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arXiv:0803.0568 · Physical Review B

Measurement of Aharonov-Bohm oscillations in mesoscopic metallic rings in the presence of a high-frequency electromagnetic field

Josef-Stefan Wenzler, Pritiraj Mohanty

Published Mar 31, 2008• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.77.121102

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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 \ensuremathτ\ensuremathϕ(P){\ensuremath{\tau}}_{\ensuremath{\phi}}(P)\ensuremathτ\ensuremathϕ​(P) agrees well with the anticipated power law \ensuremathτ\ensuremathϕ\ensuremath∝P\ensuremath−1∕5{\ensuremath{\tau}}_{\ensuremath{\phi}}\ensuremath{\propto}{P}^{\ensuremath{-}1∕5}\ensuremathτ\ensuremathϕ​\ensuremath∝P\ensuremath−1∕5 when the field-induced decoherence rate \ensuremathτac\ensuremath−1{\ensuremath{\tau}}_{\mathit{ac}}^{\ensuremath{-}1}\ensuremathτac\ensuremath−1​ is large compared to the intrinsic decoherence rate \ensuremathτo\ensuremath−1{\ensuremath{\tau}}_{o}^{\ensuremath{-}1}\ensuremathτo\ensuremath−1​, measured in the absence of external fields. As theoretically expected, we observe a decline in field-induced decoherence when \ensuremathτac\ensuremath−1\ensuremath⩽\ensuremathτo\ensuremath−1{\ensuremath{\tau}}_{\mathit{ac}}^{\ensuremath{-}1}\ensuremath{\leqslant}{\ensuremath{\tau}}_{o}^{\ensuremath{-}1}\ensuremathτac\ensuremath−1​\ensuremath⩽\ensuremathτo\ensuremath−1​. The frequency dependence of \ensuremathτ\ensuremathϕ{\ensuremath{\tau}}_{\ensuremath{\phi}}\ensuremathτ\ensuremathϕ​ shows a minimum in the oscillation amplitude at a characteristic frequency \ensuremathωac\ensuremath≃1∕\ensuremathτo{\ensuremath{\omega}}_{\mathit{ac}}\ensuremath{\simeq}1∕{\ensuremath{\tau}}_{o}\ensuremathωac​\ensuremath≃1∕\ensuremathτo​, where \ensuremathτo{\ensuremath{\tau}}_{o}\ensuremathτo​ 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.
We have measured transport through mesoscopic Aharonov-Bohm (AB) rings with two different four-terminal configurations. While the amplitude and the phase of the AB oscillations are well explained within the framework of the Landaur-Büttiker formalism, it is found that the probe configuration strongly affects the coherence time of the electrons, i.e., the decoherence is much reduced in the configuration of so-called nonlocal resistance. This result should provide an important clue in clarifying the mechanism of quantum decoherence in solids.
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.
Motivated by the interest to testable, exactly solvable models of quantum behavior in the time-dependent potentials, which may be important in studying (and in proof) basic quantum mechanical laws, as well as in considering the possibility of using the electronic components suggested to hypothetical ``quantum computers,'' we develop a method of solving the Schr\"odinger equation in a certain class of time-periodic and space-dependent one-dimensional potentials. In particular, it is shown that the quasistationary electronic state in the one-dimensional cyclic mesoscopic metallic ring in a rotating-potential field displays periodic variation of quasienergy in the function of magnetic flux threading the ring (the Aharonov-Bohm effect) and oscillation, superposed on the monotonous dependence, in the function of angular velocity of rotating potential (the effect similar to Rabi and/or Bloch oscillation). At large speed of rotation, quasienergy decreases rather than increases with the increase of angular velocity. The dependence of quasienergy on flux in space periodic potential displays standard hc∕ehc∕ehc∕e periodicity as well as the periodicity with a larger period, Nhc∕eNhc∕eNhc∕e, where NNN is the number of sites in the loop, corresponding to one flux quantum per lattice site. This is an interference effect similar to one observed in the fractional quantum Hall effect but, unlike in the latter, not requiring the concept of ``fractional electron charge,'' e∕Ne∕Ne∕N. The physical significance of the quasienergy states is clarified by studying the quantum transitions between the states as well as by investigating the energy flow between the ring and the external source of the potential.
The Aharonov-Bohm oscillations in the transmission probability of a one-dimensional mesoscopic ring between two electrodes are considered numerically where a time-periodical flux \ensuremath{\gamma}(t)=\ensuremath{\gamma}+\ensuremath{\lambda} cos\ensuremath{\omega}t is applied. Such a flux simulates a phase-coherent inelastic scattering due to the absorption/emission processes of modulation quanta. An increase of alternating flux amplitude \ensuremath{\lambda} drastically changes the Aharonov-Bohm oscillations of the transmission though the exact period remains ${\mathrm{\ensuremath{\varphi}}}_{0}$=hc/e. A frequency dependence of the transmission has abrupt steps at \ensuremath{\omega}=(E-EF{\mathit{E}}_{\mathit{F}}EF​)/n, caused by the locking of the transmission in the nth channel where EF{\mathit{E}}_{\mathit{F}}EF​ is the Fermi level. Moreover, for transmission of a narrow wave packet the time-periodical flux gives rise to two effects. The first is a fractioning of the input wave packet by the ring in such a way that the output wave function consists of a few separate wave packets. Their number, distance apart, and height essentially depend on the static flux \ensuremath{\gamma}. The second effect is a strong space squeezing of the output wave packet.