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arXiv:cond-mat/0307473 · Physical Review Letters

Two-Particle Aharonov-Bohm Effect and Entanglement in the Electronic Hanbury Brown–Twiss Setup

Peter Samuelsson, Eugene V. Sukhorukov, Μ. Büttiker

Published Jan 15, 2004• 281 citations
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Abstract

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.

DOI
10.1103/physrevlett.92.026805

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Abstract Theory predicts that electrons emitted from independent electron sources (metallic contacts) can nevertheless interfere. This interference is manifest in an exchange contribution to the shot noise correlation of currents at different contacts of a mesoscopic conductor. A geometry has been proposed in which second order (single particle) interference due to superposition of amplitudes is absent but fourth order (two‐particle) interference exhibits Aharonov‐Bohm oscillations. Recently such a geometry has been realized in an experiment and the theoretically predicted two‐particle Aharonov‐Bohm effect has been detected. We discuss Bell measurements and quantum state tomography using shot noise correlations. We discuss in addition structures in which two‐particle interference effects are generated dynamically by varying electrostatic potentials with the help of gates or by generating electron‐hole pairs by irradiating contacts of a mesoscopic conductor. These examples emphasize that two‐particle processes are not related to a particular geometry but are a general feature of multiparticle observables like shot noise correlations.

Annalen der Physik•Oct 10, 2007•0 citations
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 investigate the quantum transport in a generalized N-particle Hanbury Brown-Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.
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.
We propose a mesoscopic circuit in the quantum Hall effect regime comprising two uncorrelated single-particle sources and two distant Mach-Zehnder interferometers with magnetic fluxes, which allows us in a controllable way to produce orbitally entangled electrons. Two-particle correlations appear as a consequence of erasing of which-path information due to collisions taking place at distant interferometers and in general at different times. The two-particle correlations manifest themselves as an Aharonov-Bohm effect in noise, while the current is insensitive to magnetic fluxes. In an appropriate time interval the concurrence reaches a maximum and a Bell inequality is violated.
Theory predicts that electrons emitted from independent electron sources (metallic contacts) can nevertheless interfere. This interference is manifest in an exchange contribution to the shot noise correlation of currents at different contacts of a mesoscopic conductor. A geometry has been proposed in which second order (single particle) interference due to superposition of amplitudes is absent but fourth order (two-particle) interference exhibits Aharonov-Bohm oscillations. Recently such a geometry has been realized in an experiment and the theoretically predicted two-particle Aharonov-Bohm effect has been detected. We discuss Bell measurements and quantum state tomography using shot noise correlations. We discuss in addition structures in which two-particle interference effects are generated dynamically by varying electrostatic potentials with the help of gates or by generating electron-hole pairs by irradiating contacts of a mesoscopic conductor. These examples emphasize that two-particle processes are not related to a particular geometry but are a general feature of multiparticle observables like shot noise correlations.
We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.
Abstract Theory predicts that electrons emitted from independent electron sources (metallic contacts) can nevertheless interfere. This interference is manifest in an exchange contribution to the shot noise correlation of currents at different contacts of a mesoscopic conductor. A geometry has been proposed in which second order (single particle) interference due to superposition of amplitudes is absent but fourth order (two‐particle) interference exhibits Aharonov‐Bohm oscillations. Recently such a geometry has been realized in an experiment and the theoretically predicted two‐particle Aharonov‐Bohm effect has been detected. We discuss Bell measurements and quantum state tomography using shot noise correlations. We discuss in addition structures in which two‐particle interference effects are generated dynamically by varying electrostatic potentials with the help of gates or by generating electron‐hole pairs by irradiating contacts of a mesoscopic conductor. These examples emphasize that two‐particle processes are not related to a particular geometry but are a general feature of multiparticle observables like shot noise correlations.