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arXiv:1512.02765 · Journal of the Korean Physical Society

Proposal for locality test of the Aharonov-Bohm effect via Andreev interferometer without a loop

Kicheon Kang

Published Oct 19, 2017• 12 citations
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Abstract

We propose a quantitative test of the quantum locality in the electromagnetic interaction that generates the Aharonov-Bohm effect. For this purpose, we analyze the Lorentz-covariant field interaction approach based on the local action of gauge-invariant quantities only (“local” theory), and compare it with the standard potential-based (“nonlocal”) theory. Whereas the two approaches yield identical results for topological phase and any phenomenon involving classical equation of motion, an example violating this equivalence is presented; interference of the Andreev reflections from two independent superconducting inputs into a single normal metallic output. A well-defined phase shift of the interference is predicted in the “local” theory. In contrast, the potential-based Lagrangian fails the corresponding prediction. This result is significant as it can settle the issue of quantum locality in the electromagnetic interaction.

DOI
10.3938/jkps.71.565

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We propose a quantitative test of the quantum locality in the electromagnetic interaction that generates the Aharonov-Bohm effect. For this purpose, we analyze the Lorentz-covariant field interaction approach based on the local action of gauge-invariant quantities only (“local” theory), and compare it with the standard potential-based (“nonlocal”) theory. Whereas the two approaches yield identical results for topological phase and any phenomenon involving classical equation of motion, an example violating this equivalence is presented; interference of the Andreev reflections from two independent superconducting inputs into a single normal metallic output. A well-defined phase shift of the interference is predicted in the “local” theory. In contrast, the potential-based Lagrangian fails the corresponding prediction. This result is significant as it can settle the issue of quantum locality in the electromagnetic interaction.
We propose a quantitative test of the quantum nonlocality in the electromagnetic interaction that generates the Aharonov-Bohm effect. For this purpose, we derive an interaction Lagrangian based on the action of gauge-invariant quantities only, and compare it with the standard potential-based (nonlocal) Lagrangian. It is shown that the two models provide identical results for any phenomena involving classical equations of motion or topological quantum phases. Interestingly, we find an example violating this equivalence, that is, the interference of single charges coproduced from two independent sources. Whereas a well-defined phase shift of the interference is predicted in the local model, the standard nonlocal Lagrangian does not provide a gauge-invariant phase shift. This implies that an observation of the interference in the proposed setup can rule out the gauge-dependent potential-based model. This result has profound implications as it can settle the issue of dynamical nonlocality in the quantum electromagnetic interaction.
We propose a quantitative test of the quantum nonlocality in the electromagnetic interaction that generates the Aharonov-Bohm effect. For this purpose, we derive an interaction Lagrangian based on the local action of gauge-invariant quantities only, and compare it with the standard potential-based (nonlocal) Lagrangian. It is shown that the two models provide identical results for any phenomena involving classical equations of motion or topological quantum phases. Interestingly, we find an example violating this equivalence, that is, the interference of single charges coproduced from two independent sources. The two models yield different predictions of the interference fringe produced by the electromagnetic interaction and, therefore, one can decide which model is appropriate for describing the electromagnetic interaction in general. This result has profound implications as it can settle the issue of dynamical nonlocality in the quantum electromagnetic interaction.
Abstract In the Aharonov-Bohm (AB) effect, interference fringes are observed for a charged particle in the absence of the local overlap with the external electromagnetic field. This notion of the apparent “nonlocality” of the interaction or the significant role of the potential have recently been challenged and are under debate. The quantum electrodynamic approach provides a microscopic picture of the characteristics of the interaction between a charge and an external field. We explicitly show the gauge invariance of the local phase shift in the magnetic AB effect, which is in contrast to the results obtained using the usual semiclassical vector potential. Our study can resolve the issue of the locality in the magnetic AB effect. However, the problem is not solved in the same way in the electric counterpart wherein virtual scalar photons play an essential role.
The Aharonov-Bohm (AB) effect is a pure quantum effect that implies a measurable phase shift in the wave function for a charged particle that encircles a magnetic flux located in a region inaccessible to the particle. Classically, such a nonlocal effect appears to be impossible since the Lorentz force depends on only the magnetic field at the location of the particle. In quantum mechanics, the Hamiltonian, and thus the Schr\"odinger equation, has a local coupling between the current due to the particle and the electromagnetic vector potential A\mathbf{A}A, which extends to the entire space beyond the region with finite magnetic field. This has sometimes been interpreted as meaning that in quantum mechanics A\mathbf{A}A is in some sense more ``fundamental'' than B\mathbf{B}B in spite of the former being gauge dependent and thus unobservable. Here we shall, with a general proof followed by a few examples, demonstrate that the AB effect can be fully accounted for by considering only the gauge-invariant B\mathbf{B}B field, as long as it is included as part of the quantum action of the entire isolated system. The price for the gauge-invariant formulation is that we must give up locality---the AB phase for the particle will arise from the change in the action for the B\mathbf{B}B field in the region inaccessible to the particle.
The Aharonov--Bohm (AB) phase for a closed interferometric loop is widely regarded as gauge invariant. This conclusion is usually obtained by treating the electromagnetic source as a fixed background that is unaffected by the test charge. We investigate whether this conclusion remains valid when backreaction is included within the standard gauge-fixed formulation of quantum electrodynamics (QED). Our analysis indicates that, when the interfering branches become entangled with distinct electromagnetic field configurations, changes of the gauge-fixing condition can induce a non-vanishing shift of the total phase. This result gives rise to an apparent paradox: the total phase predicted by the QED formalism appears gauge dependent, whereas experiments robustly exhibit a definite interference shift. We examine two possible resolutions of this paradox. The standard approach attributes the observed interference only to a gauge-invariant component of the total phase and treats the remaining gauge-dependent contribution as physically irrelevant. We argue, however, that the QED formalism itself predicts the total phase governing the interference outcome and does not provide a dynamical prescription that extracts a gauge-invariant component while discarding the remaining terms. We then explore an alternative perspective in which the electromagnetic potential AμA_\muAμ​ is regarded as a physical field whose configuration is determined by the Lorenz condition together with appropriate causal and boundary conditions. From this viewpoint, the total phase can be interpreted as a well-defined physical quantity within the QED formalism. We conclude by discussing a possible experimental test based on direct measurements of open-path relative phases, which may help clarify the ontological status of electromagnetic potentials.
A field-interaction scheme is introduced for describing the Aharonov-Bohm effect, fully consistent with the principle of relativity. Our theory is based on the fact that local field interactions are present even when a particle moves only in a field-free region. The interaction Lagrangian between a charge and a flux is uniquely constructed from three principles: Lorentz covariance, linearity in the interaction strength, and a correct stationary limit of charge. Our result resolves fundamental questions raised on the standard interpretation of the Aharonov-Bohm effect, concerning its duality with the Aharonov-Casher effect and the equivalence between the potential and the field-interaction models for describing the electromagnetic interaction. Most of all, potential is eliminated in our theory, and all kind of the force-free Aharonov-Bohm effect is understood in a unified framework of the Lorentz-covariant local interaction of electromagnetic fields.