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Correlation and Entanglement, Scattering through Two Coupled Quantum Dots

Jalal Abdulrahman

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In this thesis we theoretically investigate quantum correlations and entanglement of electron scatterers through two coupled quantum dots (QDs). The interaction is described in terms of two-particle collisions modeled by two-particle scattering matrix. The correlation between the two dots is expressed in terms of density-of-states matrices. Wave packets are introduced into each system and for the entanglement measure we use concurrence.

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In this thesis we theoretically investigate quantum correlations and entanglement of electron scatterers through two coupled quantum dots (QDs). The interaction is described in terms of two-particle collisions modeled by two-particle scattering matrix. The correlation between the two dots is expressed in terms of density-of-states matrices. Wave packets are introduced into each system and for the entanglement measure we use concurrence.
We show how two qubits encoded in the orbital states of two quantum dots can be entangled or disentangled in a controlled way through their interaction with a weak electron current. The transmission/reflection spectrum of each scattered electron, acting as an entanglement mediator between the dots, shows a signature of the dot–dot entangled state. Strikingly, while a few scattered carriers produce decoherence of the whole two-dot system, a larger number of electrons injected from one lead with proper energy are able to recover its quantum coherence. Our numerical simulations are based on a real-space solution of the three-particle Schrödinger equation with open boundaries. The computed transmission amplitudes are inserted in the analytical expression for the system density matrix to evaluate the entanglement.
The properties of an electron pair confined in a coupled quantum dot (QD) system are currently being intensively investigated both experimentally and theoretically. Indeed the manipulation of the two-electron spin states is paramount for the realization of controllable entanglement so as to produce the fundamental quantum gate operations in a solid state quantum computer. The works usually concentrate on the properties of a two-electron system without going into detailed analysis of the contributions from various single-particle states or the effects produced by the constituent single QDs. Zeeman splitting is neglected as it affects only the magnitude of the exchange energy but not the single-particle state mixing. In summary, after numerically diagonalizing the two-electron Schrodinger equation in the model confinement potential of both single and laterally coupled double quantum dots, we computed the contributions from the various single-particle states to the final two-particle wave function.
We study theoretically the appearance of quantum correlations in two- and three-electron scattering in single and double dots. The key role played by transport resonances into entanglement formation between the single-particle states is shown. Both reflected and transmitted components of the scattered particle wavefunction are used to evaluate the quantum correlations between the incident carrier and the bound particle(s) in the dots. Our investigation provides a guideline for the analysis of decoherence effects due to the Coulomb scattering in semiconductor quantum dots structures.
We study theoretically the appearance of quantum correlations in two- and three-electron scattering in single and double dots. The key role played by transport resonances into entanglement formation between the single-particle states is shown. Both reflected and transmitted components of the scattered particle wavefunction are used to evaluate the quantum correlations between the incident carrier and the bound particle(s) in the dots. Our investigation provides a guideline for the analysis of decoherence effects due to the Coulomb scattering in semiconductor quantum dots structures.
We study two simple mesoscopic models of interacting two electrons; first one consists of two quantum coherent parallel conductors with long-range Coulomb interaction in some localized region and the other is of an interacting quantum dot (QD) side-coupled to a noninteracting quantum wire. We evaluate exact two-particle scattering matrix as well as two-particle current which are relevant in a two-particle scattering experiment in these models. Finally we show that the on-site repulsive interaction in the QD filters out the spin-singlet two-electron state from the mixed two-electron input states in the side-coupled QD model.