Dynamical properties of two electrons confined in a line shape three quantum dot molecules driven by an ac-field

TL;DR

This paper studies the dynamical behavior of two electrons in a three-quantum-dot molecule under an AC field using the Hubbard model and Floquet theory, revealing how electron interactions influence localization.

Contribution

It provides a detailed analysis of the dynamical properties of two electrons in a three-dot system, highlighting the role of electron interactions in dynamical localization.

Findings

Electrons can maintain localized states under specific AC fields.

Electron interaction enhances dynamical localization.

The Hamiltonian structure resembles that of two electrons in a double quantum dot.

Abstract

Using the three-site Hubbard model and Floquet theorem, we investigate the dynamical behaviors of two electrons which are confined in a line-shape three quantum dot molecule driven by an AC electric field. Because the Hamiltonian contains no spin-flip terms, the six- dimension singlet state and nine-dimensional triplet state sub-spaces are decoupled and can be discussed respectively. In particular, the nine-dimensional triplet state sub-spaces can also be divided into 3 three-dimensional state sub-spaces which are fully decoupled. The analysis shows that the Hamiltonian in each three-dimensional triplet state sub-space, as well as the singlet state sub-space for the no double-occupancy case, has the same form similar to that of the driven two electrons in two-quantum-dot molecule. Through solving the time-dependent Sch\"odinger equation, we investigate the dynamical properties in the singlet state sub-space, and find that the two electrons can maintain their initial localized state driven by an appropriately ac-field. Particularly, we find that the electron interaction enhances the dynamical localization effect. The use of both perturbation analytic and numerical approach to solve the Floquet function leads to a detail understanding of this effect.