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Physics Today

Hanbury Brown and Twiss: Important, anti-weird, beautiful

Μ. Büttiker

Published Mar 1, 2009• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.4797073

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

Peter Samuelsson, Eugene V. Sukhorukov, Μ. Büttiker

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.

arXiv:cond-mat/0307473•Physical Review Letters•Jan 15, 2004•281 citations

Aptly named Aharonov-Bohm effect has classical analogue, long history

Murray Peshkin

I am an author of the 1961 paper that first called the Aharonov-Bohm effect by that name. 1 1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). The term has since appeared in more than 1000 published papers. However, it has been suggested a few times, most recently by Peter Sturrock and Timothy Groves, that the name does not do justice to Werner Ehrenberg and Raymond Siday, who found in 1949 that the motion of electrons can be influenced by magnetic fields confined to regions that the electrons do not enter. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). I argue that the name Aharonov-Bohm effect is appropriate, although for a reason that I did not fully appreciate in 1961.The 1959 Aharonov-Bohm paper profoundly changed the way we think about electromagnetic fields in quantum mechanics. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). The gauge-invariant part of the vector potential was promoted to a real physical field, not just a convenient device for summarizing certain information about the electric and magnetic fields. In the words of C. N. Yang, “The electromagnetic field strength fµv in quantum mechanics underdescribes electromagnetism, as the Bohm-Aharonov effect demonstrates … information about the phase factor exp[ie∮(A⋅dx)/ℏc] for all closed loops correctly describes electromagnetism.” 4 4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5.See also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). A century earlier, James Clerk Maxwell changed the way we think about action at a distance by identifying what we now call the Maxwell fields as real physical things that contain energy and momentum and that enable microscopic conservation laws; they are not just mathematical functions that summarize the necessary information about the past motions of charges. Later those physical fields had to be quantized. Yakir Aharonov and David Bohm found that in quantum mechanics the Maxwell fields in a multiply connected region do not contain all the physics; the vector potential must also be endowed with reality to make sense of the subtler interactions in quantum mechanics. Neither Aharonov and Bohm nor Ehrenberg and Siday were the first to observe that magnetic fields in places where a charged particle’s wave function vanishes may influence the motion of that particle. 5 5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) F. London, Nature 140, 793 (1937). Paul Dirac, in his 1931 paper on magnetic monopoles, noted that the electron’s wavefunction must vanish on singular flux lines but said nothing about that raising any question of nonlocality. Fritz London pointed out in the 1930s that the motion of electrons in a superconducting ring depends on an external magnetic flux through the hole in the ring, where the electrons cannot go. He wrote in his 1937 paper, “The most stable state of a ring has no current, unless an external magnetic field is applied.” Like Dirac, he said nothing about a nonlocal action of the magnetic field being surprising or unusual. Of course, London, like Dirac, was focusing on something else.Ehrenberg and Siday were also focusing on something else—electron optics—when they found in 1949 that the motion of an electron can depend on the magnetic field in a region from which the electron is excluded. They chose not to mention that curious phenomenon in the abstract of their paper, although they did explicitly say elsewhere that it was “curious.”None of those earlier authors went on to conclude that such a phenomenon implies that the vector potential has to be seen as a real physical field in quantum mechanics. Only Aharonov and Bohm did that.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5. Google ScholarSee also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). Google ScholarCrossref, ISI5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) Google ScholarCrossref F. London, Nature 140, 793 (1937). , Google ScholarCrossref© 2010 American Institute of Physics.

Physics Today•Aug 1, 2010•1 citation

Aptly named Aharonov-Bohm effect has classical analogue, long history

Michael Berry

Writing about what is usually termed the Aharonov-Bohm (AB) effect, Peter Sturrock and Timothy Groves argue (Physics Today, April 2010, page 8) that the same physics was discovered a decade earlier 1 1. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). and should rightly be called the Ehrenberg-Siday effect. I agree that Werner Ehrenberg and Raymond Siday deserve recognition for their anticipation of AB. Indeed, in recent talks celebrating the 50th anniversary of AB, I began by describing the unfairly neglected paper by Ehrenberg and Siday. Nevertheless, I have come to a different conclusion from Sturrock and Groves: The expression “Aharonov-Bohm effect” is justified, for two reasons.First, although there is no doubt that the work by Ehrenberg and Siday anticipated how inaccessible magnetic flux can influence electron interference, that was as a curiosity, at the end of a paper whose main emphasis was the Hamiltonian analysis of electron optics. By contrast, Yakir Aharonov and David Bohm emphasized from the start, as an essential and general aspect of quantum mechanics, the physical influence of inaccessible fields that act nonlocally through the vector potential.Second, Ehrenberg and Siday’s semi-classical approximation—essentially applying the Dirac magnetic phase factor to electrons traveling on either side of the flux—implies a wavefunction that is multivalued and therefore not the correct solution of Schrödinger’s equation. The lack of a single-valued wavefunction leaves their prediction open to doubt. By contrast, Aharonov and Bohm derived the exact single-valued solution for waves scattered by a flux line. Recently, it was shown that the Ehrenberg-Siday approximation corresponds to the first terms in a “many-whirls” representation that treats the exact AB wavefunction as a topological sum over paths circling the flux. 2 2. M. V. Berry, J. Phys. A (in press). Attribution of credit is a delicate matter. It tends to excite strong feelings, and I write about it reluctantly. But the Ehrenberg-Siday paper does seem to exemplify the unfortunate phenomenon identified by Alfred North White-head in a 1916 address to the British Association for the Advancement of Science: “Everything of importance has been said before, by someone who did not discover it.”In a companion letter in the April 2010 issue, Alexander Ershkovich correctly points out that the AB effect is present in classical Hamiltonian mechanics, even though remote magnetic fields cannot influence Newtonian trajectories. He advocates a “search for experiments that might prove … a classical analogue of the Aharonov-Bohm effect.” Such an experiment exists already. In the classical physics of waves on a moving medium, the flow velocity acts like the vector potential in quantum mechanics, so the flow vorticity acts like the magnetic field; the analogy is precise. Fine details of the AB wavefunction were observed in ripples on the surface of water swirling irrotationally into a bathtub vortex, 3 3. M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, Eur. J. Phys. 1, 154 (1980). whose core is the analogue of inaccessible magnetic flux. REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref2. M. V. Berry, J. Phys. A (in press). Google Scholar3. M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, Eur. J. Phys. 1, 154 (1980). Google ScholarCrossref© 2010 American Institute of Physics.

Physics Today•Jul 30, 2010•12 citations

Hanbury Brown–Twiss Effect with Wave Packets

Tabish Qureshi, Ushba Rizwan

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.

arXiv:1509.02221•Quanta•Nov 29, 2017•8 citations

More variations on Aharonov-Bohm

Peter Andrew Sturrock, T. R. Groves

Having read “The Aharonov-Bohm Effects: Variations on a Subtle Theme” by Herman Batelaan and Akira Tono-mura (Physics Today, September 2009, page 38), we note with some dismay that the principal effect, that related to magnetic flux, continues to be attributed to its re-discoverers rather than to the original discoverers. Batelaan and Tonomura write, “The AB effect was already implicit in the 1926 Schrödinger equation, but it would be another three decades before theorists Yakir Aharonov and David Bohm pointed it out.” 1 1. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). That is incorrect: It took only two decades before the effect was pointed out, not by Aharonov and Bohm but by Werner Ehrenberg and Raymond “Rory” Siday. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Aharonov and Bohm cited that prior publication in their second article. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 123, 1511(1961). According to Bohm’s biographer F. David Peat, “After their first paper had been published, Bohm learned that the effect had already been postulated by a maverick physicist called Rory E. Siday.” 4 4. F. D. Peat, Infinite Potential: The Life and Times of David Bohm, Addison-Wesley, Reading, MA (1997), p. It seems curious that the biographer should use the term “postulated” rather than “proposed” and that he should comment on Siday’s personality but not on Ehrenberg’s. One of us (Sturrock) knew them both: Raymond was very smart but somewhat brash; Werner was erudite and a model of propriety, who would never have subscribed his name to an article unless he was convinced it was correct.It seems that the main scientific, rather than sociological, reason that the AB proposal was taken more seriously than the ES proposal is that the former was presented in the context of quantum mechanics, the latter in the context of electron optics. Aharonov and Bohm made a rapid transition from quantum mechanics to wave theory. Ehrenberg and Siday made a more detailed transition from geometrical optics to wave theory. For the case of magnetic flux, the two articles presented identical theoretical predictions. Our view is that the ES article was tedious but conceptually sound, whereas the AB article was lively but involved a questionable conceptual leap—namely, a relativistic generalization based on a noncovariant analysis. Soon after Sturrock arrived at Stanford University in 1955, and before the Aharonov-Bohm publication, he asked Leonard Schiff, Stanford’s quantum mechanics expert, whether Schiff found the Ehrenberg-Siday proposal convincing. He did.In the interests of accuracy and of giving credit where credit is due, we think it would be appropriate to use “Ehrenberg-Siday effect” for the case of magnetic interference and to reserve “Aharonov-Bohm effect” for electrical interference.We are indebted to Elliott Bloom, Dieter Kern, Walt Harrison, Peter Hawkes, Garret Moddel, Fabian Pease, Jeff Scargle, and Lenny Susskind for helpful discussions on this matter.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 123, 1511(1961). Google ScholarCrossref, ISI4. F. D. Peat, Infinite Potential: The Life and Times of David Bohm, Addison-Wesley, Reading, MA (1997), p. Google Scholar© 2010 American Institute of Physics.

Physics Today•Apr 1, 2010•6 citations

Hanbury Brown Twiss effect for bosons and fermions

Christoph Ira Westbrook

•Feb 7, 2019•0 citations
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 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.
I am an author of the 1961 paper that first called the Aharonov-Bohm effect by that name. 1 1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). The term has since appeared in more than 1000 published papers. However, it has been suggested a few times, most recently by Peter Sturrock and Timothy Groves, that the name does not do justice to Werner Ehrenberg and Raymond Siday, who found in 1949 that the motion of electrons can be influenced by magnetic fields confined to regions that the electrons do not enter. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). I argue that the name Aharonov-Bohm effect is appropriate, although for a reason that I did not fully appreciate in 1961.The 1959 Aharonov-Bohm paper profoundly changed the way we think about electromagnetic fields in quantum mechanics. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). The gauge-invariant part of the vector potential was promoted to a real physical field, not just a convenient device for summarizing certain information about the electric and magnetic fields. In the words of C. N. Yang, “The electromagnetic field strength fµv in quantum mechanics underdescribes electromagnetism, as the Bohm-Aharonov effect demonstrates … information about the phase factor exp[ie∮(A⋅dx)/ℏc] for all closed loops correctly describes electromagnetism.” 4 4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5.See also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). A century earlier, James Clerk Maxwell changed the way we think about action at a distance by identifying what we now call the Maxwell fields as real physical things that contain energy and momentum and that enable microscopic conservation laws; they are not just mathematical functions that summarize the necessary information about the past motions of charges. Later those physical fields had to be quantized. Yakir Aharonov and David Bohm found that in quantum mechanics the Maxwell fields in a multiply connected region do not contain all the physics; the vector potential must also be endowed with reality to make sense of the subtler interactions in quantum mechanics. Neither Aharonov and Bohm nor Ehrenberg and Siday were the first to observe that magnetic fields in places where a charged particle’s wave function vanishes may influence the motion of that particle. 5 5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) F. London, Nature 140, 793 (1937). Paul Dirac, in his 1931 paper on magnetic monopoles, noted that the electron’s wavefunction must vanish on singular flux lines but said nothing about that raising any question of nonlocality. Fritz London pointed out in the 1930s that the motion of electrons in a superconducting ring depends on an external magnetic flux through the hole in the ring, where the electrons cannot go. He wrote in his 1937 paper, “The most stable state of a ring has no current, unless an external magnetic field is applied.” Like Dirac, he said nothing about a nonlocal action of the magnetic field being surprising or unusual. Of course, London, like Dirac, was focusing on something else.Ehrenberg and Siday were also focusing on something else—electron optics—when they found in 1949 that the motion of an electron can depend on the magnetic field in a region from which the electron is excluded. They chose not to mention that curious phenomenon in the abstract of their paper, although they did explicitly say elsewhere that it was “curious.”None of those earlier authors went on to conclude that such a phenomenon implies that the vector potential has to be seen as a real physical field in quantum mechanics. Only Aharonov and Bohm did that.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5. Google ScholarSee also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). Google ScholarCrossref, ISI5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) Google ScholarCrossref F. London, Nature 140, 793 (1937). , Google ScholarCrossref© 2010 American Institute of Physics.
Writing about what is usually termed the Aharonov-Bohm (AB) effect, Peter Sturrock and Timothy Groves argue (Physics Today, April 2010, page 8) that the same physics was discovered a decade earlier 1 1. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). and should rightly be called the Ehrenberg-Siday effect. I agree that Werner Ehrenberg and Raymond Siday deserve recognition for their anticipation of AB. Indeed, in recent talks celebrating the 50th anniversary of AB, I began by describing the unfairly neglected paper by Ehrenberg and Siday. Nevertheless, I have come to a different conclusion from Sturrock and Groves: The expression “Aharonov-Bohm effect” is justified, for two reasons.First, although there is no doubt that the work by Ehrenberg and Siday anticipated how inaccessible magnetic flux can influence electron interference, that was as a curiosity, at the end of a paper whose main emphasis was the Hamiltonian analysis of electron optics. By contrast, Yakir Aharonov and David Bohm emphasized from the start, as an essential and general aspect of quantum mechanics, the physical influence of inaccessible fields that act nonlocally through the vector potential.Second, Ehrenberg and Siday’s semi-classical approximation—essentially applying the Dirac magnetic phase factor to electrons traveling on either side of the flux—implies a wavefunction that is multivalued and therefore not the correct solution of Schrödinger’s equation. The lack of a single-valued wavefunction leaves their prediction open to doubt. By contrast, Aharonov and Bohm derived the exact single-valued solution for waves scattered by a flux line. Recently, it was shown that the Ehrenberg-Siday approximation corresponds to the first terms in a “many-whirls” representation that treats the exact AB wavefunction as a topological sum over paths circling the flux. 2 2. M. V. Berry, J. Phys. A (in press). Attribution of credit is a delicate matter. It tends to excite strong feelings, and I write about it reluctantly. But the Ehrenberg-Siday paper does seem to exemplify the unfortunate phenomenon identified by Alfred North White-head in a 1916 address to the British Association for the Advancement of Science: “Everything of importance has been said before, by someone who did not discover it.”In a companion letter in the April 2010 issue, Alexander Ershkovich correctly points out that the AB effect is present in classical Hamiltonian mechanics, even though remote magnetic fields cannot influence Newtonian trajectories. He advocates a “search for experiments that might prove … a classical analogue of the Aharonov-Bohm effect.” Such an experiment exists already. In the classical physics of waves on a moving medium, the flow velocity acts like the vector potential in quantum mechanics, so the flow vorticity acts like the magnetic field; the analogy is precise. Fine details of the AB wavefunction were observed in ripples on the surface of water swirling irrotationally into a bathtub vortex, 3 3. M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, Eur. J. Phys. 1, 154 (1980). whose core is the analogue of inaccessible magnetic flux. REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref2. M. V. Berry, J. Phys. A (in press). Google Scholar3. M. V. Berry, R. G. Chambers, M. D. Large, C. Upstill, J. C. Walmsley, Eur. J. Phys. 1, 154 (1980). Google ScholarCrossref© 2010 American Institute of Physics.
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.
Having read “The Aharonov-Bohm Effects: Variations on a Subtle Theme” by Herman Batelaan and Akira Tono-mura (Physics Today, September 2009, page 38), we note with some dismay that the principal effect, that related to magnetic flux, continues to be attributed to its re-discoverers rather than to the original discoverers. Batelaan and Tonomura write, “The AB effect was already implicit in the 1926 Schrödinger equation, but it would be another three decades before theorists Yakir Aharonov and David Bohm pointed it out.” 1 1. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). That is incorrect: It took only two decades before the effect was pointed out, not by Aharonov and Bohm but by Werner Ehrenberg and Raymond “Rory” Siday. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Aharonov and Bohm cited that prior publication in their second article. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 123, 1511(1961). According to Bohm’s biographer F. David Peat, “After their first paper had been published, Bohm learned that the effect had already been postulated by a maverick physicist called Rory E. Siday.” 4 4. F. D. Peat, Infinite Potential: The Life and Times of David Bohm, Addison-Wesley, Reading, MA (1997), p. It seems curious that the biographer should use the term “postulated” rather than “proposed” and that he should comment on Siday’s personality but not on Ehrenberg’s. One of us (Sturrock) knew them both: Raymond was very smart but somewhat brash; Werner was erudite and a model of propriety, who would never have subscribed his name to an article unless he was convinced it was correct.It seems that the main scientific, rather than sociological, reason that the AB proposal was taken more seriously than the ES proposal is that the former was presented in the context of quantum mechanics, the latter in the context of electron optics. Aharonov and Bohm made a rapid transition from quantum mechanics to wave theory. Ehrenberg and Siday made a more detailed transition from geometrical optics to wave theory. For the case of magnetic flux, the two articles presented identical theoretical predictions. Our view is that the ES article was tedious but conceptually sound, whereas the AB article was lively but involved a questionable conceptual leap—namely, a relativistic generalization based on a noncovariant analysis. Soon after Sturrock arrived at Stanford University in 1955, and before the Aharonov-Bohm publication, he asked Leonard Schiff, Stanford’s quantum mechanics expert, whether Schiff found the Ehrenberg-Siday proposal convincing. He did.In the interests of accuracy and of giving credit where credit is due, we think it would be appropriate to use “Ehrenberg-Siday effect” for the case of magnetic interference and to reserve “Aharonov-Bohm effect” for electrical interference.We are indebted to Elliott Bloom, Dieter Kern, Walt Harrison, Peter Hawkes, Garret Moddel, Fabian Pease, Jeff Scargle, and Lenny Susskind for helpful discussions on this matter.REFERENCESSection:ChooseTop of pageREFERENCES <<CITING ARTICLES1. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 123, 1511(1961). Google ScholarCrossref, ISI4. F. D. Peat, Infinite Potential: The Life and Times of David Bohm, Addison-Wesley, Reading, MA (1997), p. Google Scholar© 2010 American Institute of Physics.