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arXiv:quant-ph/0402028 · Physical Review Letters

External Time-Varying Fields and Electron Coherence

Jen-Tsung Hsiang, Lawrence H. Ford

Published Jun 22, 2004• 17 citations
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Abstract

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.

DOI
10.1103/physrevlett.92.250402

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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.
The quantum state of the electromagnetic field produced by a known current distribution consists of a coherent state multiplied by a time-dependent phase factor. This nonclassical phase factor includes a dynamic component that vanishes in the quasistatic limit of slowly varying currents. The dynamic phase of the field is observable in electron interferometer experiments, where it can substantially modify the Aharonov-Bohm (AB) effect when retardation effects are significant. An alternative interpretation of the AB effect in which half of the usual phase shift is associated with the test particle while the other half occurs in the source of the external field is suggested. Any geometric interpretation of the dynamic phase would require Hamiltonians that are nonphysical in nature which may have implications for the concept of geometric phases in general.
Dipole interference is studied when atomic systems are coupled to classical electromagnetic fields. The interaction between the dipoles and the classical fields induces a time-varying Aharonov-Casher phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be observable and almost as large as the corresponding one for coherent electrons. We analyze different trajectories in order to show the dependence of the decoherence factor with the velocity of the particles.
We review different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and for neutral particles with permanent dipole moments. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore can be observed. We analyse different trajectories in order to show the dependence of the decoherence factor on the velocity of the particles.
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.
Electron interference phenomena are now easily observable with the advent of bright and yet coherent field-emission electron beams. The interaction of electron waves with electromagnetic fields is essentially described by the Aharonov–Bohm (AB) effect. However, the AB effect has long been disputed due to a feature that cannot be understood in terms of classical electrodynamics. This paper describes the experiments that confirmed its existence and discusses its expanding applications to the observation of electromagnetic fields in the microscopic region.