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Interference between two indistinguishable electrons from independent sources

Abstract

Very much like the ubiquitous quantum interference of a single particle with itself1, quantum interference of two independent, but indistinguishable, particles is also possible. For a single particle, the interference is between the amplitudes of the particle’s wavefunctions, whereas the interference between two particles is a direct result of quantum exchange statistics. Such interference is observed only in the joint probability of finding the particles in two separated detectors, after they were injected from two spatially separated and independent sources. Experimental realizations of two-particle interferometers have been proposed2,3; in these proposals it was shown that such correlations are a direct signature of quantum entanglement4 between the spatial degrees of freedom of the two particles (‘orbital entanglement’), even though they do not interact with each other. In optics, experiments using indistinguishable pairs of photons encountered difficulties in generating pairs of independent photons and synchronizing their arrival times; thus they have concentrated on detecting bunching of photons (bosons) by coincidence measurements5,6. Similar experiments with electrons are rather scarce. Cross-correlation measurements between partitioned currents, emanating from one source7,8,9,10, yielded similar information to that obtained from auto-correlation (shot noise) measurements11,12. The proposal of ref. 3 is an electronic analogue to the historical Hanbury Brown and Twiss experiment with classical light13,14. It is based on the electronic Mach–Zehnder interferometer15 that uses edge channels in the quantum Hall effect regime16. Here we implement such an interferometer. We partitioned two independent and mutually incoherent electron beams into two trajectories, so that the combined four trajectories enclosed an Aharonov–Bohm flux. Although individual currents and their fluctuations (shot noise measured by auto-correlation) were found to be independent of the Aharonov–Bohm flux, the cross-correlation between current fluctuations at two opposite points across the device exhibited strong Aharonov–Bohm oscillations, suggesting orbital entanglement between the two electron beams.

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Figure 1: The two-particle Aharonov–Bohm interferometer.
Figure 2: Colour plot of the conductance of the two separate MZIs as function of the modulation gate voltage and the magnetic field that decayed in time.
Figure 3: Analysis and two-dimensional FFT of auto-correlation (shot noise) for an open ‘middle gate’.
Figure 4: Cross-correlation of the current fluctuations in D2 and D4.

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Acknowledgements

We thank Y. Imry, U. Gavish, M. Buttiker, P. Samuelsson and D. Rohrlich for discussions. The work was partly supported by the Israeli Science Foundation (ISF), the Minerva foundation, the German Israeli Foundation (GIF), the German Israeli Project cooperation (DIP), and the Ministry of Science - Korea Program. Y.C. was supported by the Korea Research Institute of Standards and Science (KRISS), the Korea Foundation for International Cooperation of Science and Technology (KICOS), the Nanoscopia Center of Excellence at Hanyang University through a grant provided by the Korean Ministry of Science and Technology, and by the Priority Research Centers Program funded by the Korea Research Foundation.

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Correspondence to M. Heiblum.

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Neder, I., Ofek, N., Chung, Y. et al. Interference between two indistinguishable electrons from independent sources. Nature 448, 333–337 (2007). https://doi.org/10.1038/nature05955

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