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Physical Review A

Analysis of Aharonov-Bohm effect due to time-dependent vector potentials

B. Lee, E. Yin, T. Kenneth Gustafson, R. Y. Chiao

Published Apr 1, 1992• 37 citations
Publisher

Abstract

We analyze and propose a method to detect the Aharonov-Bohm effect due to time-varying vector potentials, specifically those arising from a coherent light source. We show that the effect is feasible for use as a light-intensity detector. The quantum limit of detection is that of a single photon. Such a system would be a quantum-nondemolition measurement since no photon absorption occurs.

DOI
10.1103/physreva.45.4319

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We analyze and propose a method to detect the Aharonov-Bohm effect due to time-varying vector potentials, specifically those arising from a coherent light source. We show that the effect is feasible for use as a light-intensity detector. The quantum limit of detection is that of a single photon. Such a system would be a quantum-nondemolition measurement since no photon absorption occurs.
Abstract In this article, we review a new approach to the scalar Aharonov-Bohm effect for both the electromagnetic and gravitational interaction. For both interactions a quantum system is placed in a time-dependent electromagnetic or gravitational potential, but with no force (spatial derivative of the potential) acting on the quantum system. Nevertheless, we show that the energy levels of the quantum system develop side bands which can be detected as the signature of this version of the scalar Aharonov-Bohm effect. We briefly look at the specific experimental setups required to detect the energy side bands.
Whether the time-dependent Aharonov-Bohm (AB) effect even exists or not has been the subject of long-standing debate. There are two factors complicating the problem. First, in the closed spacetime line integral of the vector potential that is thought to give the AB-phase shift, how to treat the time-varying vector potential is highly nontrivial. Second, the time-varying magnetic flux generates induced electric field even outside the solenoid. In the present paper, motivated by a recent work by Gao, we re-investigate the role of the induced electric field with the utmost care. This analysis reveals a highly nontrivial effect of the induced electric field, which turns out to be useful for verifying the very existence of the time-dependent AB-effect.
The Aharonov-Bohm (AB) effect highlights the fundamental role of electromagnetic potentials in quantum mechanics. While extensively studied in the static case, the impact of a time-varying magnetic flux on the electron's phase shift remains an open and debated question. In this paper, we derive the AB phase shift for a time-dependent magnetic vector potential and show that it is proportional to the time average of enclosed magnetic flux. Our analysis reveals that the AB phase is continuously accumulated as the electron traverses its path, challenging the conventional view that it emerges instantaneously at the point of interference. This generalized AB effect may provide deeper insight into the role of gauge-dependent potentials in quantum mechanics and also suggest novel experimental tests using alternating or pulsed magnetic flux.
We study the effect of a time-varying solenoidal vector potential for a quantum particle confined to a ring. The setup appears to be a time-varying version of the Aharonov-Bohm effect, but since the particle moves in the presence of fields, it is not strictly an Aharonov-Bohm effect. The results are similar to the ac Stark effect, but with a time-varying electric field coming from the vector potential, rather than the scalar potential. We compare and contrast the present effect with the standard ac Stark effect. The signature of this setup is the generation of quasi-energy sidebands which are observable via spectroscopy.
The canonical Aharonov–Bohm effect is usually studied with time-independent potentials. In this work, we investigate the Aharonov–Bohm phase acquired by a charged particle moving in time-dependent potentials. In particular, we focus on the case of a charged particle moving in the time-varying field of a plane electromagnetic wave. We work out the Aharonov–Bohm phase using both the potential (i.e. ∮Aμdxμ\oint A_\mu \mathrm{d}x ^\mu ∮Aμ​dxμ ) and the field (i.e. 12∫Fμνdσμν\frac{1}{2}\int F_{\mu \nu } \mathrm{d}\sigma ^{\mu \nu }21​∫Fμν​dσμν ) forms of the Aharonov–Bohm phase. We give conditions in terms of the parameters of the system (frequency of the electromagnetic wave, the size of the space–time loop, amplitude of the electromagnetic wave) under which the time-varying Aharonov–Bohm effect could be observed.