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arXiv:1212.4008 · WORLD SCIENTIFIC eBooks

Hanbury Brown–Twiss Interferometry with Electrons: Coulomb vs. Quantum Statistics

Gordon Baym, Kan Shen

Published Apr 1, 2014• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/9789814472906_0024

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I read with interest Daniel Kleppner’s lucid column on Hanbury Brown’s “steamroller.” Kleppner mentions an aspect of the Hanbury Brown and Twiss (HBT) effect that at first seemingly defied a quantum interpretation; he terms it “anti-weird,” since in certain cases a completely classical understanding is possible. Other aspects of the Hanbury Brown physics are truly weird in the sense that they violate a Bell inequality. I and collaborators Peter Samuelsson and Eugene Sukhorukov have proposed an interferometry experiment with fermions in an electrical conductor. Carriers are injected into the conductor from two contacts, and the cross correlation of the electrical current is measured at two other contacts along the conductor. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 In that arrangement, it is possible to investigate the Aharonov–Bohm effect in the fermionic HBT interferometer. Our initial discussions of such an effect date back to the early 1990s. 2 2. M. Büttiker, Phys. Rev. Lett. 68, 843 (1992); Physica B 175, 199 (1991). https://doi.org/10.1016/0921-4526(91)90713-O My collaborators and I found a geometry in which the conductance (intensity) shows no Aharonov–Bohm signature, but the current correlation (intensity correlation) is nevertheless a periodic function of the Aharonov–Bohm flux. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 We termed our finding the two-particle Aharonov–Bohm effect. The effect was recently observed by a group headed by Moty Heiblum at the Weizmann Institute of Science. His team cooled a mesoscopic conductor to tens of millikelvin and measured its conductance and noise correlations. 3 3. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007). https://doi.org/10.1038/nature05955 Theoretical work by Carlo Beenakker at Leiden University has shown that due to orbital quasiparticle entanglement, 4 4. C. W. J. Beenakker, in Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics “E. Fermi,” vol. 162, G. Casati et al. , eds., IOS Press, Washington, DC (2006). the two-particle effect is equivalent at zero temperature to a violation of a Bell inequality. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 The case of nonzero temperature is more complicated and is still a subject of research. 5 5. P. Samuelsson, I. Neder, M. Büttiker, Phys. Rev. Lett. (in press). The possibility of observing truly weird quantum physics is certain to increase interest in Hanbury Brown’s physics.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 , Google ScholarCrossref2. M. Büttiker, Phys. Rev. Lett. 68, 843 (1992); Google ScholarCrossref Physica B 175, 199 (1991). https://doi.org/10.1016/0921-4526(91)90713-O , , Google ScholarCrossref3. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007). https://doi.org/10.1038/nature05955 , Google ScholarCrossref4. C. W. J. Beenakker, in Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics “E. Fermi,” vol. 162, G. Casati et al. , eds., IOS Press, Washington, DC (2006). Google Scholar5. P. Samuelsson, I. Neder, M. Büttiker, Phys. Rev. Lett. (in press). Google Scholar© 2009 American Institute of Physics.

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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.
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.
I read with interest Daniel Kleppner’s lucid column on Hanbury Brown’s “steamroller.” Kleppner mentions an aspect of the Hanbury Brown and Twiss (HBT) effect that at first seemingly defied a quantum interpretation; he terms it “anti-weird,” since in certain cases a completely classical understanding is possible. Other aspects of the Hanbury Brown physics are truly weird in the sense that they violate a Bell inequality. I and collaborators Peter Samuelsson and Eugene Sukhorukov have proposed an interferometry experiment with fermions in an electrical conductor. Carriers are injected into the conductor from two contacts, and the cross correlation of the electrical current is measured at two other contacts along the conductor. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 In that arrangement, it is possible to investigate the Aharonov–Bohm effect in the fermionic HBT interferometer. Our initial discussions of such an effect date back to the early 1990s. 2 2. M. Büttiker, Phys. Rev. Lett. 68, 843 (1992); Physica B 175, 199 (1991). https://doi.org/10.1016/0921-4526(91)90713-O My collaborators and I found a geometry in which the conductance (intensity) shows no Aharonov–Bohm signature, but the current correlation (intensity correlation) is nevertheless a periodic function of the Aharonov–Bohm flux. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 We termed our finding the two-particle Aharonov–Bohm effect. The effect was recently observed by a group headed by Moty Heiblum at the Weizmann Institute of Science. His team cooled a mesoscopic conductor to tens of millikelvin and measured its conductance and noise correlations. 3 3. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007). https://doi.org/10.1038/nature05955 Theoretical work by Carlo Beenakker at Leiden University has shown that due to orbital quasiparticle entanglement, 4 4. C. W. J. Beenakker, in Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics “E. Fermi,” vol. 162, G. Casati et al. , eds., IOS Press, Washington, DC (2006). the two-particle effect is equivalent at zero temperature to a violation of a Bell inequality. 1 1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 The case of nonzero temperature is more complicated and is still a subject of research. 5 5. P. Samuelsson, I. Neder, M. Büttiker, Phys. Rev. Lett. (in press). The possibility of observing truly weird quantum physics is certain to increase interest in Hanbury Brown’s physics.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. Samuelsson, E. V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004). https://doi.org/10.1103/PhysRevLett.92.026805 , Google ScholarCrossref2. M. Büttiker, Phys. Rev. Lett. 68, 843 (1992); Google ScholarCrossref Physica B 175, 199 (1991). https://doi.org/10.1016/0921-4526(91)90713-O , , Google ScholarCrossref3. I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, V. Umansky, Nature 448, 333 (2007). https://doi.org/10.1038/nature05955 , Google ScholarCrossref4. C. W. J. Beenakker, in Quantum Computers, Algorithms and Chaos, Proceedings of the International School of Physics “E. Fermi,” vol. 162, G. Casati et al. , eds., IOS Press, Washington, DC (2006). Google Scholar5. P. Samuelsson, I. Neder, M. Büttiker, Phys. Rev. Lett. (in press). Google Scholar© 2009 American Institute of Physics.
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.
Louis de Broglie's discovery of the wave nature of matter 80 years ago and the subsequent development of quantum mechanics by Erwin Schrodinger, Werner Heisenberg and Paul Dirac solved many riddles of those days and determined physics of the whole 20th century. Yet, after this long time, matter wave interferometry is as up to date as it was in 1927 when Louis de Broglie's hypothesis was verified, e.g., by Davisson and Germer. Atom interferometry, ion interferometry and Bose-Einstein condensates are today's fascinating applications based on de Broglie's discovery. The focus of the present contribution are Hanbury Brown-Twiss anti-correlations (i.e. interferences between two fermions (electrons)) and the quantitative observation of decoherence by electron biprism interferometry.
The Hanbury Brown–Twiss (HBT) effect, at the quantum level, is essentially an interference of one particle with another, as opposed to interference of a particle with itself. Conventional treatments of identical particles encounter difficulties while dealing with entanglement. A recently introduced label-free approach to indistinguishable particles is described, and is used to analyze the HBT effect. Quantum wave-packets have been used to provide a better understanding of the quantum interpretation of the HBT effect. The effect is demonstrated for two independent particles governed by Bose–Einstein or Fermi–Dirac statistics. The HBT effect is also analyzed for pairs of entangled particles. Surprisingly, entanglement has almost no effect on the interference seen in the HBT effect. In the light of the results, an old quantum optics experiment is reanalyzed, and it is argued that the interference seen in that experiment is not a consequence of non-local correlations between the photons, as is commonly believed. Quanta 2017; 6: 61–69.