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arXiv:cond-mat/0308223 · Physical Review Letters

Magnetic-Field-Dependent Transmission Phase of a Double-Dot System in a Quantum Ring

Martin Sigrist, Andreas Fuhrer, Thomas Ihn, K. Ensslin, Sergio E. Ulloa, W. Wegscheider, Max Bichler A

Published Aug 4, 2004• 79 citations
arXivHTMLPDF

Abstract

The Aharonov-Bohm effect is measured in a four-terminal open ring geometry. Two quantum dots are embedded in the structure, one in each of the two interfering paths. The number of electrons in the two dots can be controlled independently. The transmission phase is measured as electrons are added to or taken away from the individual quantum dots. Although the measured phase shifts are in qualitative agreement with theoretical predictions, the phase evolution exhibits unexpected dependence on the magnetic field. Phase lapses are found only in certain ranges of the magnetic field.

DOI
10.1103/physrevlett.93.066802

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The Aharonov-Bohm effect is measured in a four-terminal open ring geometry. Two quantum dots are embedded in the structure, one in each of the two interfering paths. The number of electrons in the two dots can be controlled independently. The transmission phase is measured as electrons are added to or taken away from the individual quantum dots. Although the measured phase shifts are in qualitative agreement with theoretical predictions, the phase evolution exhibits unexpected dependence on the magnetic field. Phase lapses are found only in certain ranges of the magnetic field.
We consider the phase-coherent transport of electrons passing through an Aharonov–Bohm ring while interacting with a tunnel charge in a double quantum dot (representing a charge qubit) which couples symmetrically to both arms of the ring. For Aharonov–Bohm flux Φ AB = h /2 e we find that electrons can only be transmitted when they flip the charge qubit's pseudospin parity an odd number of times. The perfect correlations of the dynamics of the pseudospin and individual electronic transmission and reflection events can be used to entangle the charge qubit with an individual passing electron.
For a two-terminal modified Aharonov-Bohm (AB) ring with a quantum dot inserted in one arm and threaded by a magnetic flux, the phase rigidity is observed experimentally in the linear response regime, and also established theoretically. We show that this phase rigidity can be broken, even in the linear response regime, by applying a time-varying field on the dot, together with the magnetic flux through the AB ring. This provides another way of observing the continuous variation of the transmission phase through a two-terminal mesoscopic system.
The nonequilibrium real-time dynamics of electron coherence is explored in the quantum transport through the double-dot Aharonov-Bohm interferometers. We solve the exact master equation to find the exact quantum state of the device, from which the changes of the electron coherence through the magnetic flux in the nonequilibrium transport processes is obtained explicitly. We find that the relative phase between the two charge states of the double dot localizes to π2\fracπ{2}2π​ or −π2-\fracπ{2}−2π​ for all different magnetic flux. This nontrivial phase localization process can be manifested in the measurable occupation numbers.
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.
The nonequilibrium real-time dynamics of electron decoherence is explored in the quantum transport through the nanoscale double-dot Aharonov-Bohm interferometers. We solve the exact master equation to find the exact quantum state of the device, from which the changes of the electron coherence through the magnetic flux in the nonequilibrium transport processes is obtained explicitly. We find that the relative phase between the two charge states of the degenerate double dot localizes to $\frac{\ensuremath{\pi}}{2}$ or $\ensuremath{-}\frac{\ensuremath{\pi}}{2}$ for all different magnetic fluxes, due to decoherence. This nontrivial decoherence process can be manifested in the measurable occupation numbers.
A double quantum dot inserted in parallel between two metallic leads allows to entangle the electron spin with the orbital (dot index) degree of freedom. An Aharonov-Bohm orbital phase can then be transferred to the spinor wavefunction, providing a geometrical control of the spin precession around a fixed magnetic field. A fully coherent behaviour is obtained in a mixed orbital/spin Kondo regime. Evidence for the spin precession can be obtained, either using spin-polarized metallic leads or by placing the double dot in one branch of a metallic loop.