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Quantum Transport Through Two Series Aharonov–Bohm Interferometers

Chong Yang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The electronic transport through series Aharonov–Bohm interferometers is investigated. We study the effect of the algebraic sum and the difference of two magnetic fluxes the quantum transport. We print the figure of local state density through transform the system to an effective decoupled one and verify the effect of magnetic fluxes difference on Fano effect.

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arXiv:1807.03616•Quantum Science and Technology•Jul 1, 2019•18 citations
The electronic transport through series Aharonov–Bohm interferometers is investigated. We study the effect of the algebraic sum and the difference of two magnetic fluxes the quantum transport. We print the figure of local state density through transform the system to an effective decoupled one and verify the effect of magnetic fluxes difference on Fano effect.
We investigate a non-Hermitian Aharonov-Bohm (AB) ring system with a quantum dot (QD) embedded in each of its two arms. The energy levels of the QDs are complex in order to take into account the physical gain or loss of the ring system during its interacting processes with the environment. When there is magnetic flux threading through the ring, by allocating the flux phase factor into the tunneling amplitudes between the QDs and the leads in different ways, the Hamiltonian of the system can be written into different formalisms. We calculate the transmission through the ring by using these different non-Hermitian Hamiltonians and prove that it is not dependent on the way we treat the phase factor, as in the Hermitian case. In addition, with appropriate parameters, the asymmetric Fano profile will show up in the conductance spectrum just by tuning the physical gain and loss of the system. The Fano effect originates from the interferences of electrons traversing different channels which are broadened or narrowed down due to the interaction between the QDs and the environment. The proof we provide and the transport properties revealed in this paper demonstrate the influences of the environment on an otherwise isolated system and pave the way for the further studies on non-Hermitian AB ring systems.
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.
Recent works showed that the Aharonov-Bohm (AB) phase difference for a quantum charged particle can be written in terms of electric and magnetic fluxes in a space-time surface whose boundaries are the possible particle worldlines in the interferometer, relative to the possible paths. After presenting this result in a more detailed way, reinforcing its topological nature, we study the magnetic and electric versions of the AB effect in different inertial reference frames. We find a particular reference frame for a magnetic AB effect where the magnetic flux has a null contribution for the AB phase difference, which is entirely due to an electric flux. Also, we find a particular reference frame for an electric AB effect where the electric flux has a null contribution for the AB phase difference, which is entirely due to a magnetic flux. In this sense, the nomenclatures magnetic AB effect and electric AB effect lose their meaning. We have electromagnetic AB effects.
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.
Abstract We study the quantum transport through two specific atomtronic circuits: a Y -junction and a ring-shaped condensate pierced by an effective magnetic flux. We demonstrate that for bosons, the two circuits display Andreev-like reflections. For the Y -junction, the transport depends on the coupling strength of the Y -junction. For the ring-shaped condensate, the transport crucially depends on the particle statistics. For interacting bosons we find that the Aharonov–Bohm interference effect is absent. By breaking the translational invariance of the ring, the flux dependence can be restored. A complementary view of the problem is obtained through a specific non-equilibrium quench protocol. We find that the steady-state is independent of the flux, however the actual time-dynamics depends on the flux. The dynamics of the full closed system can be fitted with an approximated open system approach. For all the protocols we studied, we find striking differences in the dynamics of the Bose–Hubbard model and the Gross–Pitaevskii equation.