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Journal of Physics Conference Series

Entanglement variations in model core-shell quantum dots

Pier Paolo Marchisio, J. P. Coe, Irene D’Amico

Published Sep 1, 2010• 0 citations
Publisher

Abstract

We model a core-shell quantum dot using a one dimensional system of two interacting electrons with a potential that can vary from one corresponding to a dot with comparable width of core and shell to one where the core well width becomes very small, but is always non-zero, while the shell becomes wide. We calculate the entanglement due to the spatial degrees of freedom and also the site or local entanglement found in a partition of the potential accessible to measurement. We quantify both using the linear entropy of the reduced density matrix. A sharp variation of the entanglement had been seen in earlier work for the transformation from a one dimensional model core-shell dot to a double dot [1]. We investigate whether the spatial entanglement and energy derivatives display any discontinuity as the core well width becomes small and if the two-electron state is always bound to the core well.

DOI
10.1088/1742-6596/245/1/012051

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We model a core-shell quantum dot using a one dimensional system of two interacting electrons with a potential that can vary from one corresponding to a dot with comparable width of core and shell to one where the core well width becomes very small, but is always non-zero, while the shell becomes wide. We calculate the entanglement due to the spatial degrees of freedom and also the site or local entanglement found in a partition of the potential accessible to measurement. We quantify both using the linear entropy of the reduced density matrix. A sharp variation of the entanglement had been seen in earlier work for the transformation from a one dimensional model core-shell dot to a double dot [1]. We investigate whether the spatial entanglement and energy derivatives display any discontinuity as the core well width becomes small and if the two-electron state is always bound to the core well.
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.
The time-dependent quantum Monte Carlo method for fermions is introduced and applied in the calculation of the entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by this method allow one to build reduced density matrices for each electron, and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small, and is determined mostly by the spatial quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case, the outermost opposite-spin electrons interact like bosons, which prevails their entanglement, while the inner-shell electrons remain largely at their Hartree-Fock geometry. Our findings are in close correspondence with the numerically exact results, wherever such comparison is possible.
We model quantum dot nanostructures using a one-dimensional system of two interacting electrons. We show that strong and rapid variations may be induced in the spatial entanglement by varying the nanostructure geometry. We investigate the position-space information entropy as an indicator of the entanglement in this system. We also consider the expectation value of the Coulomb interaction and the ratio of this expectation to the expectation of the confining potential and their link to the entanglement. We look at the first derivative of the entanglement and the position-space information entropy to infer information about a possible quantum phase transition.
Recently, there has been considerable interest in investigating quantum entanglement in two-electron systems, such as two-electron model atoms and quantum dots. In this work, the quantum entanglement of the helium atom and helium-like ions are explored using the two-electron wave functions constructed by the BBB-spline basis. As a measure of the spatial entanglement, the linear entropy of the reduced density matrix is investigated for the ground state and the singlet excited 1sns1S1sn{s}^{1}S1sns1S states, with n=2n=2n=2--10, of the helium atom. The variation of the spatial entanglement with the nuclear charges Z=2Z=2Z=2--15 for the helium-like ions is reported. Results are compared with the existing predictions.
Semiconductor quantum dots (QDs) are one of the leading candidates for realizable qubits, as well as for many other advances in quantum computing and quantum communication. The spatial overlapping of wavefunctions describing each single electron in these nanoscale devices results in tunable spatial entanglement. In this article, we explore the case of two electrons in two-dimensional double quantum dot systems. We compute the two-particle wavefunction through a variational method combined with Hermite finite elements and study the spatial entanglement of electrons. We show that symmetry in the geometry of the double quantum dots plays a role in obtaining optimal entanglement, while a broken symmetry can lead to additional resonances in entanglement that are associated with the crossings of states. We also show that one can finely tune the level of spatial entanglement by altering the geometry of the quantum dots or by applying external fields, which corresponds to an “entanglement spectroscopy.” Finally, we study how impurities in the potential profile of the QDs affect the level of entanglement.
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.