Effect of confinement potential geometry on entanglement in quantum dot-based nanostructures

TL;DR

This study investigates how the geometry of confinement potentials in quantum dot nanostructures affects electron entanglement, revealing controllable variations and potential for tailored quantum applications.

Contribution

It introduces a parametrized confinement potential model allowing continuous transition between structures and analyzes the impact on entanglement using exact diagonalization methods.

Findings

Entanglement varies significantly with confinement shape and size.

Wave function at symmetric points indicates entanglement levels.

Counterintuitive relationship between entanglement and Coulomb interaction.

Abstract

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 of 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.