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3 Impurity Effects in Two-Electron Coupled Quantum Dots: Entanglement Modulation

Diego S Acosta Coden, Rodolfo H. Romero, Alejandro Ferrón, Sergio S. Gómez

Published Mar 7, 2013• 18 citations
OpenAlex

Abstract

We present a detailed analysis of the electronic and optical properties of two-electron quantum dots with a two-dimensional Gaussian confinement potential. We study the effects of Coulomb impurities and the possibility of manipulating the entanglement of the electrons by controlling the confinement potential parameters. The degree of entanglement becomes highly modulated by both the location and charge screening of the impurity atom, resulting in two regimes: one of low entanglement and the other of high entanglement, with both of them mainly determined by the magnitude of the charge. It is shown that the magnitude of the oscillator strength of the system could provide an indication of the presence and characteristics of impurities and, therefore, the degree of entanglement.

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We present a detailed analysis of the electronic and optical properties of two-electron quantum dots with a two-dimensional Gaussian confinement potential. We study the effects of Coulomb impurities and the possibility of manipulating the entanglement of the electrons by controlling the confinement potential parameters. The degree of entanglement becomes highly modulated by both the location and charge screening of the impurity atom, resulting in two regimes: one of low entanglement and the other of high entanglement, with both of them mainly determined by the magnitude of the charge. It is shown that the magnitude of the oscillator strength of the system could provide an indication of the presence and characteristics of impurities and, therefore, the degree of entanglement.
We present a detailed analysis of the electronic and optical properties of two-electron quantum dots with a two-dimensional Gaussian confinement potential. We study the effects of Coulomb impurities and the possibility of manipulating the entanglement of the electrons by controlling the confinement potential parameters. The degree of entanglement becomes highly modulated by both the location and charge screening of the impurity atom, resulting in two regimes: one of low entanglement and the other of high entanglement, with both of them mainly determined by the magnitude of the charge. It is shown that the magnitude of the oscillator strength of the system could provide an indication of the presence and characteristics of impurities and, therefore, the degree of entanglement.
We theoretically consider the effects of having unintentional charged impurities in laterally coupled two-dimensional double (GaAs) quantum-dot systems, where each dot contains one or two electrons and a single charged impurity. Using molecular orbital and configuration interaction methods, we calculate the effect of the impurity on the two-electron energy spectrum of each individual dot as well as on the spectrum of the coupled-double-dot two-electron system. We find that the singlet-triplet exchange splitting between the two lowest-energy states, both for the individual dots and the coupled-dot system, depends sensitively on the location of the impurity and its coupling strength (i.e. the effective charge). A strong electron-impurity coupling breaks down the equality of the two doubly occupied singlets in the left and the right dots, leading to a mixing between different spin singlets. As a result, the maximally entangled qubit states are no longer fully obtained in the zero-magnetic-field case. Moreover, a repulsive impurity results in a triplet-singlet transition as the impurity effective charge increases or the impurity position changes. We comment on the impurity effect in spin qubit operations in the double-dot system based on our numerical results.
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.
Quantum dot structures confine electrons in a small region of space. Some properties of semiconductor quantum dots, such as the discrete energy levels and shell filling effects visible in addition spectra, have analogies to those of atoms and indeed dots are sometimes referred to as 'artificial atoms'. However, atoms and dots show some fundamental differences due to electron correlations. For real atoms, the kinetic energy of electrons dominates over their mutual Coulomb repulsion energy and for this reason the independent electron approximation works well. For quantum dots the confining potential may be shallower than that of real atoms leading to lower electron densities and a dominance of mutual Coulomb repulsion over kinetic energy. In this strongly correlated regime the independent electron picture leads to qualitatively incorrect results. This thesis concentrates on few-electron quantum dots in the strongly correlated regime both for quasi-one-dimensional and two-dimensional dots in a square confining potential. In this so-called 'Wigner' regime the ground-state electronic charge density is localised near positions of classical electrostatic minima and the interacting electronic spectrum consists of well separated spin multiplets. In the strongly correlated regime the structure of low-energy multiplets is explained by mapping onto lattice models with extended-Hubbard and Heisenberg effective Hamiltonians. The parameters for these effective models are calculated within a Hartree approximation and are shown to reproduce well the exact results obtained by numerical diagonalisation of the full interacting Hamiltonian. Comparison is made between square dots and quantum rings with full rotational symmetry. In the very low-density regime, direct diagonalisation becomes impractical due to excessive computer time for convergence. In this regime a numerical renormalisation group method is applied to one-dimensional dots, enabling effective spin-interactions to be pr
We calculate the spatial entanglement between two electrons trapped in a nanostructure for a broad class of confinement potentials, including single and double quantum dots, and core-shell quantum dot structures. By using a parametrized confinement potential, we are able to switch from one structure to the others with continuity and to analyze how the entanglement is influenced by the changes in the confinement geometry. We calculate the many-body wave function by ``exact'' diagonalization of the time-independent Schr\"odinger equation. We discuss the relationship between the entanglement and specific cuts of the wave function, and show that the wave function at a single highly symmetric point could be a good indicator for the entanglement content of the system. We analyze the counterintuitive relationship between spatial entanglement and Coulomb interaction, which connects maxima (minima) of the first to minima (maxima) of the latter. We introduce a potential quantum phase transition which relates quantum states characterized by different spatial topology. Finally we show that by varying shape, range, and strength of the confinement potential, it is possible to induce strong and rapid variations in the entanglement between the two electrons. This property may be used to tailor nanostructures according to the level of entanglement required by a specific application.
Confined geometries such as semiconductor quantum dots are promising candidates for fabricating quantum computing devices. When several quantum dots are in proximity, spatial correlation between electrons in the system becomes significant. In this paper, we employ a variational formulation for calculating accurate two-electron wavefunctions in configuration space, irrespective of potential geometry. To evaluate the Coulomb integrals with high accuracy, a numerical integration method using multiple Gauss quadratures is used. With this approach, we investigate the confinement of two electrons in double quantum dots, and evaluate the spatial entanglement. We investigate the dependence of spatial entanglement on various geometrical parameters. We derive the two-particle wavefunctions in the asymptotic limit of the separation distance between quantum dots and obtain universal saturation values for the spatial entanglement. Resonances in the entanglement values due to avoided level crossings of states are observed. We also demonstrate the formation of electron clusters and show that the entanglement value is a good indicator for the formation of such clusters. Further, we show that a precise tuning of the entanglement values is feasible with applied external electric fields.