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Journal of Applied Physics

Electron transport through two irreducibly-coupled Aharonov-Bohm rings with applications to nanostructure quantum computing circuits

C. A. Cain, C. H. Wu

Published Sep 1, 2011• 5 citations
Publisher

Abstract

We investigated several classes of two coupled Aharonov-Bohm rings that share a finite center common path, where the phase of the electron wave function can be modulated by two distinct magnetic fluxes. The coupling is similar to two coupled atoms. The behavior of charge accumulation along the center common path or, equivalently, the bonding and anti-bonding of the two rings can be achieved as the two applied fluxes are varied. Thus, when three external terminals are connected to such coupled rings, the behavior of the electron transport is divided into several classes, depending on the number of atoms in each ring and the locations of the terminals. The results are presented here. The applicable electron wave computing circuits are discussed. In particular, a half-adder construction is shown here by employing the symmetric and anti-symmetric properties of the transmission of a given terminal when the sign of the flux is changed. The analogy of two coupled rings with respect to two spins allows one to make a further connection with traditional spintronics-based schemes.

DOI
10.1063/1.3631782

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We investigated several classes of two coupled Aharonov-Bohm rings that share a finite center common path, where the phase of the electron wave function can be modulated by two distinct magnetic fluxes. The coupling is similar to two coupled atoms. The behavior of charge accumulation along the center common path or, equivalently, the bonding and anti-bonding of the two rings can be achieved as the two applied fluxes are varied. Thus, when three external terminals are connected to such coupled rings, the behavior of the electron transport is divided into several classes, depending on the number of atoms in each ring and the locations of the terminals. The results are presented here. The applicable electron wave computing circuits are discussed. In particular, a half-adder construction is shown here by employing the symmetric and anti-symmetric properties of the transmission of a given terminal when the sign of the flux is changed. The analogy of two coupled rings with respect to two spins allows one to make a further connection with traditional spintronics-based schemes.
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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.
We analyze the posibility of employing the mesoscopic-nanoscopic ring of a normal metal in a doubly degenerate persistent current state with a third auxihilary level and in the presence of the Aharonov-Bohm flux equal to the half of the normal flux quantum ℏc/e\hbar c/eℏc/e as a qubit. The auxiliary level can be effectively used for all fundamental quantum logic gate (qu-gate) operations which includes the initialization, phase rotation, bit flip and the Hadamard transformation as well as the double-qubit controlled operations (conditional bit flip). We suggest a tentative realization of the mechanism as either the mesoscopic structure of three quantum dots coherently coupled by mesoscopic tunnelling in crossed magnetic and electric fields, or as a nanoscopic structure of triple anionic vacancy (similar to F3F_3F3​ centers in alkali halides) with one trapped electron in one spin projection state.
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 calculate the oscillations of the dc conductance across a mesoscopic ring, simultaneously tuned by applied magnetic and electric fields orthogonal to the ring. The oscillations depend on the Aharonov-Bohm flux and of the spin-orbit coupling. They result from mixing of the dynamical phase, including the Zeeman spin splitting, and of geometric phases. By changing the applied fields, the geometric phase contribution to the conductance oscillations can be tuned from the adiabatic (Berry) to the nonadiabatic (Ahronov-Anandan) regime. To model a realistic device, we also include nonzero backscattering at the connection between ring and contacts, and a random phase for electron wave function, accounting for dephasing effects.
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.