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Journal of Physics A Mathematical and Theoretical

Two-particle Aharonov–Bohm effect in electronic interferometers

Janine Splettstoesser, Peter Samuelsson, Michael V. Moskalets, Μ. Büttiker

Published Aug 12, 2010• 12 citations
Publisher

Abstract

We review recent theoretical investigations on the two-particle Aharonov–Bohm effect and its relation to entanglement production and detection. The difficulties of the entanglement detection due to dephasing and finite temperature are discussed regarding a recent experimental realization of a two-particle Aharonov–Bohm interferometer [15]. We also discuss a theoretical proposal for a two-particle Aharonov–Bohm interferometer, which as against the finite bias setup is driven with dynamical single-electron sources allowing for the tunable production of time-bin entanglement.

DOI
10.1088/1751-8113/43/35/354027

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We review recent theoretical investigations on the two-particle Aharonov–Bohm effect and its relation to entanglement production and detection. The difficulties of the entanglement detection due to dephasing and finite temperature are discussed regarding a recent experimental realization of a two-particle Aharonov–Bohm interferometer [15]. We also discuss a theoretical proposal for a two-particle Aharonov–Bohm interferometer, which as against the finite bias setup is driven with dynamical single-electron sources allowing for the tunable production of time-bin entanglement.
In this work we discuss a theory for entanglement generation, characterization and detection in fermionic two-particle interferometers (2PIs) at finite temperature. The motivation for our work is provided by the recent experiment by the Heiblum group (Neder et al 2007 Nature 448 333) realizing the two particle interferometer proposed by Samuelsson et al (2004 Phys. Rev. Lett. 92 026805). The experiment displayed a clear two-particle Aharonov–Bohm effect, however with an amplitude suppressed due to finite temperature and dephasing. This raised qualitative as well quantitative questions about entanglement production and detection in mesoscopic conductors at finite temperature. As a response to these questions, in our recent work (Samuelsson et al 2009 Phys. Rev. Lett. 102 106804), we presented a general theory for finite temperature entanglement in mesoscopic conductors. Applied to the 2PI we showed that the emitted two-particle state in the experiment was clearly entangled. Moreover, we demonstrated that the entanglement of the reduced two-particle state, reconstructed from measurements of average currents and current cross correlations, constitutes a lower bound to the entanglement of the emitted state. The present work provides an extended and more detailed discussion of these findings.
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 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.
In controlled dephasing a controlled environment causes dephasing of transport through a mesoscopic system. As a result of their interaction the states of the two subsystems are entangled. In this paper we discuss how their entanglement influences dephasing using as an example the ``which path detector,'' where the dephasing of transport through a quantum dot (QD) due to the interaction with a quantum point contact (QPC) is detected by means of an Aharonov-Bohm (AB) interferometer. In particular, we calculate the suppression $\ensuremath{\nu}$ of AB oscillations as a function of the bias eV\mathrm{eV}eV applied to the QPC and the coupling $\ensuremath{\Gamma}$ of the QD to the leads. At low temperatures the entanglement produces a smooth crossover from $\ensuremath{\nu}\ensuremath{\propto}(eV/\ensuremath{\Gamma}{)}^{2},$ when $\mathrm{eV}\ensuremath{\ll}\ensuremath{\Gamma}$ to $\ensuremath{\nu}\ensuremath{\propto}eV/\ensuremath{\Gamma},$ for $\mathrm{eV}\ensuremath{\gg}\ensuremath{\Gamma}.$
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.