Observation of Aharonov-Bohm Effect by Electron Holography

Tonomura, Akira; Matsuda, Tsuyoshi; Suzuki, Ryō; Fukuhara, A.; Osakabe, Nobuyuki; Umezaki, H.; Endo, Junji; Shinagawa, K.; Sugita, Y.; Fujiwara, Hideo

doi:10.1103/physrevlett.48.1443

Cited by 259 publications

(175 citation statements)

References 20 publications

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“…The reality of the Aharonov-Bohm effect has been confirmed by numerous experiments, beginning with the work of Chambers [2] and continuing with that of Tonomura and coworkers [3] using electron holography. If the electromagnetic field undergoes fluctuations on a time scale shorter than the integration time of the experiment, then the effect is a loss of contrast in the interference pattern.…”

mentioning

confidence: 70%

External Time-Varying Fields and Electron Coherence

Hsiang

Ford

2004

Phys. Rev. Lett.

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The effect of time-varying electromagnetic fields on electron coherence is investigated. A sinusoidal electromagnetic field produces a time varying Aharonov-Bohm phase. In a measurement of the interference pattern which averages over this phase, the effect is a loss of contrast. This is effectively a form of decoherence. We calculate the magnitude of this effect for various electromagnetic field configurations. The result seems to be sufficiently large to be observable. 03.65.Yz,41.75.Fr The well-known Aharonov-Bohm phase [1] arises when coherent electrons traverse two distinct paths in the presence of an electromagnetic field. Let the two paths in spacetime be denoted by C 1 and C 2 . The phase difference due to the electromagnetic field, the AharonovBohm phase, is the line integral of the vector potential around the closed spacetime path ∂Ω = C 1 − C 2 :By Stoke's theorem, it can also be expressed as a surface integral of the field strength tensor over a two dimensional surface Ω bounded by ∂Ω:This leads to the remarkable result that the electron interference pattern is sensitive to shifts in the field strength in regions from which the electrons are excluded. The reality of the Aharonov-Bohm effect has been confirmed by numerous experiments, beginning with the work of Chambers [2] and continuing with that of Tonomura and coworkers [3] using electron holography. If the electromagnetic field undergoes fluctuations on a time scale shorter than the integration time of the experiment, then the effect is a loss of contrast in the interference pattern. The role of a fluctuating Aharonov-Bohm phase in decoherence has been discussed by several authors [4,5,6,7,8,9,10]. The amplitude of the interference oscillations is reduced by a factor ofwhere the angular brackets can denote either an ensemble or a time average. In the case of Gaussian or quantum fluctuations with ϑ = 0, this factor becomesThis form also holds in the case of thermal fluctuations [8].In our treatment, we assume an approximation in which the electrons move on classical trajectories. More generally, the electrons are in wavepacket states. However, under many circumstances, the sizes of the wavepackets can be small compared to the path separation, so the classical path approximation is good. Wavepacket sizes which have been realized in experiments [11] can be less than 1 µm, which is one to two orders of magnitude smaller than the other length scales characterizing the paths. A more detailed discussion of the effects of finite wavepacket size was given in Ref. [7].The purpose of the present paper is to discuss a particularly simple version of this type of decoherence produced by a classical, sinusoidal electromagnetic field. If the period of oscillation of the field is short compared to the time scale over which the interference pattern can be measured, then a time average must be taken in Eq. (3), with a resulting loss of contrast.We consider the case of a linearly polarized, monochromatic electromagnetic wave of frequency ω which propagates in a di...

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confidence: 70%

External Time-Varying Fields and Electron Coherence

Hsiang

Ford

2004

Phys. Rev. Lett.

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“…Since then, the concept of AB (Aharonov and Bohm) phase has been accepted in modern physics [2], such as condensed matter physics [3,4,5,6], particle physics [7], non-abelian gauge theories [8], gravitational physics [9,10] and laser dynamics [11]. To observe AB phase in condensed matter physics, the whole system needs to maintain phase coherence, in a tiny ring of the diameter 1 µm and at low temperatures below 1 K, typically [3].…”

Section: Introductionmentioning

confidence: 99%

Aharonov-Bohm effect in charge-density wave loops with inherent temporal current switching

Tsubota¹,

Inagaki²,

Matsuura³

et al. 2012

EPL

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The Aharonov-Bohm (AB) effect has been accepted and has promoted interdisciplinary scientific activities in modern physics. To observe the AB effect in condensed matter physics, the whole system needs to maintain phase coherence, in a tiny ring of the diameter 1 µm and at low temperatures below 1 K. We report that AB oscillations have been measured at high temperature 79 K by use of charge-density wave (CDW) loops in TaS 3 ring crystals. CDW condensate maintained macroscopic quantum coherence, which extended over the ring circumference 85 µm. The periodicity of the oscillations is h/2e in accuracy within a 10 % range. The observation of the CDW AB effect implies Frohlich superconductivity in terms of macroscopic coherence and will provide a novel quantum interference device running at room temperature.

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“…The Aharanov-Bohm [47] effect can be thought as an example of Berry's phase, and its first experimental verification was done resorting to electron holography [49]. Its existence has been verified in other domains, for instance, using an optical fiber [50].…”

Section: Geometric Phases In Quantum Theorymentioning

confidence: 99%

“…Let us start mentioning that this kind of experiments require the observation of the relative displacement of the interference patterns, i.e., a sole interference pattern does not suffice. The experimental detection of the phase shift variation, ∆φ, needs one value of A, and a second one, say A 0 , which plays the role of a reference parameter, see, for instance, the reference beam mentioned in [49]. Hence the fringes related to φ( A) are compared against those emerging from φ( A 0 ), and, in consequence, φ( A) − φ( A 0 ) can be obtained.…”

Section: Geometric Phases In Quantum Theorymentioning

confidence: 99%

Test of some fundamental principles in physics via quantum interference with neutrons and photons

Camacho¹,

Camacho-Galván²

2007

Rep. Prog. Phys.

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The limitations and possibilities that the concept of quantum interference offers as a tool for testing fundamental physics are explored here. The use of neutron interference as an instrument to confront against measurement readouts some of the principles behind metric theories of gravity will be analyzed, as well as some discrepancies between theory and experiment. The main restrictions that this model embodies for the study of some of the features of the structure of space-time will be explicitly pointed out. For instance, the conditions imposed by the necessary use of the semiclassical approximation. Additionally, the role that photon interference could play as an element in this context is also considered. In this realm we explore the differences between first-order and secondorder coherence experiments, and underline the fact that the Hanbury-Brown-Twiss effect could open up some interesting experimental possibilities in the analysis of the structure of space-time.The void, in connection with the description of wave phenomena, implicit in the principles of metric theories is analyzed. The conceptual difficulties, that this void entails, are commented.

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Observation of Aharonov-Bohm Effect by Electron Holography

Cited by 259 publications

References 20 publications

External Time-Varying Fields and Electron Coherence

External Time-Varying Fields and Electron Coherence

Aharonov-Bohm effect in charge-density wave loops with inherent temporal current switching

Test of some fundamental principles in physics via quantum interference with neutrons and photons

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