluctuations of partitioned electrons. A quantum point contact was used to inject single-mode electrons into a mesoscopic electron beam splitter device. The beam splitter output currents showed negative cross-covariance, indicating that the electrons arrived individually at the beam splitter and were randomly partitioned into two output channels. As the relative time delay between the outputs was changed, the observed ringing in the cross-covariance was consistent with the bandwidths used to monitor the fluctuations. The result demonstrates a fermion complement to the Hanbury Brown and Twiss experiment for photons.
In quantum mechanics it is possible to pack an arbitrary number of bosons into the same quantum state. The maximum occupancy for fermions, however is one. Back in 1956 two British scientists, Hanbury Brown and Twiss, conducted a classic experiment that showed that photons, a type of boson, have a tendency to bunch into clusters. Their experiment comprised two light sources and two detectors set up to measure the light that was transmitted and reflected by a beam splitter at the centre of the experimental configuration (see figure a). The bunching was observed by measuring the intensity correlation between the two coherent beams of light as a function of time. Hanbury Brown and Twiss measured the likelihood of observing a fluctuation in one detector at a particular time when a signal was detected at an earlier time in the other detector. The positive correlation they found was consistent with the bunching property of bosons.
A longstanding goal of Akira Tonomura was to observe Hanbury Brown--Twiss anti-correlations between electrons in a field-emission free electron beam. The experimental results were reported in his 2011 paper with Tetsuji Kodama and Nobuyuki Osakabe [Phys. Rev. A 83, 063616 (2011)]. An open issue in such a measurement is whether the observed anti-correlations arise from quantum statistics, or are simply produced by Coulomb repulsion between electrons. In this paper we describe a simple classical model of Coulomb effects to estimate their effects in electron beam interferometry experiments, and conclude that the experiment did indeed observe quantum correlations in the electron arrrival times.
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.
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.
This thesis deals with the measurement of the quantum intensity correlations in gases of metastable Helium. The measurement has been performed on thermal gases of bosonic 4He and fermionic 3He, as well as on Bose-Einstein condensates. In 1956, Robert Hanbury Brown et Richard Twiss measured the correlation between photons emitted from a single thermal source. The consequently demonstrated that the photons emitted by such a source tend to arrive grouped on a detector. This bunching characterises bosons from a non-coherent source. Fermions show an anti-bunching behaviour in the same conditions. By using metastable Helium atoms, that can be detected individually through the use of micro-channel plates, we have been able to show a similar bunching of bosons 4He from thermal sources around the microkelvin. As expected, the coherence of the Bose-Einstein condensates did not produce a particular correlation. The measurement on thermal gases of fermionic 3He has demonstrated the anti-bunching. Particular effort has been employed in describing the micro-channel plates based delay-line detector, the key to the experiment.
Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. This interference is a direct result of quantum exchange statistics, however, it is observed only in the joint probability to find the particles in two separated detectors. Here we report the first observation of such interference fringes between two independent and non-interacting electrons in an interferometer proposed by Yurke et al. and Samuelsson et al. Our experiment resembles the "Hanbury Brown and Twiss" (HBT) experiment, which was performed with classical waves. In the experiment, two independent and mutually incoherent electron beams were each partitioned into two trajectories. The combined four trajectories enclosed an Aharonov-Bohm (AB) flux (but not the two trajectories of a single electron). While individual currents were found to be independent of the AB flux, as expected, the cross-correlation between current fluctuations in two opposite points across the device exhibited strong AB oscillations. This is a direct signature of orbital entanglement between two electrons even though they never interact with each other.