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arXiv:quant-ph/9702024 · Physical Review A

Aharonov-Bohm interference in the presence of metallic mesoscopic cylinders

Silviu Olariu

Published Jan 1, 1997• 0 citations

Abstract

This work studies the interference of electrons in the presence of a line of magnetic flux surrounded by a normal-conducting mesoscopic cylinder at low temperature. It is found that, while there is a supplementary phase contribution from each electron of the mesoscopic cylinder, the sum of these individual supplementary phases is equal to zero, so that the presence of a normal-conducting mesoscopic ring at low temperature does not change the Aharonov-Bohm interference pattern of the incident electron. It is shown that it is not possible to ascertain by experimental observation that the shielding electrons have responded to the field of an incident electron, and at the same time to preserve the interference pattern of the incident electron. It is also shown that the measuring of the transient magnetic field in the region between the two paths of an electron interference experiment with an accuracy at least equal to the magnetic field of the incident electron generates a phase uncertainty which destroys the interference pattern.

DOI: 10.1103/physreva.55.94

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This work studies the interference of electrons in the presence of a line of magnetic flux surrounded by a normal-conducting mesoscopic cylinder at low temperature. It is found that, while there is a supplementary phase contribution from each electron of the mesoscopic cylinder, the sum of these individual supplementary phases is equal to zero, so that the presence of a normal-conducting mesoscopic ring at low temperature does not change the Aharonov-Bohm interference pattern of the incident electron. It is shown that it is not possible to ascertain by experimental observation that the shielding electrons have responded to the field of an incident electron, and at the same time to preserve the interference pattern of the incident electron. It is also shown that the measuring of the transient magnetic field in the region between the two paths of an electron interference experiment with an accuracy at least equal to the magnetic field of the incident electron generates a phase uncertainty which destroys the interference pattern.

Ever since Yakir Aharonov and David Bohm pointed out, in 1959, that electrons propagating around a magnetic field through a field-free vacuum should exhibit a quite surprising interference effect, its experimental and theoretical investigation has been contributing to our understanding of the fundamental character of the quantum theory. The recent appearance of this Aharonov–Bohm effect in a rather different context may eventually have a profound effect on our view of the solid state on a “mesoscopic” scale—between the microscopic and the truly macroscopic.

A quantum ring device that can turn on and off the external magnetic field on the ring is developed.The device is to study the effect of the interaction between electrons and external magnetic fields on Aharonov-Bohm interference.The switching is realized by employing a superconducting shield gate and turning on and off the superconductivity on the gate with applied current or magnetic field.The electron interference due to Aharonov-Bohm effect is observed regardless of the presence of the external magnetic field on the electron path of the ring.The result is consistent with the fact that effects of potentials on charged particles exists even in the region where all the field vanish hence no direct interaction between electron and magnetic field is allowed.

We report measurements of Aharonov-Bohm oscillations in normal metal rings in the presence of high-frequency electromagnetic fields. The power dependence of the decoherence time scale ${\ensuremath{\tau}}_{\ensuremath{\phi}}(P)$ agrees well with the anticipated power law ${\ensuremath{\tau}}_{\ensuremath{\phi}}\ensuremath{\propto}{P}^{\ensuremath{-}1∕5}$ when the field-induced decoherence rate ${\ensuremath{\tau}}_{\mathit{ac}}^{\ensuremath{-}1}$ is large compared to the intrinsic decoherence rate ${\ensuremath{\tau}}_{o}^{\ensuremath{-}1}$, measured in the absence of external fields. As theoretically expected, we observe a decline in field-induced decoherence when ${\ensuremath{\tau}}_{\mathit{ac}}^{\ensuremath{-}1}\ensuremath{\leqslant}{\ensuremath{\tau}}_{o}^{\ensuremath{-}1}$. The frequency dependence of ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ shows a minimum in the oscillation amplitude at a characteristic frequency ${\ensuremath{\omega}}_{\mathit{ac}}\ensuremath{\simeq}1∕{\ensuremath{\tau}}_{o}$, where ${\ensuremath{\tau}}_{o}$ is evaluated from the oscillation amplitude using the standard mesoscopic theory. Both the suppression in the oscillation amplitude and the concomitant change in conductivity allow a direct measurement of the intrinsic decoherence time scale.

Incoherence introduced in two-path experiments by interactions with scatterers in thermal equilibrium is examined with an energy-momentum approach previously used for the M\"ossbauer effect. Oscillations in intensity with variations in the magnetic flux are shown to be insensitive to random phase changes in the individual scattering amplitudes. Inelastic incoherent scattering may be suppressed when there are a large number of scatterers. A small loss of phase coherence negligible in cases of practical interest can occur even via elastic scattering, which does not perturb the environment. The temperature dependence of the loss of interference, analogous to the Debye-Waller factor, may be tested by experiment.

We study a simple model of dephasing of Aharonov-Bohm oscillations in the transmission of an electron across a mesoscopic ring. A magnetic impurity in one of the arms of the ring couples to the electron spin via an exchange interaction. This interaction leads to spin flip scattering and induces dephasing via entanglement. This is akin to the models evoked earlier to explain destruction of interference due to which-path information in double-slit experiments. Total transmission is found to be symmetric under flux reversal but not the spin polarization.